What Is Quantum Information Science?
By: Jack Krupansky
Tags: Quantum Information Sci, Quantum Information, Quantum Info Science, Quantum Computing, Quantum Communication

We need a lot more computing power to tackle much larger and much more complex computing challenges in the decades ahead. Ditto for communication, measurement, and sensing. That’s where quantum effects come in. The quantum effects of physics are at the atomic and subatomic level, brought to us courtesy of quantum mechanics, and hold the key to major advances — quantum leaps — in computing, communication, measurement, and sensing. Quantum information science is the broad umbrella for the theory, science, engineering, technology, infrastructure, and applications related to exploiting quantum effects (quantum mechanics) in the areas of computing, communication, and measurement and sensing.

Before we get too excited, we need to bear in mind that quantum information science is primarily still at the research stage now and for the next two to five years, or even longer. Quite a few organizations are experimenting with the technology and even developing prototypes, but the technology is far from being ready for development and deployment of production-ready applications.

That caveat out of the way, quantum information science holds tremendous promise.

This informal paper is intended to give a relatively high-level overview and introduction to the emerging field of quantum information science. The intended audience would include executives, managers — both technical and non-technical, policy analysts, the media — both general and technical, and technical staff who may have heard of some aspects of quantum computing, but would like more of the bigger picture for quantum information science.

Less-ambitious readers with limited time and patience can read the first few pages of this paper, stopping as soon as they have gleaned enough information to satisfy their interests, although there may be specific sections later in the paper that may have significant value to them.

There is a Wikipedia page for Quantum information science, but I did not find it to be as enlightening as I would have hoped, so this informal paper is my own introduction to this topic.

Although quantum information science can be fairly math-intensive, this informal paper will stick to plain English. So,

No math. No equations or messy formulas. Or math symbols. No matrices or vectors.

No equations or messy formulas. Or math symbols. No matrices or vectors. No Greek symbols.

No German. No long words that begin with “eigen”.

No long words that begin with “eigen”. No physics jargon. Except to explain some of the terms, but in plain language.

Except to explain some of the terms, but in plain language. No long list of famous names from physics.

No pictures or diagrams. Keep things simple.

The three main subfields under the umbrella of quantum information science (QIS) are:

Quantum computing — includes hardware (quantum computers), software, algorithms, and applications. Quantum communication — includes quantum networking, quantum Internet, quantum cryptography, and quantum information theory. Quantum metrology and quantum sensing — includes detection of objects.

My apologies that the content at those three links is not as suitable as I would prefer for a high-level introduction, but they’re representative of the current state of affairs (mixed and so-so, at best.) It’s on my to-do list to write more suitable content in those three areas.

This informal paper will introduce some of the concepts from each of these subfields, but won’t serve as an in-depth tutorial for any of those subfields.

Quantum information science is also critically dependent on advanced and specialized materials science and engineering in order to actually construct devices which can exploit quantum effects. These are not proper subfields of quantum information science alone, but they do have an important, critical role.

Quantum information science may sometimes be used to refer to only:

Quantum computing alone. This isn’t ideal, but it is a common usage.

Quantum computing and quantum communication together, but excluding quantum metrology and quantum sensing.

Quantum information is common across all of the subfields of quantum information science. More on that later.

Other quantum areas related to quantum information science:

Some other terms you hear associated with quantum information science:

Quantum information processing — not just quantum computing, but quantum communication, quantum networking, and quantum metrology and quantum sensing, or any subfield concerned with capturing, storing, manipulating, or communicating quantum information (quantum state).

— not just quantum computing, but quantum communication, quantum networking, and quantum metrology and quantum sensing, or any subfield concerned with capturing, storing, manipulating, or communicating quantum information (quantum state). Quantum information processing system — commonly a quantum computer, but generally any hardware system which is capable of processing quantum information.

— commonly a quantum computer, but generally any hardware system which is capable of processing quantum information. Quantum-based technology — a loose reference to any technology which is based in whole or in significant part on some aspect of quantum information science.

— a loose reference to any technology which is based in whole or in significant part on some aspect of quantum information science. Quantum technologies — sometimes used as a synonym for quantum information science.

— sometimes used as a synonym for quantum information science. Quantum technology, quantum technologies — another loose reference to any technology which is based in whole or in significant part on some aspect of quantum information science.

— another loose reference to any technology which is based in whole or in significant part on some aspect of quantum information science. Quantum information technologies — ditto.

— ditto. Quantum applications — It is ambiguous whether quantum applications are included under quantum information science specifically since the term quantum information science and technology is sometimes used when applications are to be included.

— It is ambiguous whether quantum applications are included under quantum information science specifically since the term quantum information science and technology is sometimes used when applications are to be included. Quantum science — vague term which may may simply be a synonym for quantum information science, or refer to applications of quantum information science for the natural sciences, such as simulation of physics, chemistry, or biology. Or, it may simply be a synonym for quantum physics or quantum mechanics. It all depends on the context in which it is used.

Here’s a list of the sections to follow:

What is quantum information science? What’s so special about quantum information science? QIS What disciplines are involved with quantum information science? What is quantum? Quantum mechanics Quantum physics Quantum chemistry Quantum computational chemistry Quantum biology Quantum field theory Quantum theory Quantum system Isolated quantum system Quantum effects Quantum resource Quantum state Wave function Linear algebra Quantum information Measurement Qubit Quantum bit Qutrits, qudits, and qumodes Phase Interference Environmental interference Stationary qubits and flying qubits Quantum error correction (QEC) Logical and physical qubits Quantum programs, quantum logic gates, and quantum circuits Unitary transforms Quantum algorithms Algorithmic building blocks Hybrid quantum/classical algorithms Variational quantum algorithms Quantum computer as a coprocessor Quantum advantage and quantum supremacy Exponential speedup Quantum parallelism Quantum communication Quantum networking Quantum internet Quantum channel Quantum teleportation Quantum key distribution (QKD) Alice and Bob Quantum storage Quantum metrology and quantum sensing Quantum sensors Quantum-enabled sensors Quantum detection Quantum sensing and detection Quantum simulators Quantum-inspired computing Theory and practice Science and engineering Hardware and software Device NISQ device Fault-tolerant quantum computer Applications Algorithms Quantum simulation Natural sciences and quantum simulation What are the biggest factors holding back quantum computing? When will quantum computing finally take off for practical applications? Quantum cryptography and post-quantum cryptography QIST — Quantum information science and technology Experimentation and prototyping vs. development and production Quantum computer science Quantum software engineering Standardization Education and training History Quantum information science is a misnomer Glossary What’s next?

What is quantum information science?

The National Quantum Initiative Act passed by the U.S. Congress in 2018 explicitly defines quantum information science as:

The term “quantum information science” means the use of the laws of quantum physics for the storage, transmission, manipulation, computing, or measurement of information.

Quantum information science is based on any aspect of quantum effects which can be observed, measured, controlled, or communicated in some manner.

As noted at the start, quantum information science includes not just theory and science, but also engineering, technology, infrastructure, and applications.

Quantum effects will be described shortly.

What’s so special about quantum information science?

There are three key advantages of quantum information science over classical methods:

Quantum computing offers much greater performance than classical computing through quantum parallelism which offers an exponential speedup — evaluating many (all) possibilities in parallel, in a single calculation. Quantum communication offers inherent security through quantum entanglement — also known as spooky action at a distance, in contrast to security as a problematic afterthought for classical communication and networking. Quantum metrology and quantum sensing offer much greater accuracy and precision for measurements of physical quantities and detection of objects.

All of these advