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Quantum Information Science
An Emerging Field of Interdisciplinary Research and Education 
in Science and Engineering
 
NSF Workshop	October 28-29, 1999	Arlington, Virginia
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National Science Foundation

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Quantum Information Science
An Emerging Field of Interdisciplinary Research 
and Education in Science and Engineering



Report of the NSF Workshop
October 28-29, 1999 
Arlington, Virginia

Steering Committee 
C. H. Bennett       IBM
D. P. DiVincenzo    IBM
N. Gershenfeld      MIT
H. M. Gibbs         University of Arizona 
H. J. Kimble        Caltech 
J. Preskill         Caltech
U. V. Vazirani      UC/Berkeley
D. J. Wineland      NIST
C. Yao              Princeton University
		
Any opinions, findings, conclusions, or recommendations expressed in this report
are those of the participants, and do not necessarily represent the official
views, opinions, or policy of the National Science Foundation.

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Contents

Preface

Executive Summary

Introduction

Birth of a new science

   Compressibility and capacity
   Quantum entanglement
   Quantum key distribution
   Models of quantum computation
   Quantum complexity classes
   Quantum searching and lower bounds
   Quantum communication complexity
   Quantum error-correcting codes
   Fault-tolerant quantum computation
   Quantum information processing in AMO physics
   Nuclear magnetic resonance and quantum computation

Challenges and opportunities

   New quantum algorithms
   Quantum simulation
   Complexity theory
   Quantum cryptography
   Complexity-based cryptography
   Quantum error correction and fault tolerance
   Precision measurement and quantum control
   Many-party quantum entanglement
   The quantum -- classical boundary
   Quantum information and fundamental physics
   Quantum information processing with atoms and photons
   Quantum information processing in condensed matter
   Toward scalable NMR quantum computation

Quantum information, curiosity, and community

Fostering the continued success of quantum information science

The role of NSF

Agenda

Quantum Information Science Workshop Attendees

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PREFACE

Quantum Information Science (QIS) is an emerging field with the potential to
cause revolutionary advances in fields of science and engineering involving
computation, communication, precision measurement, and fundamental quantum
science.  The roots of this field go back about twenty years, when pioneers such
as Charles Bennett, Paul Benioff, Richard Feynman, and others began thinking
about the implications of combining quantum mechanics with the classical Turing
computing machine.

	The field of QIS began an explosive growth in the early to mid 1990's as a
consequence of several simultaneous stimuli: Peter Shor demonstrated that a
quantum computer could factor very large numbers super-efficiently.  The
semiconductor industry realized that the improvement of computers according to
Moores law would all too soon reach the quantum limit, requiring radical
changes in technology.  Developments in the physical sciences produced trapped
atomic ions, advanced optical cavities, quantum dots, and many other advances
that made it possible to contemplate the construction of workable quantum logic
devices.  Furthermore, the need for secure communications drove the 
investigations of quantum communication schemes that would be tamper proof.

	In the course of supporting leading-edge research, several divisions at NSF
had been supporting QIS-related projects for some time.  However, the growing
excitement and opportunities in QIS called for a careful examination of the
NSF's role in this new field, particularly since QIS required fundamental
research in many areas of science and technology to reach its potential. 
Furthermore, QIS represents an important scientific basis for other national
programs involving the quantum world, such as the Nanoscience and Technology
Program.  Strong investments in QIS by defense agencies and by science agencies
around the world also indicated the perceived importance of QIS.

	In this context, Robert Eisenstein, Ruzena Bajcsy, and Eugene Wong, Assistant
Directors for the NSF Directorates of Mathematical and Physical Sciences,
Computer and Information Science and Engineering, and Engineering, respectively,
formed the QIS Working Group to organize a workshop to further explore NSFs
role in this field.  The Working Group then recruited the QIS Steering
Committee, consisting of leaders of the QIS community.  The Steering Committee
then organized the QIS workshop, which took place in Arlington Virginia, October
28-29, 1999.  It was attended by approximately 100 scientists and engineers from
all related disciplines.  The workshop itself was an extremely stimulating
event, due in part to the presence of a large fraction of the international
leaders in the field.  As one person put it: you could raise almost any question
in QIS, and the pioneer on that point would be there to address it.

	The workshop comprised oral sessions, breakout sessions, and an evening town
meeting, which included further contributions and much discussion.  The agenda
and a list of attendees are appended.  After the meeting the Steering Committee,
listed on the first page of the workshop report, assembled an overview of the
field, and made several recommendations regarding the role of NSF in meeting the
needs of the field.  Logistics for the workshop itself were handled very capably
by Denise Henry.  The report was reformatted for NSF systems by Ramona
Winkelbauer, while publishing services were provided by Kelly DuBose and the NSF
Publishing and Information Dissemination Service.  The report is now being
distributed widely throughout the QIS community and among federal agencies.  The
QIS Working Group is optimistic that the NSF will be responsive to the
recommendations of this report.

	Note that the report does not contain references to the literature.  This
was a deliberate decision to make the report as generally accessible as
possible, without the normal scholarly detail and bibliographic information. 
There are a number of web sites that contain both historical and current
research information on the field of QIS.  Those listed below will link with
others:

http://www.QUBIT.ORG/
http://www.euroquantum.org/
http://theory.caltech.edu/~preskill/ph229/

	Finally, we would like to express our deep gratitude to the Steering
Committee for their service in organizing and writing the report on the NSF QIS
workshop.  The meeting was an exceptionally stimulating experience for those in
attendance, and the report is as wise as it is compelling.  We believe that this
will be a significant event in the field of QIS. 


NSF Quantum Information Science Working Group:

Joseph L. Dehmer, Physics Division, MPS
Michael J. Foster, Division of Experimental and Integrative Activities, CISE
Lawrence S. Goldberg, Division of Electrical and Communications Systems, ENG
John W. Lightbody, Jr., Physics Division, MPS
Arthur Sanderson, Division of Electrical and Communications Systems, ENG
Hollis H. Wickman, Division of Materials Research, MPS

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Executive Summary

Quantum information science (QIS) is a new field of science and technology,
combining and drawing on the disciplines of physical science, mathematics,
computer science, and engineering. Its aim is to understand how certain
fundamental laws of physics discovered earlier in this century can be harnessed
to dramatically improve the acquisition, transmission, and processing of
information. The exciting scientific opportunities offered by QIS are attracting
the interest of a growing community of scientists and technologists, and are
promoting unprecedented interactions across traditional disciplinary boundaries.
Advances in QIS will become increasingly critical to our national
competitiveness in information technology during the coming century.

	The information technology revolution of the past several decades has been
driven by steady advances in the miniaturization of electronic circuitry on
silicon chips, allowing performance to double roughly every 18 months ("Moore's
law"). But in fewer than 20 years, this shrinkage will reach atomic dimensions,
necessitating a new paradigm if progress is to continue at anything like the
rate we have become used to. Accordingly, considerable thought and long-range
planning are already being devoted to the challenges of designing and
fabricating devices at the atomic scale and getting them to work reliably, a
field broadly known as nanotechnology.

	However, it has long been known that atoms and other tiny objects obey laws
of quantum physics that in many respects defy common sense. For example,
observing an atom disturbs its motion, while not observing it causes it to
spread out and behave as if it were in several different places at the same
time. Until about five years ago, such quantum effects have mostly been seen as
a nuisance, causing small devices to be less reliable and more error-prone than
their larger cousins.

	What is new, and what makes QIS a single coherent field despite spanning
several traditional disciplines, is the realization that quantum effects are not
just a nuisance, but in fact can be exploited to perform important and otherwise
impossible information-processing tasks. Already quantum effects have been used
to create unbreakable codes, and a quantum computer, if one can be built in the
future, could easily perform some computations that would take longer than the
age of the universe on today's supercomputers. The way in which quantum effects
speed up computation is not a simple quantitative improvement, like solving a
hard problem more quickly by using a faster processor or many processors working
in parallel. Rather it is a qualitative improvement, like the improvement one
gets from calculating with decimal instead of Roman numerals. For the first
time, the physical form of information has a qualitative rather than merely a
quantitative bearing on how efficiently the information can be processed, and
the things that can be done with it.

	For this reason, even aside from its technological implications, QIS is an
intellectually exciting field, with far-reaching implications for the basic
mathematical and physical sciences, both theoretical and experimental. It is
already providing a wholly new language for describing how Nature works, and new
ways of thinking about a wide variety of scientific and technical questions. As
with any revolutionary scientific insight, the long-term implications cannot be
clearly anticipated, but we are confident that they will be profound. We also
expect that the emergence of QIS will have an extensive eventual impact on how
science is taught at the college and secondary level, and will bring a deeper
understanding of quantum physics to a broad segment of the lay public.

	While the potential economic impact of QIS is enormous, so are the problems
that must be overcome before new quantum technologies can come to fruition.
These problems are broad and deep, encompassing theory, experiment, and
engineering. It is important to build the foundations of QIS that will provide
the tools to solve these problems and enable progress toward more specific
technical goals.

	The development of QIS faces special problems because of its long time
horizon and its intrinsically interdisciplinary nature. Researchers in the field
work at the margins of the traditional disciplines, and therefore sometimes find
it difficult to attain funding or to advance their careers. The very best
students are attracted by the excitement generated by QIS, but are uncertain how
to pursue that interest within a conventional academic department. Most
worrisome, the excellent young scientists who receive advanced degrees doing QIS
research are often forced to leave the field because of a lack of stable funding
to support their work, despite the manifest relevance of QIS to the long-term
economic health of the nation.

	The National Science Foundation can and should play the leading role in
addressing these problems and in fostering the continued success of quantum
information science. We therefore recommend that:

o   NSF establish and maintain a stable long-term multi-disciplinary initiative 
    supporting QIS research, suitably coordinated across the existing NSF 
    divisions.

o   The majority of the funding in this program support individual investigators 
    or small groups pursuing curiosity-driven, peer-reviewed research that will 
    contribute to the development of the foundations of QIS.

o   Limited funding for national-scale efforts be considered, especially if it 
    will support necessary technical infrastructure or promote interdisciplinary 
    contact and collaboration.

o   Attention be directed toward nurturing the careers of young scientists 
    engaged in QIS research.

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Introduction

Quantum physics, information theory, and computer science are among the crowning
intellectual achievements of the past century. Now, as the twenty-first century
dawns, a new synthesis of these themes is underway. The emerging discipline of
quantum information science (QIS) is providing profound new insights into
fundamental problems relating to both computation and physical science. The
flourishing of this new field in the next century may guide the way to
revolutionary advances in technology and in our understanding of the physical
universe.

	The basic mathematical principles of quantum theory, which govern all known
physical systems found in Nature, were established nearly 75 years ago. It was
recognized early on that these principles imply that information encoded in
quantum systems has weird and counterintuitive properties, yet the systematic
study of quantum information began surprisingly recently. The explosive recent
development of quantum information science can be attributed to two essential
converging factors. First, the deepening understanding of classical information,
coding, cryptography, and computational complexity acquired in the preceding
decades has laid foundations that are ripe for extension to the quantum realm.
Second, the development of sophisticated new laboratory techniques has provided
the essential tools for manipulating and monitoring the behavior of single
quanta in atomic, electronic, and nuclear systems.

	While today's digital computers process classical information encoded in
bits, a quantum computer processes information encoded in quantum bits, or
qubits. A qubit is a quantum system that can exist in a coherent superposition
of two distinguishable states, and can be entangled with other such systems. The
two distinguishable states might be, for example, internal electronic states of
an individual atom, polarization states of a single photon, or spin states of an
atomic nucleus.  Entanglement is a subtle quantum kind of correlation having no
classical equivalent, and can be roughly described by saying that two systems
are entangled when their joint state is more definite and less random than the
state of either system by itself. Two obvious properties of classical
information are that it can be read and copied without being disturbed, and that
the state of a composite system can be fully specified by specifying the state
of each of its parts. But information carried by a quantum system flouts such
common-sense principles. Indeed, quantum information can be exploited to perform
tasks that would be impossible or very difficult in a classical world.

For example:

o   Today's digital supercomputers would take billions of years to find the 
    prime factors of a number that is a few hundred digits long, whereas 
    large-scale quantum computers, if they can eventually be built, might 
    perform that task in just seconds.

o   A classical computer requires a time proportional to N to search for a 
    particular item in a list of N items, whereas a quantum computer can perform 
    the search in a time proportional to the square root of N.

o   If quantum information rather than classical information is exchanged 
    between processors, then the amount of communication required to perform 
    certain distributed computing tasks can be drastically reduced.

o   A quantum computer could efficiently and accurately simulate the evolution 
    of quantum many-body systems and quantum field theories that cannot be 
    simulated on classical computers without making unjustified approximations.

o   If quantum information is exchanged, cryptographic protocols can be devised
    in which privacy is ensured by principles of fundamental physics. In 
    contrast, the security of public-key cryptosystems that are currently in 
    widespread use rests on the assumption that decrypting a message requires a 
    time-consuming computation (such as prime factorization), an assumption	that 
    could prove unwarranted if large-scale quantum computers become available. 

	Of the recent theoretical discoveries concerning quantum information, one of
the most important and unexpected is that noisy quantum devices (if not too
noisy) can reliably store and process suitably encoded quantum states.
Ordinarily, complex quantum states like those that arise during intermediate
stages of a quantum computation are extraordinarily fragile. But if a logical
qubit is encoded, not as a single physical qubit, but instead in the form of
entanglement among several physical qubits, it becomes far more robust. The new
quantum error-correcting codes and fault-tolerant methods will be an essential
part of any future effort to create, maintain, and manipulate intricate
many-qubit quantum states.

	With ongoing technological improvements, quantum information processing of
moderate complexity should soon be feasible in a variety of physical
implementations. It is reasonable to hope that one such implementation will
eventually enable a full-scale quantum computer, but not any time soon. The
technology of quantum cryptography is more mature and much closer to commercial
realization. We also anticipate that QIS research will have a substantial impact
on other quantum technologies, such as nanoscale engineering and precision
metrology. Irrespective of the long-term technological implications, new
capabilities for quantum information processing will undoubtedly drive exciting
new discoveries in basic science.

	It can also be foreseen that the emergence of quantum information science
will have an extensive impact on science education. Quantum mechanics is usually
taught at the undergraduate and graduate levels as part of the standard physics
and chemistry curriculum, but the emphasis is more on applications than on
developing a solid comprehension of the subjects strange and seductive
foundations. A course in quantum information science, by contrast, creates the
opportunity and motivation for the student to confront the bare foundations
without distractions. Students of physics, chemistry, mathematics, computer
science, and engineering have the necessary background to benefit from such a
course at an early undergraduate level. With appropriate modifications, it could
even be given in high school, providing a valuable introduction to one of the
great scientific ideas of the twentieth century, and a compelling illustration
of the dictum that the universe is stranger and simpler than we can imagine.

	The potential of quantum information technology is starting to be recognized
by commercial companies and the defense establishment. But for this potential to
be properly fulfilled, stable long-term support aimed at foundational scientific
issues will be sorely needed. In recognition of this need and the importance of
the field, a major initiative in quantum information has been launched in
Europe. In the US, the National Science Foundation can nurture the development
of quantum information science far more effectively than more mission-oriented
agencies, or profit-seeking companies.

	Future advances in quantum information science will require the combined
effort of people with expertise in a wide variety of disciplines, including
mathematics, computer science and information theory, theoretical and
experimental physics, chemistry, materials science, and engineering. This
profoundly interdisciplinary character is one of the most exhilarating aspects
of the field. NSF can accelerate progress by encouraging collaboration and
interaction among workers with widely disparate training and expertise.
Furthermore, progress in quantum information can be sustained only by a
substantial inflow of new talent, so it is also especially important to promote
interdisciplinary education that will enable students to contribute effectively
to this emerging scientific enterprise.
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Birth of a new science

Quantum information science has arisen in response to a variety of converging
scientific challenges. One goal is to probe the foundations of the theory of
computation. What limits are imposed on computation by the fundamental laws of
physics, and how can computational power be enhanced by exploiting the structure
of these laws? Another goal is to extend the theory of communication. What are
the ultimate physical limits on the performance of a communication channel, and
how might quantum phenomena be harnessed by new communication protocols? Yet
another challenge is to understand and overcome the quantum effects that
constrain how accurately we can monitor and manipulate physical systems. What
new strategies can be devised to push back the frontier of quantum-limited
measurements, or to control the behavior of intricate quantum systems?

	While quantum information science is a broad and rapidly expanding field,
there are a few underlying recurrent themes. The theory of classical
information, computation, and communication developed extensively during the
twentieth century. Though undeniably useful, this theory cannot fully
characterize how information can be used and processed in the physical world --
a quantum world. Some achievements of quantum information science can be
described as generalizations or extensions of the classical theory that apply
when information is represented as a quantum state rather than in terms of
classical bits (Fig. 1).

	What makes this quest intellectually compelling is that the results are so
surprising. At first glance, quantum effects seem to compromise our efforts to
store, transmit, and process information, because quantum states are highly
unstable and cannot be observed without being disturbed. Indeed, as the
components of integrated circuits continue to shrink toward the atomic scale,
quantum phenomena will pose increasingly serious limitations on the performance
of information processing hardware, and one important task of quantum
information science will be to illuminate whether and how such obstacles can be
overcome. But the great surprise is that the news about quantum effects is not
all bad -- far from it! The fragility of quantum information becomes a very
positive feature when it is recognized that eavesdropping on a quantum
communication channel necessarily leaves a detectable imprint, so that
communicating with qubits provides better privacy than communicating with
classical bits. Far more astonishing, the intrinsic complexity of quantum
information ensures that quantum systems of modest size are endowed with truly
vast computational power, so that a quantum computer acting on just hundreds of
qubits is capable in principle of performing tasks that could never be performed
by conventional digital computers.

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(See Figure 1 here.)
Figure 1: The well-established theory of classical information and computation
is actually a subset of a much larger topic, the emerging theory of quantum
information and computation.
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	Another recurrent theme is quantum entanglement, the non-classical
correlations exhibited among the parts of a composite quantum system. A book
expressed in classical bits can be read one page at a time. But if a typical
"quantum book" were read one page at a time, hardly any of the information
encoded in the book could be discerned. Instead, nearly all of the information
resides in the correlations among the pages. This feature of quantum
information, that it is typically encoded in the intricate correlations among
the parts of a system, is the crucial way that quantum information differs from
classical information, and underlies much of the magic of quantum computation
and communication.

	For example, while the number of bits of information encoded in a classical
processor grows linearly with the size of the processor, the number of
parameters needed to describe the state of a quantum processor grows
exponentially with its size. The speedup achieved by quantum algorithms can be
attributed to this separation in complexity between classical and quantum
information, which arises because of the entanglement among the parts of a
quantum system. Entanglement is also an essential feature of quantum
error-correcting codes. These codes protect information by storing it in the
correlations among the parts of the system; thus tearing a page from a suitably
encoded quantum book does not destroy any encoded information, since that page
by itself carries no information. Entanglement can also be viewed as a key
resource that enables quantum communication protocols such as quantum
teleportation, superdense coding, and quantum key distribution. A major goal of
quantum information science is to characterize and quantify quantum
entanglement, and to formulate new ways in which it can be exploited and
manipulated.

	A third recurrent theme is the laboratory manipulation of matter at the
level of individual atoms or single quanta. Until recently, measurements of
quantum systems were typically carried out on ensembles of many similarly
prepared systems. Now, techniques for trapping and cooling atomic particles, and
for nanofabrication of tiny electrical circuitry, are making it possible to
monitor continuously the coherent interactions of an atom, photon, or electron.
The information- theoretic approach to quantum dynamics provides an
indispensable tool for understanding and controlling the behavior of these
systems.

	Let us briefly review some of the milestones already reached by quantum
information science. Most have been achieved in just the past few years, and
have generated a host of fascinating new questions.
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Compressibility and capacity

Classical information theory was launched by Claude Shannon, who discovered how
to quantify the compressibility of a classical message, and how to characterize
the capacity of a classical communication channel. The compressibility of a
quantum message can also be quantified, and at least in the case where each
letter of the message is a pure quantum state, the answer is closely analogous
to that found by Shannon.
	
	A quantum channel is one that conveys qubits rather than classical bits. The
capacity of such a channel turns out to be a subtle concept, and a variety of
important questions remain open. Several different types of channel capacity can
be formulated and studied; in particular, it is important to distinguish between
the amount of classical information and the amount of quantum information that
can be reliably transmitted over a quantum channel. It has been shown that the
classical capacity of a quantum channel can be enhanced if the communicating
parties share a pre-existing entangled quantum state ("superdense coding"), and
that the quantum capacity can be enhanced by two-way classical communication
between the parties. One peculiar implication of the latter result is indicated
in (Fig. 2).

	One of Shannon's great insights was that a random code can reach the maximum
achievable communication rate over a classical channel. A major surprise is that
the corresponding statement does not apply for quantum channels -- codes with a
higher asymptotic rate than the random codes have been constructed. 

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(See Figure 2 here.)
Figure 2: A surprising property of the quantum channel capacity that illustrates
a counterintuitive feature of quantum information. If a quantum channel is so
noisy that it has no capacity to send quantum information, then using the
channel twice in the same direction also sends no quantum information. But if
the two transmissions are in opposite directions, the capacity is nonvanishing.
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Quantum entanglement

Quantum entanglement is a subtle nonlocal correlation among the parts of a
quantum system that has no classical analog. Thus entanglement is best
characterized and quantified as a feature of the system that cannot be created
through local operations that act on the different parts separately, or by means
of classical communication among the parts.

	In the case of a pure quantum state of a system divided into two parts, the
entanglement can be completely characterized because it can be reversibly
converted to a standard currency. If many identical copies of a given state are
available, then it is possible with local operations and classical communication
to "distill" the entanglement into a standard form -- many copies of a two-qubit
Bell pair. And the Bell pairs, with local operations and classical
communication, can be transformed back into many copies of the original state,
with negligible losses. Thus the number of distillable Bell pairs provides a
universal measure of bipartite pure state entanglement.

	The situation is far more subtle and interesting for the case of entangled
bipartite mixed states, or for pure-state entanglement with more than two parts.
For example, some bipartite mixed states exhibit bound entanglement -- though
entanglement is necessary to create these states, none of this entanglement can
be distilled into Bell pairs. Another significant surprise is that even
bipartite states with no entanglement can exhibit a peculiar kind of quantum
nonlocality. One can construct a quantum book with two pages, such that it is
impossible to read the book one page at a time, even though the two pages are
not entangled with one another.

	Since entanglement cannot be created locally, an entangled state shared by
two widely separated parties can be a valuable resource (Fig. 3). One
application of shared entanglement is a novel quantum communication protocol
called quantum teleportation. If one party (Alice) possesses a qubit in an
unknown state, she cannot observe the state without disturbing it. But if she
shares a Bell pair with another party (Bob), then Alice can convey a perfect
replica of her state to Bob by sending him just two bits of classical
information. In the process, the shared Bell pair is consumed, and Alices
original is destroyed. An odd feature of quantum teleportation is that the
unknown state can take values in a continuum; nevertheless, thanks to the
pre-existing shared entanglement, Bob needs to receive only two classical bits
to recover the perfect replica. This protocol has been convincingly demonstrated
in the laboratory. 
_______________________________________________________________________________
(See Figure 3 here.)
Figure 3: Two related tasks that require quantum entanglement as a resource. In
quantum teleportation, Alice receives a qubit in an unknown state, and destroys
it by performing a Bell measurement on that qubit and a member of an entangled
pair of qubits that she shares with Bob. She sends a two-bit classical message
(her measurement outcome) to Bob, who then performs a unitary transformation on
his member of the pair to reconstruct a perfect replica of the unknown state. In
superdense coding, Alice receives a two-bit classical message, transmits the
message by performing a unitary transformation on a member of an entangled pair
that she shares with Bob, and then sends that qubit to Bob. Thus one qubit
suffices to carry two classical bits of information.
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Quantum key distribution

Today's protocols for secure Internet commerce depend on the presumed
intractability of factoring large numbers, and would become insecure if fast
factoring algorithms are discovered, or if large-scale quantum computations
become practical. Although unconditionally secure encryption and authentication
techniques do exist, they are used mainly in ultra-secure settings such as the
Moscow-Washington hotline, because they depend on a resource that is difficult
to provide in a commercial setting -- a supply of truly random key information
shared between the communicating parties but kept secret from everyone else.
Quantum key distribution (QKD) provides a secure way of generating such key
information.

	Unlike other potential applications of quantum information science, quantum
key distribution is practical with current technology, at least over moderate
ranges such as tens of km of optical fiber, or ground-to-satellite optical
links. Prototype QKD systems operating up to 48 km over conventional optical
fiber, and 1 km through open air at ground level, are already functioning. An
intermediate experimental goal for QIS research, easier than building a
full-scale quantum computer, is the construction of quantum repeaters, which
would make quantum key distribution feasible over arbitrarily large distances.

	Quantum key distribution has recently been proved "unconditionally secure"
against an adversary who eavesdrops on the quantum transmission in any way
allowed by the laws of quantum mechanics, but only under idealized assumptions
that do not yet correspond to existing practical implementations. In all
likelihood this gap can be closed, by a combination of theory (strengthening the
existing proofs to cover more realistic sources, in particular dim coherent
states) and experiment (single-photon sources and improved detectors). While
current QKD implementations have concentrated on demonstrating basic
feasibility, future implementations will include a quantitative analysis of
potential eavesdropping and the privacy amplification protocols used to defeat
it, so as to optimize the rate of safe key generation for any given combination
of source, channel, and detector. 
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Models of quantum computation

The classical theory of computational complexity is founded on the modern
Church-Turing thesis, which asserts that any "reasonable" model of computation
can be efficiently simulated on a probabilistic Turing machine (a universal
computer with access to a random number generator). But as far as we know,
simulation of an n-qubit quantum computer on a classical computer requires a
computation time that grows exponentially in n. Thus, while the theorems of
classical complexity theory will stand forever as mathematical truths, they do
not accurately portray the computational power woven into the laws of Nature.

	Rather, the computational model dictated by physical law is the quantum
Turing machine, or the equivalent quantum circuit model; these models can
efficiently and accurately simulate the evolution of any quantum system governed
by interactions that are local in space and time. A quantum circuit consists of
wires and gates, but where the wires carry qubits, and the gates are unitary
transformations. A computer that can execute just one generic two-qubit gate is
adequate to perform universal quantum computation -- it can approximate any
unitary transformation acting on n qubits to any desired accuracy. In the
quantum circuit model, it is also assumed that qubits can be initialized in a
particular standard state and measured in a particular standard basis. The final
output of a quantum computation is obtained by measuring the qubits. Because of
the randomness of the quantum measurement procedure, typical quantum algorithms
are not deterministic; there is a probability distribution of possible outputs.
Such algorithms can nonetheless be very useful, if for example the output
provides the correct solution to a hard problem with high probability, and the
correctness of the solution can be easily verified.
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Quantum complexity classes

A dramatic example of a hard problem that can be efficiently solved by a quantum
computer is the problem of finding the prime factors of a large composite
integer. Though there is no proof, it is widely believed that prime
factorization is an intractable problem on a classical computer, and indeed the
presumed intractability of this problem and related problems is the basis of
much of modern cryptography. Thus, a large-scale quantum computer would be a
highly valuable code- breaking tool.

	So far, only a few such explicit examples are known of quantum algorithms
that achieve superpolynomial speedups compared to the corresponding classical
algorithms. Meanwhile, the broader task of erecting a new theory of
computational complexity compatible with quantum mechanics is now well underway,
though still far from complete. For example, the class of problems that are
efficiently solvable on a quantum computer (denoted BQP, for "bounded error
probability, quantum polynomial time") is known to be contained in the classical
complexity class P#P; in particular, a quantum computer can be simulated on a
classical computer with a memory of polynomial size.

	The natural quantum analog of the NP class for classical computation is
denoted BQNP ("bounded error probability, quantum nondeterministic polynomial").
A problem is in NP if a trial answer offered by a "witness" can be verified in a
time that grows no faster than a polynomial of the size of the input to the
problem. Similarly, a computational problem is in BQNP if its solution can be
verified in polynomial time on a quantum computer, but where the "witness" is a
quantum state. It has been shown that the ground state energy problem is BQNP
complete -- the problem is to decide whether a "local" Hamiltonian (a sum of
Hermitian operators, each involving a constant number of qubits) has an
eigenvalue smaller than a specified energy E. Thus any problem in BQNP can be
reduced to an instance of the ground state energy problem after running for a
polynomial time on a quantum computer. This result is the quantum analog of the
Cook-Levin theorem, the centerpiece of classical complexity theory.

	The study of interactive proofs, which combine randomness, non-determinism
and interaction, has proved to be one of the most fruitful directions in
classical computational complexity theory. A problem is in the class IP if a
"prover" with great computational power can convince a "verifier" that he/she is
able to solve the problem correctly. Recently quantum interactive proof systems
have been defined and studied: a problem is in QIP if the prover can convince
the verifier, but where now prover and verifier exchange qubits rather than
classical bits. Quite surprisingly, it has been shown that one and one half
rounds of quantum communication between prover and verifier are as powerful as
many rounds of quantum communication. 
_______________________________________________________________________________

Quantum searching and lower bounds

Suppose that we are confronted by a very large unsorted database containing N
items, and we are to locate one particular item. This search problem is
particularly important, since it captures the essence of NP-hard problems such
as satisfiability. A classical exhaustive search requires of order N steps to
succeed with appreciable probability. But surprisingly, a quantum computer can
perform the search in only of order   steps. The quantum search algorithm
achieves a quadratic speedup relative to the classical search, in contrast to
the superpolynomial speedup achieved by the quantum factoring algorithm, but
quantum searching can be applied to a much broader spectrum of interesting
problems.

	Apart from devising new quantum algorithms that are faster than classical
algorithms, it is also of great interest to obtain lower bounds on the resources
needed by a quantum computer to solve a problem. In fact, for the database
search problem, a tight lower bound has been found, so that the known quantum
search algorithm is actually optimal -- no faster solution is possible. Although
quadratic quantum speedups can be attained for a wide variety of problems, some
problems have been formulated for which it can be shown that no quantum speedup
is possible at all.
_______________________________________________________________________________

Quantum communication complexity

The power of quantum computation arises from the exponentially-many hidden
degrees of freedom in the state of an n-qubit system. Can these degrees of
freedom be tapped for super-efficient communication? The answer to this question
is actually quite subtle. On the one hand, it is known that at least n qubits
must be transmitted to send a message that is n bits long. But on the other
hand, there are certain specialized communication tasks for which qubits really
do offer a substantial advantage.

	For example, suppose that two parties each maintain a calendar with N
entries, and they want to find a time when both are available for a meeting. In
the worst case, they will need to exchange of order N bits of classical
information in order to have a reasonable probability of successfully arranging
their date. The same task can be performed by exchanging only of order log N
qubits of quantum information. Qubits offer a far more dramatic advantage for
the problem of dealing hands containing  from a deck of N cards. Classically, of
order bits must be exchanged. But the same task can be performed, with a success
probability 1-?, by exchanging only of order log N log(1/?) qubits.
_______________________________________________________________________________

Quantum error-correcting codes

One of the most surprising recent developments in quantum information science,
and one of the most important, is the discovery that unknown quantum states, if
properly encoded, can be protected from errors (Fig. 4). Since the complex
states that arise at intermediate stages of a quantum computation are
extraordinarily fragile, quantum error correction will be essential to prevent
large scale quantum computers from crashing. The state of a quantum computer can
be viewed as a vector in an abstract space of very high dimension. On first
acquaintance, it sounds strange that a vector that takes values in a continuum
(in contrast to the discrete values assumed by a classical bit string) can be
protected against damage. How will we know if the vector drifts slightly in an
unexpected direction? The secret of quantum error correction is to encode a
quantum state in a cleverly selected subspace of a larger vector space. Errors
that move the vector in a direction perpendicular to the code subspace can
easily be detected and reversed, while errors parallel to the code subspace
cause trouble. But if the code subspace is carefully chosen, typical errors will
have only a very small component along the code subspace, and encoded
information will be well protected.
_______________________________________________________________________________
(See Figure 4 here.)
Figure 4: A simple quantum error-correcting code. A single qubit of quantum
information can be encoded as a highly entangled state of five qubits. If one of
the qubits is heavily damaged by an interaction with the environment, the
encoded quantum state can still be recovered perfectly.
_______________________________________________________________________________
	
	The principles of quantum error correction were discovered less than five
years ago, and the subject has developed explosively. Many explicit examples of
quantum error-correcting codes have now been constructed. Nearly all of these
fit into a beautiful unifying framework: the code subspace can be characterized
as a simultaneous eigenspace of all the generators of an abelian group, the
codes stabilizer group. "Good" codes have been shown to exist -- the number of
encoded qubits and the number of errors that can be corrected both scale
linearly with the size of the code block.
_______________________________________________________________________________

Fault-tolerant quantum computation

The existence of abstract quantum-error correcting codes is not in itself
sufficient to ensure that quantum information can be stored reliably. The
difficulty is that recovery from error requires a complex quantum computation,
and further errors will inevitably occur as we carry out the recovery operation.
Furthermore, we want more than reliable storage, we want to be able to process
quantum information accurately. We need to devise procedures for error recovery
and computation that are sufficiently robust as to work effectively even if
implemented imperfectly. In particular, errors tend to propagate from one qubit
to another when the qubits interact through the operation of a quantum gate --
our procedures must be designed to keep this error propagation under control. 

	In fact, such fault-tolerant procedures can be formulated for any of the
stabilizer quantum codes. When these procedures are used, quantum error
correction really does improve the precision of a quantum computation, provided
that the quantum gates are sufficiently accurate, and the decoherence times are
sufficiently long. Indeed, an accuracy threshold for quantum computation can be
established: if the probability of error per quantum gate is below a critical
value, then an arbitrarily long quantum computation can be completed with
negligible probability of error. The length of the code block needed to ensure
good accuracy grows only polylogarithmically with the size of the computation to
be performed.

	The discovery of fault-tolerant methods has greatly improved the prospects
for unleashing the power of quantum computation in realizable devices. Moreover,
the new methods ensure that very intricate quantum systems can in principle be
accurately controlled, with broad potential implications for basic physical
science and for technology.
_______________________________________________________________________________

Quantum information processing in AMO physics

Atomic, molecular, and optical (AMO) physics has long been at the forefront of
the manipulation and control of individual quantum systems, with particularly
spectacular developments resulting from the trapping and cooling of single
electrons, ions, and neutral atoms. These advances are now enabling realizations
of conditional quantum dynamics at the single-quantum level that are suitable
for the implementation of quantum logic.

	Nonlinear optics has been extended into the domain of single atoms and
photons, leading to a demonstration of a quantum phase gate in which one photon
induces a conditional phase shift on another via their mutual interactions with
an atom in an optical cavity. Single trapped atoms have been cooled to the zero
point of motion, and a quantum gate has been implemented by conditionally
exciting a single phonon in an ion trap. 
_______________________________________________________________________________
(See Figure 5 here.)
Figure 5: Photograph of five beryllium ions in a lithographically fabricated RF
trap. The separation between ions is approximately 10 microns.
_______________________________________________________________________________

	Since these initial demonstrations, experiments with trapped ions have
continued to yield impressive achievements in the coherent manipulation of
quantum systems, including the deterministic generation of entanglement between
two ions in a trap. Further experiments with RF micro-traps will be able to
extend this exquisite control of both internal states and quantized ion motion
to larger systems (Fig. 5).

	Experiments with single atoms and photons in cavity quantum electrodynamics
(cavity QED) have also attained remarkable success. Number states of the
radiation field have been created and quantum non-demolition detection of single
photons accomplished. By integrating the techniques of laser cooling and
trapping with those of cavity QED, real-time trapping of individual atoms has
been achieved. Atoms can be tracked with precision approaching the standard
quantum limit, leading to a new form of atomic microscopy.

	On the theoretical front, AMO physics has provided important models for the
implementation of quantum information processing that bridge the gap between
abstract quantum algorithms and real physical systems. These models have
stimulated new experimental advances, and have led to more detailed
understanding of the interplay between physical dynamics and quantum
information. For example, new quantum error correction protocols have been
developed that are adapted to the dominant decoherence mechanism in ion trap and
cavity QED computers, including a protocol that protects against certain types
of dissipative events to all orders in the error probability.

	AMO physics has led the advances in modern quantum measurement science for
twenty years, in part because the fundamental physical mechanisms associated
with both coherent and dissipative processes can be well-understood
theoretically and accessed with great technical power in the laboratory. Indeed,
many experiments in AMO physics have reached and in some cases have exceeded the
standard quantum limits associated with zero-point or vacuum fluctuations.
_______________________________________________________________________________

Nuclear magnetic resonance and quantum computation

NMR has an unusual place among the prospective approaches for manipulating
quantum information. While there are significant challenges to scaling ensemble
quantum computing to large systems, it has been used in experimental simulations
of non-trivial quantum algorithms, and has led to practical applications of
quantum computing.

	In NMR quantum computation, qubits are stored in the orientation of nuclear
spins, which have very long coherence times. Exchange coupling through bonds
provides a coherent nonlinear interaction, and gates are implemented by using
radio frequency pulses to modify the spin evolution. Although the bonds cannot
be switched on and off, their influence can be controlled through the
spectroscopic techniques of refocusing and decoupling, so that a desired
effective Hamiltonian can be synthesized from a known one. The most distinctive
feature of NMR quantum computing is that a qubit is stored, not in a single
underlying degree of freedom, but in about 1022 redundant copies.

	Since the Zeeman splitting between nuclear spin states is a tiny fraction of
the thermal energy in room-temperature NMR systems, the quantum state of the
spins is very highly mixed. It therefore comes as a surprise that coherent
processing of pure quantum states can be faithfully simulated in these systems.
Among the achievements attained using NMR are simulations of quantum
computations that require fewer logical steps than their classical counterparts,
quantum error correction protocols, and efficient simulations of other quantum
systems. These successes have raised intriguing and fundamental questions about
the power of quantum information processing with highly mixed states.

	The interaction between NMR and quantum computing has been beneficial in
both directions. The demonstration of universal computation in molecules has led
the chemistry community to realize that viewing a molecule as an
information-processing device provides an entirely new language with
applications far from computation. For example, an important unsolved
spectroscopic problem had been exchanging the product operator coefficients
between remote spins, so that a sensitive species could be used to read out
information from an important but less-sensitive one. This kind of exchange is
needed for the studies of complex molecular structure and function that are the
foundation of modern synthetic chemistry and drug design. Following the initial
NMR experiments for quantum computing, it was shown that the spin exchange
problem could be solved by writing it in terms of the logical SWAP operations
that are a computational primitive. The experimental demonstration of this
protocol promises to have widespread applications. 

	Efforts are underway to make NMR quantum computing technology less expensive
and more accessible (Fig. 6).

_______________________________________________________________________________
(See Figure 6 here.)
Figure 6: A "desktop quantum computer." Inexpensive table-top devices now under
development, like the one sketched here, will be able to outperform the costly
commercial NMR spectrometers that are used in current studies of room
temperature ensemble quantum computation.
_______________________________________________________________________________

Challenges and opportunities

Quantum information science is a very new field, so new that many promising
aspects of it have hardly been explored. Here we compile just a sampling of
challenging open questions and problems.

	Many of these unsolved problems span the traditional disciplinary boundaries.
A common thread is the challenge of characterizing what can be achieved with
quantum information processing, and how it can be achieved. We emphasize in
particular that the physical requirements for quantum-state manipulation are
entirely different from those for classical information processing; therefore it
is essential that investigations of the potential physical implementations of
quantum information processing be broad-based and exploratory.
_______________________________________________________________________________

New quantum algorithms

While the factoring and search algorithms are exciting breakthroughs that hint
at the potential of quantum algorithms, our understanding of what quantum
computers can do is still quite limited. It is very important to seek new
quantum algorithms that can speed up the solutions to interesting problems.

	The factoring algorithm makes use of a quantum Fourier transform that can be
efficiently computed for any abelian group. The same ideas enable quantum
computers to break a wide variety of cryptosystems. In fact, essentially all
quantum algorithms that achieve exponential speedups fit into a common general
framework: they find a hidden subgroup in an abelian group. Recent work shows
that normal hidden subgroups in a non-abelian group can also be found
efficiently. A major challenge is to extend this framework to the general
non-abelian hidden subgroup problem. 

	Several problems seem to be excellent candidates to be solved by efficient
quantum algorithms, but such algorithms have not yet been found. One example is
graph isomorphism: given two graphs, can one be transformed to the other by a
permutation of the vertices? Graph isomorphism can be expressed as a hidden
subgroup problem in the symmetric group Sn. Other important examples are
breaking the Ajtai-Dwork cryptosystem, which involves finding short vectors in
certain types of lattices, and breaking cryptosystems based on classical linear
error-correcting codes. 
_______________________________________________________________________________

Quantum simulation

In the long run, one of the most important applications of quantum computers is
likely to be simulating the dynamics of quantum systems with many degrees of
freedom. Much can be done to determine how quantum computers can best be used to
address simulation problems of physical interest. Examples include the
properties of quantum chromodynamics in real time or at finite nucleon density,
or the behavior of quantum antiferromagnets and strongly correlated electron
systems.

	A particular challenge will be to determine if M-theory is susceptible to
efficient simulation on a quantum computer. M-theory has been proposed as a
unified description of all of the forces of Nature, including gravity. It can be
formulated in terms of the quantum mechanics of very large matrices, but because
of the intrinsic nonlocality of the theory, these matrices do not admit an
obvious decomposition as a tensor product of smaller systems. It would be
exciting to discover that no efficient simulation is possible, which would
suggest that the computational power woven into the laws of Nature is even
greater than we now suspect.

	Quantum simulation may also play an important role in the evolution of new
quantum technologies. Validating and characterizing the design of even
relatively simple quantum devices will press the limits of conventional digital
computing. In particular, a quantum computer would be an extremely valuable tool
for the development of practical implementations of quantum feedback control.
_______________________________________________________________________________

Complexity theory

The class of efficiently solvable problems on a quantum computer, BQP, is known
to be contained in PSPACE, and is unlikely to contain NP. However, we do not yet
know much about its relationship to other complexity classes. For example, is
BQP contained in the polynomial hierarchy? In particular, does the power of
approximate counting suffice to simulate quantum computation? There is evidence
that BQP is not contained in MA (one-round interactive proofs), since there is
an oracle relative to which the recursive Fourier sampling problem is not
contained in MA.

	The recent developments on the quantum analog of NP and quantum interactive
proofs open up a number of fundamental issues. It should now be possible to
classify a wide variety of problems about quantum systems as either being
efficiently simulable on a quantum computer or BQNP-complete (much like the
classification developed by the classical theory of NP-completeness). It is an
open question to put the work on quantum interactive proofs in the framework of
probabilistically checkable proofs, which is a deep and important part of
computational complexity theory.

	There are novel computational resources, other than time and space, that
should be studied. One interesting question arises in the context of bulk NMR
quantum computation with weakly polarized nuclear spins. Consider an n-spin
system, which is described as a separable mixed state at every step in its
evolution. Thus each instantaneous state is described by a probability
distribution over orientations of n classical tops. However, if the evolution of
the system is quantum mechanical (described by quantum gates), then it is not
known whether such a system can be efficiently simulated on a classical
computer, or whether it can simulate a universal quantum computation. Another
intriguing question, which can also be posed in the context of bulk NMR quantum
computation, is whether it is possible to carry out universal quantum
computation if the initial state of the system is highly mixed. One recent
result addresses the power of a quantum computer in which all qubits but one are
initially in the uniformly mixed state. It was shown that if we restrict our
attention to faithful simulations of a universal quantum computation, then such
mixed state quantum computers are no more powerful than classical computers.

	Apart from being important for a study of quantum computers, there are
techniques of a fundamentally quantum nature that have provided new insights
into classical complexity theory. Two examples are the linear lower bound on the
communication complexity of the inner-product function and the reformulation of
the log-rank conjecture for communication complexity. It is quite possible that
the new method of quantum adversaries could provide an important new technique
for classical computation as well.
_______________________________________________________________________________

Quantum cryptography

Besides privacy and authentication, conventional cryptography includes other
goals. For instance, a digital signature scheme allows Alice to send a message
to Bob in such a way that Bob can verify that the message is really from Alice
and that it has not been altered at all. A zero-knowledge proof allows Alice to
prove to Bob that she knows how to solve a particular problem without Bob
learning anything about how Alice's solution works. One particularly intriguing
example is "secure distributed computation," in which two or more cooperating
parties evaluate a function of all of their inputs. Though some of the parties
may be malicious or unreliable, the computation may nevertheless be reliable
(the bad parties cannot alter the result) and discreet (the bad parties cannot
learn any more about the others' inputs than is implied by the value of the
function).

	There are classical solutions to these problems, but all rely on making some
sort of assumption, such as a limitation on the computational power of a
cheater. An important goal of QIS is to formulate quantum protocols that might
allow us to weaken or remove these assumptions.

	Many classical cryptographic protocols are built from simpler ("primitive")
protocols. An important 'primitive for two-party secure distributed computation'
is called bit commitment, the mathematical equivalent of Alice's locking a bit
in a safe and sending it to Bob.  Bob cannot open the box until Alice gives him
the key, but Alice cannot change her choice once she has given the box to Bob.
It has recently been shown that unconditionally secure bit commitment is not
allowed by the laws of quantum physics -- if Alice and Bob have quantum
computers, then whenever Bob is unable to determine the value of Alice's bit,
Alice can safely change her bit without Bob finding out. Still, it is of
interest to develop two-party distributed computation schemes in which cheating
is computationally difficult (though not absolutely impossible) with a quantum
computer.
_______________________________________________________________________________

Complexity-based cryptography

Since quantum computation compromises the security of much of classical
cryptography, it is extremely important to develop a new cryptography that is
immune to quantum cryptanalysis. For example, are there one-way functions that
are easy for a quantum computer to evaluate, but hard for a quantum computer to
invert? To design such primitives, we need to understand the limitations of
quantum computation much better than we do today.

	So far, three techniques have been developed for proving lower bounds on the
running time of quantum algorithms: the hybrid argument, the method of
polynomials, and the method of quantum adversaries. Extending this bag of tricks
will better enable us to devise new cryptosystems that are invulnerable to a
quantum attack.

	It has been shown that any quantum algorithm for inverting a random
permutation on N elements requires at least of order  steps. Since random
permutations are regarded as good models for one-way functions, this result
provides some positive evidence for the existence of one-way functions immune to
quantum cryptanalysis. On the other hand, no non-trivial lower bound is known
for the problem of finding a collision in a random 2-1 function. Since random
2-1  functions are regarded as good models for collision intractable hash
functions (a fundamental cryptographic primitive), it is very important to
understand the complexity of this problem.
_______________________________________________________________________________

Quantum error correction and fault tolerance

It is of great interest to refine the estimates of the accuracy threshold for
quantum computation, as the threshold will define the specifications that must
be met by the hardware components of a future quantum computer. Current
estimates vary over a broad range, depending on assumptions about what protocol
is used and how the noise is modeled; according to the most optimistic
estimates, an error probability per gate as high as 10-3 can be tolerated. It is
important to obtain more rigorous estimates that would apply to a broad spectrum
of conceivable protocols. 

	It is also important to optimize the circuitry that implements the error
recovery or the fault-tolerant quantum gates. Perhaps an even more promising
approach to improving the threshold would be to investigate schemes for fault
tolerance beyond the purview of the standard quantum circuit model. Drawing on
analogies with classical error correction techniques will very likely be helpful.

	Important computational efficiency considerations remain open. Current fault
tolerant constructions require polylogarithmic overhead in time and in space.
How much can these overhead requirements be reduced? In the classical case,
constant overhead in time is sufficient, but it is not known whether this
applies in the quantum case.

	Also in need of further study are more general noise models. Much work on
fault tolerance has focused on the problem of combating uncorrelated stochastic
errors, but schemes that can overcome strongly-correlated noise should also be
formulated and analyzed. More generally, there is a need to better understand
how a quantum code can be devised that is well matched to the expected noise
processes in a specific physical system.

	Finally, new approaches to fault tolerance should be developed that achieve
robustness through the design of the physical hardware. A particularly promising
idea is to encode quantum information in the topological properties of the
entanglement of many-body systems with local interactions. Topological quantum
computation is a rich and promising subject, combining deep questions about
topology, quantum error correction, and many-body quantum dynamics.
_______________________________________________________________________________

Precision measurement and quantum control

Quantum information processing and quantum error correction will provide the
laboratory scientist with unprecedented tools; these can be exploited to devise
new strategies for performing interesting high-precision measurements.

	An experimenter detects a time-dependent weak classical force by monitoring
the response of a sensitive quantum system. But since observing the quantum
system necessarily disturbs it, there are intrinsic limitations on the accuracy
of the measurement. Quantum information theory has taught us that strategies
that exploit entangled quantum states can collect more information than
strategies that do not, so we can anticipate that the most precise measurement
methods will require entangled probes (Fig. 7). Much work must be done to infer
what resources are required to carry out a measurement of specified accuracy,
and how best to deploy those resources under realistic laboratory conditions.

_______________________________________________________________________________
(See Figure 7 here.)
Figure 7: An example illustrating that, in a quantum setting, the best way to
measure something can be a subtle issue. Two spins point along the same axis;
they are parallel in case (a), anti-parallel in case (b). If the spins were
measured one at a time, then the information collected about the spin axis would
be the same in both cases. In fact, though, more information about the axis can
be collected in case (b), because the optimal quantum measurement is an
entangled measurement that acts on both spins at once.
_______________________________________________________________________________

	Closely related to the challenge of high-precision measurement is the
challenge of controlling quantum states. To control a system effectively, one
needs to collect information about its behavior. Hence quantum control is
particularly delicate -- monitoring a system necessarily exerts back action on
the system. Formulating effective protocols for quantum control poses daunting
problems for both theorist and experimentalist.
_______________________________________________________________________________

Many-party quantum entanglement

The entanglement of a two-part pure quantum state can be conveniently quantified
by the number of Bell pairs that can be distilled by local operations and
classical communication. But it is still not known if it is possible to express
the entanglement of a pure state with more than two parts in terms of some such
standard currency. For example, it is unclear whether a three-party "cat" state
should be regarded as possessing an entirely different kind of nonlocality than
two-party Bell pairs. 

	A universal measure of many-particle pure-state entanglement, if one can be
formulated, would have many applications. It might enable us to identify new
kinds of quantum critical points at which the degree of entanglement of the
ground state of a Hamiltonian changes discontinuously, or to characterize which
kinds of quantum dynamics are hard to simulate on a classical computer.
_______________________________________________________________________________

The quantum -- classical boundary

A deep and long-standing fundamental problem is to understand and precisely
define the transition from classical to quantum behavior. There are many systems
in which quantum effects have a strength that depends on an adjustable
parameter. It is usually easy to recognize the difference between a system that
behaves very classically and one that behaves very "quantumly," but is there a
sharp boundary between the two? And if so, where is the boundary? (Fig. 8)

_______________________________________________________________________________
See Figure 8 here.)
Figure 8: The quantum--classical boundary. A classical computer can efficiently
simulate a system that behaves classically, but not one that behaves
"quantumly." Hence it is possible to identify a sharp transition between the
quantum and classical phases of some physical systems.
_______________________________________________________________________________
  
	Arguably, the most interesting observation ever made about the difference
between quantum and classical is that a classical system cannot efficiently
simulate a quantum system. We can try to use this idea to establish a well
defined boundary between quantum and classical behavior. Indeed, the intrinsic
accuracy threshold for quantum computation can be regarded as just such a phase
boundary. Below the critical noise rate, there is long-range entanglement in the
system, whereas above the threshold the entanglement between two subsystems
decays exponentially as the subsystems are separated. The study of such
transitions has barely begun, and there are many open questions. In particular,
universality classes and critical exponents associated with long-range
entanglement are yet to be identified.
_______________________________________________________________________________

Quantum information and fundamental physics

The Standard Model of particle physics provides a marvelously accurate
description of the fundamental constituents and their interactions down to
distances of order 10-16 cm. But the most compelling fundamental questions
concern physics at the Planck scale, 10-33 cm, where spacetime undergoes strong
quantum fluctuations. While it seems hopeless to explore physics at these scales
directly in high-energy accelerator experiments, a large-scale quantum computer
might provide an incisive indirect probe of quantum gravity. At least one
proposed model of physics at the Planck scale dictates that the dynamics of the
universe actually can be efficiently simulated by a classical Turing machine.
Since the factoring of numbers with of order 1000 digits is believed to be
beyond the capability of any conceivable classical computer, a quantum computer
of the future that achieves such a task will convincingly rule out any such
model of Planckian physics!

	Another possible way for quantum information science to illuminate the
fundamental interactions is suggested by the discovery of fault-tolerant quantum
computation. If quantum mechanics breaks down at very short distances, then we
might say the "qubits" of the fundamental theory are continually subjected to
errors -- that is, to deviations from unitary evolution. Yet somehow, these
errors are unseen at the larger distance scales we are currently capable of
probing. How can it be so? Until quite recently, we lacked the tools to
productively investigate this sort of question. But now hierarchical quantum
error-correcting techniques have been found that exhibit this kind of behavior:
the error rate gets smaller and smaller at higher and higher levels of the
hierarchy. Could fault-tolerance be woven into the fundamental laws, so that the
error rate flows to zero in the infrared limit? A broadening interface between
quantum information science and fundamental physics can be anticipated, with
tremendous potential payoffs.
_______________________________________________________________________________

Quantum information processing with atoms and photons

AMO physics provides powerful laboratory systems for the exploration of quantum
information processing, quantum measurement, and quantum information dynamics.
Because the relevant physical mechanisms and sources of dissipation can be
understood and easily modeled, these systems are especially well suited for
testing and developing error correction protocols. Existing experiments have
achieved remarkable control of few-qubit systems. Extending this level of
control to larger systems will require understanding and eliminating various
sources of decoherence such as patch-effect fields and laser intensity and
frequency fluctuations. But given the impressive rate of progress to date, it
seems reasonable to anticipate that quantum information processing involving
tens of qubits will be achieved within a decade.

	Apart from their potential relevance to quantum computation and
communication, the new capabilities arising from AMO physics will push the
science of precision measurement into a radically new domain. Time-frequency
standards, gravitational wave detection, and the characterization of solid state
devices at low temperature are just a few of the frontiers of advanced metrology
that will be affected.
_______________________________________________________________________________
 
Scaling
 
For quantum information processing to scale to increasing numbers of qubits, new
experimental options must be explored to avoid a debilitating increase in
technical overhead. One option in cavity QED is to move from more traditional
Fabry-Perot cavities to nano-fabricated cavities in photonic bandgap materials.
It might then be possible to trap and manipulate individual atoms by exploiting
the powerful tools of lithography, while still maintaining strong coupling
between individual atoms and single photons. A different option is to build an
array of small traps, where atoms can be shuttled from one trap to another.
_______________________________________________________________________________

Quantum networks
 
One specific challenge is to combine the complimentary paradigms of flying and
standing qubits in the construction of quantum networks for quantum
communication and distributed quantum computation. As illustrated in Fig. 9,
multiple atom-cavity systems located at spatially separated "nodes" could be
linked via optical fibers to create a network of quantum information processors
with quantum-coherent interconnects. A complete set of elementary network
operations has been proposed and analyzed, including fault-tolerant local
processing of quantum information, transmission of quantum states between nodes,
and the distribution of quantum entanglement. If it could be realized, such a
quantum Internet might support a wide range of quantum protocols.

_______________________________________________________________________________
(See Figure 9 here.)
Figure 9: Illustration of a protocol for the realization of a quantum network.
An applied laser beam (omega(t)) transfers quantum information from the internal
state of an atom in one cavity to a photon state, via the atom-cavity coupling
g. The photon travels along an optical fiber, enters a second cavity, and the
information is transferred to an atom in that cavity. Nonlocal entanglement can
be created among the atoms in the two cavities. By expanding from two cavities
to a larger set interconnected by optical fiber, complex quantum networks can be
realized.
_______________________________________________________________________________

Optical lattices

Beyond ions traps and cavity QED, another system with promise for quantum
information processing is an "optical lattice," in which neutral atoms are
trapped by the AC-Stark shift produced by a set of intersecting laser beams.
Because the atoms are neutral, they interact very weakly with the environment.
Dissipation arising from inelastic photon scattering can be suppressed, as can
other forms of dissipation such as coupling to phonons, defects, and impurities.
Optical lattices have tremendous flexibility -- a wide range of properties
characterizing the lattice potential can be adjusted through laser beam
geometry, polarization, intensity, and frequency. These adjustable "knobs"
permit one to design interactions such that atoms interact strongly only during
logic operations (e.g., via dipole-dipole interactions), but otherwise are
isolated from each other and the environment. Substantial theoretical work needs
to be done to assess the long-term potential of optical lattices as quantum
information processing systems.
_______________________________________________________________________________

Quantum information processing in condensed matter

The ideas of quantum information processing are beginning to influence the
agenda of condensed matter physics and materials science. A remarkable variety
of proposed implementations of quantum bits and gates have been put forward, and
their implications for experimental directions in these fields are being
actively assessed by workers in the community. 

	Having been concerned for most of its history with bulk or collective
properties, condensed matter physics is now beginning to address the behavior of
systems where individual quantum properties are important. Qubits might
conceivably be implemented in any of these systems, although so far only the
rudiments of quantum gate operations have been achieved. The continuing quest
for coherent information processing in a condensed matter setting will address
some of the most fundamental problems in the quantum mechanics of individual
systems.

	Many specific quantum-gate technologies based on solid-state physics have
been proposed. They include:

Ultra-small superconducting structures. In these, the qubit can be embodied
	either in the quantum state of flux of a SQUID (superconducting quantum
	interference device) or in the quantized Cooper-pair number of a small
	superconducting island. Single-qubit rotation has recently been observed
	(Fig. 10).

_______________________________________________________________________________
(See Figure 10 here.)
Figure 10: Quantum coherence in a superconducting Cooper-pair box. Cooper pairs
of electrons can tunnel through the Josephson junction barrier onto the island
electrode, and quantum information can be encoded in the number of Cooper pairs
on the island. Coherent oscillations in the number of pairs were recently
observed. 
_______________________________________________________________________________	
	

Quantum dots. Such structures have been the focus of nano-device technology both
	as optical and electronic devices. As quantum gates, their quantized
	electron number or spin can function as the qubit; switching of the quantum
	state might be achieved either by optical or electrical means.

Semiconductor optical microcavities. These devices, long researched for their
	applications in solid- state microlasers, are approaching the point at which
	the coherent manipulation of single photons is becoming a possibility. In
	addition, these can be coupled to atomic-like qubits in the form of embedded
	single-electron quantum dots. This proposal has many contacts with existing
	thrusts in optoelectronics.

Impurities in semiconductors. Integrated-circuit technology demands greater and
	greater control over the precise profile of dopant impurity concentrations
	in semiconductor devices. If this technology is developed to the extent that
	control of impurities atom-by-atom is achieved, quantum computation might
	become possible. The nuclear or electronic spins of individual phosphorus
	impurities are the qubits in this scheme, and transistors control operations
	between these qubits.

Various other systems, which are conceivable only because of the long
	development of science and technology in condensed-matter physics, have been
	proposed for implementing quantum computing devices -- for example, using the
	orbital states of electrons floating on the surface of liquid helium, or the
	edge states of the quantum Hall effect. Undoubtedly, many other proposals
	will emerge as the workers in the various subfields of condensed-matter
	physics turn their imagination to the problem.

	We envision a variety of specific ways in which quantum information science
will influence the agenda of research in condensed-matter materials science in
the coming years:
_______________________________________________________________________________	

Phase coherence

The observation and characterization of quantum phase coherence has been a
long-standing theme of mesoscopic physics; quantum computing gives a definite
focus to this theme and asks new questions about how systems can be tailored to
exhibit a high degree of coherence. In the superconducting community, the
achievement of controlled single-qubit operations will be tantamount to
achieving the long-standing goal of Macroscopic Quantum Coherence (MQC) in
SQUIDs and related structures.
_______________________________________________________________________________	

Entanglement

Some much-studied condensed matter systems, such as highly correlated electron
systems and frustrated anti-ferromagnets, have very highly entangled many-body
ground states, and the properties of the quasiparticle excitations of these
systems reflect that underlying entanglement. But quantum entanglement among
quasiparticles has had only a limited role in the description of solid-state
phenomena, where single-particle descriptions have held the dominant place. (In
certain subfields, such as in the optical physics of highly excited
semiconductors, correlations among particles have received prominent attention.)
New structures being proposed will result in the controlled generation of
two-particle and eventually many-particle entanglement in a large variety of
solid-state systems; this will require theory to explore how these various forms
of entanglement can be characterized, and how well they can survive interaction
with the various types of solid-state environments.
_______________________________________________________________________________	

Readout

The "readout" requirements of quantum computing will provide additional impetus
behind the drive to achieve high quantum efficiency measurements of, for
example, single spins in solids; it will require the mastery of the subtle and
counterintuitive issues of the quantum measurement problem, such as the
construction of non-demolition measurements. Solid state researchers will have
to travel the road now being explored in atomic physics, in which Schrdinger
cat states are controllably created and undone, and measurements can be
performed and then reversed again.
_______________________________________________________________________________	

Fabrication and control

The structures that are proposed and that will be needed for this fundamental
research will require a close encounter with state-of-the-art materials science
and applied research in fabrication and in device physics. In a few of the
proposals, individual dopant impurities in a semiconductor must be placed, one
at a time, with unprecedented accuracy; new ion-beam or scanned probe deposition
techniques will have to be developed to address this requirement. Some of the
proposals for sensitive quantum measurement require the construction of
magnetic-semiconducting heterostructures that have not been previously
contemplated. The specifications of quantum gate operations put unprecedented
demands on the bandwidth and precision of high-frequency gated control of
microstructures. 1/f noise phenomena must be completely understood and
suppressed in these structures. Many of these directions are ones that are
already part of the agenda of advanced device technologies, but quantum
computing probably pushes some of these technologies harder than any other
computing schemes.
_______________________________________________________________________________	

Communication

Quantum communications has engendered further thinking about how a solid state
bit can be made mobile, and this has brought solid-state optics into the
picture. Several proposals focus on the existence of various technologies,
arising out of work on solid-state lasers, for the production of high
quality-factor microcavities; it is known that quantum dots and other small
quantum structures can be grown inside such cavities, and proposals for quantum
gate operations, and for the transmission of a qubit as a photon emitted by the
cavity, have been developed and will be the subject of future experimental
research. Finally, there is even the possibility of using electrons themselves
as mobile qubits; several proposals have been made for a Bell-type experiment,
in which all steps -- creation of entanglement, separation of the two particles,
detection of the quantum states -- are done electronically in a mesoscopic
device.
_______________________________________________________________________________	

Unorthodox implementations

Solid state physics is very versatile, and while the above survey can give some
idea of how quantum information science and solid state physics may develop
together in the future, it should not preclude an unforeseen departure from this
"orthodox" view. For example, there is some discussion indicating that a
recently identified gapped, fractional quantum Hall state (the "v=5/2" state)
may be the first "nonabelionic" state of matter, exhibiting quasiparticles with
non-abelian, anyonic statistics. This discovery may actually have a real bearing
on quantum information processing: calculations have indicated that nonabelionic
matter may be uniquely suited as a medium for fault tolerant quantum
computation. Will the v=5/2 state be the basis of a quantum computer? Probably
not; but we should be open to possibilities like this, and to even more exotic-
sounding ones.
_______________________________________________________________________________

Toward scalable NMR quantum computation

Many groups around the world are now using NMR to investigate small quantum
computers, because of the familiarity and availability of the required
spectrometers. A fundamental limitation will come in, however, beyond roughly 10
qubits. This is because room-temperature NMR uses a very weakly polarized
sample, which leads to a partition function normalization that decreases
exponentially as qubits are added. Although experimental refinements might reach
the classical simulation limit of tens of qubits, it cannot scale beyond that.
To go further, near-unity spin polarization is needed. Although this might be
achieved by cooling the entire sample to millikelvin temperatures, that would
eliminate the beneficial protection of intra-molecular coherence through
translational thermalization. A more promising alternative is to cool just the
nuclear spin system, which is routinely accomplished with optical pumping of
rare-gas atoms. An open question is whether this will be possible with more
complex molecules and in solids; if it is, the other parameters of this system
are already close to what is needed for scaling to significant sizes.

	It is important to view this scaling effort in the context of the
complementary experimental approaches; as they progress they are all likely to
grow together. Optical pumping for NMR draws on insights from AMO physics, and,
in turn, NMR points to techniques for manipulating ensembles and effective
Hamiltonians that are applicable to the alternatives. And the experimental
progress in NMR to date has been driving the development of higher-level quantum
programming tools that will be needed in any quantum computer.
_______________________________________________________________________________

Quantum information, curiosity, and community

The development of conventional information technology has been neatly separated
into physical scientists investigating underlying devices, and computer
scientists working on architectures and applications. This division in both
academia and industry has resulted in many of the most compelling questions
about the meaning and manipulation of information being left neglected at the
interface between hardware and software.

	In contrast, one of the most striking features of the emerging science of
quantum information is its transcendence of the division between abstract bits
and physical quanta. To contribute in an arena where information content and
physical embodiment are so intimately integrated, the early investigators needed
mastery of many aspects of physics, computer science, engineering, and
mathematics. An example that illustrates the symbiosis of computer science and
physics is the successful adaptation of classical error correction ideas to
quantum systems, an advance critical to the long-term viability of the field.

	QIS has stimulated strong cross links between computation science and
mathematical physics, and among areas such as AMO physics (e.g., NMR,
cavity-QED, ion traps), condensed matter physics (e.g., electron/nuclear spins
in semiconductors, single-electron transistors, coupled super-conducting
systems), and engineering (e.g., nanotechnology, feedback, scalability, quantum-
limited metrology). Direct evidence of these vibrant interfaces can be seen from
the makeup of attendees at conferences and workshops on QIS.

	Quantum information science is a field whose initial and future successes
are clearly tied to its interdisciplinary nature. And, as is often the case in a
scientific revolution, many researchers in QIS find themselves at the margins of
their home disciplines, with their activities stretching the conventional limits
of physics, computer science, mathematics, or electrical engineering. Indeed, a
remarkable new generation of young researchers is growing up in an intellectual
environment in which the traditional distinctions of discipline make less and
less sense.

	These developing cross links between diverse communities can be expected to
directly benefit not only QIS, but science and technology more broadly, by
catalyzing connections between various subfields of mathematics, physics, and
engineering that might otherwise go unexplored. A principal benefit to industry
is the cadre of young scientists and engineers who are being trained in new ways
to help confront the challenges that lie beyond the end of VLSI scaling. For
example, experimental investigations of possible physical implementations have
nearly always been carried out in small laboratories, enabling students to be
involved in all aspects of the research, from nano- fabrication to control
theory to quantum algorithms.

	Many of the best upcoming students are attracted to the study of quantum
information because of its intellectual and technological impact. For them, QIS
is not a specialized application to be encountered late in their education, but
an organizing principle that drives an enormous appetite for learning about
quantum systems and about the tools relevant for manipulating them. This ground
swell among young people manifests itself in enormously over-subscribed new
courses taught across disciplinary boundaries. Courses in QIS can be aimed at
the early undergraduate level, enabling an education in physics and other
technical fields to reach a broader and more enthusiastic audience.

	The continuing investigation of the intimate connections between information
and physical systems may also enhance the role of science in society. Numerous
magazines and newspaper articles have already been published in response to the
lay-person's fascination with computers and quantum physics. As quantum
mechanics and information science continue to meld, this broad interest in QIS
will help to bring science to a growing portion of the populace.
_______________________________________________________________________________

Fostering the continued success of quantum information science
 
Quantum information science has emerged as one of the most exciting scientific
developments of the past decade. As described in the preceding sections, initial
advances in QIS have encompassed a broad and remarkable landscape, ranging from
super-fast quantum algorithms for computation and communication to fault
tolerant architectures for quantum computers to the realization of quantum gates
for the physical implementation of quantum logic. Beyond contributions to
fundamental knowledge, these advances in QIS are of great potential
technological significance to our society as information processing and
communication march inexorably into the quantum realm.

	In attempting to understand how best to foster the continued success of QIS,
one should recognize that the most spectacular advances in the field have
largely sprung from individual "zealots" who ventured beyond the boundaries of
traditional disciplines and who did so without dedicated support for their
activities (and in some cases, with active discouragement). The QIS community is
largely a self-organized group of otherwise independent researchers drawn
together by the intellectual excitement and potential of the field, sharing a
strong incentive to learn as much as possible across a broad front, since no one
can say from where the next great discovery will emerge. Moreover, the tools
forged on one front are as likely as not to be employed on another, whether in
investigations of physical dynamics with intrinsic fault tolerance, of new
quantum algorithms, or of the engineering of materials for the new quantum
components.

	The brief history of QIS points to the essential role of "small science"
driven by individual investigators. It is very important to continue to foster
the research of individuals, and to encourage interactions across the
traditional boundaries in physics, computer science, and engineering.
Significant advances have sprung from unexpected quarters in the past, and
further surprises should be expected -- not just the emergence of new research
directions but also the appearance of talented new people working in the field.

	These considerations argue for stable long-term support of multidisciplinary
research carried out by investigators either individually or in small
collaborations. In the current scheme of things, there is a dearth of support
for scientists and engineers whose research is aimed at foundational issues.
Moreover, there is a pressing need to overcome structural problems of
"dislocation." That is, students who are interested in quantum information
science cannot be sure in which department to pursue that interest. Having
nonetheless succeeded, these young graduates face yet another hurdle in that
universities are reluctant to hire faculty working in a new and less established
area that is not well matched to the department structure in academia.

	In the end, there is no simple and obvious strategy for best fostering the
continued advancement of a new field as diverse and dynamic as QIS. For each
prescription for success there are conflicts and contradictions. For example, on
the experimental front, the "individual PI" model will become increasingly
difficult to sustain since the technical requirements for most experiments in
QIS continue to become ever more daunting. There is thus a tension between
maintaining diversity in investigations of physical systems and pursuing such
investigations at the cusp of technical capability. Certainly instrumentation
programs to support technically intensive research in QIS are vital to success.
But equally certain is that the demand will greatly exceed the supply of funding
for such programs. In concert with the various government agencies, industrial
research laboratories, and national laboratories, the community will have to
devise new research strategies that, on the one hand, foster the contributions
of individual PIs and, on the other hand, address the question of optimal
resource utilization.
_______________________________________________________________________________

The role of NSF

The NSF can meet the need for stable, long-term support aimed at laying the
foundations for a new science in a way that more mission-oriented agencies
cannot (and have not). Although arguably the most spectacular results in QIS to
date relate to large-scale quantum computation for cryptanalysis, NSF programs
should be much more broadly based and should emphasize the development of a
whole new area of science. As highlighted in preceding sections, promising
topics "beyond the Shor" include quantum metrology, quantum networks and
communication, and quantum components at the nanoscale. We note that, while the
US (via the NSA in particular) has taken the lead in the effort to develop a
large-scale quantum computer, we lag far behind the European community in
establishing collaborations and research programs directed toward the broader
foundations of QIS.

	Much work in QIS will be hard to fund through traditional mechanisms because
it is speculative and far from mainstream activities. An important role for NSF
is to encourage "far out ideas" in new areas and to sustain long-term support
directed toward "hard problems." However, the cycle of peer review and the
organization of programs tend to favor incremental progress in well established
areas instead. Furthermore, in the emerging arena of QIS, the traditional
discipline- based organization of education and research may not be appropriate.
Thus meeting the needs of the QIS community poses special problems, and we do
not pretend to know the answers. Central issues are that support for QIS
research should be coordinated among the NSF divisions, and that advocacy for
QIS at NSF should be vested in some tangible form -- advocates are essential to
provide institutional memory at NSF and to ensuring long-term stability.

	We favor support directed toward individual investigators engaged in "small
science," which we feel will be more productive than funding concentrated in
large centers. However, we do not preclude the concept of centers altogether;
the cost of infrastructure and the benefits of collaboration could lead to a
persuasive case that a portion of funding should be directed to center support.
Novel concepts may be effective, such as "virtual centers" that promote
exchanges of students and post-doctoral scholars. NSF-sponsored workshops might
also help to foster productive interdisciplinary collaborations.

	Especially important is the development of the careers of young people.
Although QIS attracts the very best students, it is difficult for these students
to continue to advance their careers after graduate school. While in part this
is an unavoidable situation in a rapidly developing new field, the NSF can play
an indispensable role by providing funding opportunities to help establish and
maintain young careers. These young people are a vital resource not only for QIS
but for the nation, in view of the ever increasing impact of information
technology on our society.
_____________________________________________________________________________

                                    AGENDA
                  NSF Workshop on Quantum Information Science

                          Arlington Hilton, Gallery I


Day 1, October 28, 1999

Morning Session
---------------
8:30 - 9:00 NSF Welcome, Introduction

Overview talks
-------------- 
A. Ekert, Chair
9:00 - 9:35     C. Bennett, Overview of Quantum Information
9:35 - 10:10    U. Vazirani, Quantum and Classical Complexity
10:10 - 10:45   G. Brassard, Quantum Communication and Cryptography
10:45 - 11:00   Coffee break
11:00 - 11:35   J. Preskill, Future Directions of Quantum Information                                 
                Science
11:35 - 12:10   J. Kimble, Physical Implementations of Quantum Logic

12:15 - 1:30    Lunch
-----------------------

Afternoon Session - Physical Systems
------------------------------------ 
B. Whaley, Chair
1:45 - 2:15       D. Wineland, Trapped Ion Quantum Computation
2:15 - 2:45	    Y. Maguire, Ensemble Quantum Computing via NMR
2:45 - 3:15	    P. Zoller, Quantum Computing with Atoms
3:15 - 3:45	    R. Hughes, Activities in Quantum Information Science at LANL
3:45 - 4:15	    Coffee break
4:15 - 4:45	    B. Kane, Semiconductor Spin Quantum Computing 
4:45 - 5:15	    Y. Nakamura, Quantum Bit in a Single-Cooper-Pair Box
5:15 - 5:45	    S. Koch, Quantum Effects in Excitonic Systems

8:00 - 10:00 Town Meeting

J. Dehmer, M. Foster, L. Goldberg, Jack Lightbody, Art Sanderson, Hollis Wickman
NSF Representatives


Day 2, October 29, 1999

Morning Session
---------------
C. Caves, Chair

8:30 - 9:00      A. Ekert, European Activities in Quantum Information Science
9:00 - 9:30      H. Everitt, Other U.S. Agencies Activities in Quantum 
                 Information Science Quantum Information and Algorithms
9:30 - 10:00     D. Aharanov, Error Correction and Fault Tolerance	
10:00 - 10:15    Coffee break 
10:15 - 10:45    A. Kitaev, Topological Quantum Computing
10:45 - 11:15    D. DiVincenzo, Protecting Quantum States via Symmetrization
11:15 - 11:45    S. Lloyd, Quantum Modeling
11:45 - 12:15    M. Freedman, Quantum Field Theories and Quantum Computing

12:30 - 1:45	Lunch
-----------------------

2:00 - 4:00 Afternoon Breakout 
------------------------------

Group I - Quantum Algorithms for Computation and Communication, Leader: C.
Bennett (with D. DiVincenzo as scribe)

Group II - Quantum Information and the Physical Sciences, Leader: J. Preskill
(with C. Hood as scribe)

Group III - Physical Implementations, Leader: J. Kimble (with N. Amer as scribe)

4:00 - 5:00	Joint session with feedback from breakout groups, including
-----------------------------------------------------------------------
recommendations for workshop report 
-----------------------------------

5:00        Adjourn 
-------------------
_____________________________________________________________________________

                Quantum Information Science Workshop Attendees

Name                         Institution

Dorit Aharonov               UC/Berkeley
Nabil Amer                   IBM/Yorktown
Ruzena Bajcsy                NSF
Charles Bennett              IBM/Yorktown
Joseph Bordogna              NSF
Jack Boudreaux               NIST
Giles Brassard               University of Montreal
Phil Bucksbaum               University of Michigan
Aubrey Bush                  NSF
Denise Caldwell              NSF
Carlton Caves                University of New Mexico
Isaac Chuang                 Stanford University
Charles Clark                NIST
Arnold Dahm                  Case Western University
Frederica Darema             NSF
Pankaj Das                   UC/SD
Richard de Millo             Bellcore
Joseph Dehmer                NSF
Dennis Deppe                 University of Texas
David DiVincenzo             IBM/Yorktown
Mark Dykeman                 Michigan State University
Joseph Eberly                University of Rochester
Robert Eisenstein            NSF
Artur Ekert                  Oxford University
Stephen Elbert               NSF
Michael Evangelist           NSF
Henry Everitt                ARO
Amr Fahmy                    Harvard Medical School
Yeshaiahu Fainman            UC/SD
Eugene Fan                   DOD
Nancy Forbes                 Litton TASC
Lance Fortnow                NEC Research Institute
Michael Foster               NSF
Michael Freedman             Microsoft Corporation
Don Gammon                   Naval Research Laboratory
George Gamato
Neil Gershenfeld             MIT
Hyatt Gibbs                  University of Arizona
Gerald Gilbert               Mitre Corporation
Lawrence Goldberg            NSF
Jozef Gruska                 Informatics
Sanjay Gupta                 Virginia Tech
Timothy Havel                Harvard Medical School
Mark Heiligman               NSA
Peter Hendrickson            NRO
Richard Hilderbrandt         NSF
Murray Holland               University of Colorado
William Holton               North Carolina State University
Cristina Hood                Caltech
Richard Hughes               Los Alamos National Laboratory
Richard Isaacson             NSF
Poul Jessen                  University of Arizona
Nick Jones
Paul Julienne                NIST
Subhash Kak                  Louisiana State University
Bruce Kane                   University of Maryland
Boris Kayser                 NSF
Galina Khitrova              University of Arizona
Jeff Kimble                  Caltech
Christopher King             Northeastern University
Alexey Kitaev                Caltech
Tom Kitchens                 DOE
Stefan Koch                  University of Marburg
Marvin Kruger                NSA
Rudolph Krutar               North Carolina State University
Chun-Lim Lau                 Booz-Allen & Hamilton Inc.
Jean-Pierre Leburton         University of Illinois/UC
Zachary Lemnios
Paul Lett                    NIST
Jack Lightbody               NSF
Seth Lloyd                   MIT
Samuel Lomonaco              University of Maryland/BC
Yael Maguire                 MIT
Stephen Mahoney              NSF
Pierpaolo Malinverni         European Commission
Edgar Martinez               DARPA
Keith Miller                 DOD
Martin Morf                  Stanford University
Yasunobu Nakamura            NEC Research Laboratories
Nasser Peyghambarian         University of Arizona
John Preskill                Caltech
Winston Roberts              NSF
Steven Rolston               NIST
Mary Beth Ruskai             University of Massachusetts/Lowell
John Salasin                 DARPA
Arthur Sanderson             NSF
Barry Schneider              NSF
Keith Schwab                 NSA/Caltech
Alexander Sergienko          Boston University
Francisco Serpa
Louis Sica                   Naval Research Laboratory
Karen Sollins                NSF
Duncan Steel                 University of Michigan
Bruce Taggart                NSF
T.J. Tarn                    Washington University
Yosef Gavriel Tirat-Gefen
Nikzad Toomarian
Umesh Vazirani               UC/Berkeley
Dan Ventura                  Penn State University
Nolan Wallach                UC/SD
Ian Walmsley                 University of Rochester
Richard Webb                 University of Maryland
Tom Weber                    NSF
Birgitta Whaley              UC/Berkeley
Hollis Wickman               NSF
Carl Williams                NIST
David Wineland               NIST
Andrew Yao                   Princeton University
Zeke Zalcstein               NSF
Roger Ziemer                 NSF
Peter Zoller                 University of Innsbruck


OMB Clearance Number: OMB-3145-0058
Publication Number: NSF-00-101
_____________________________________________________________________________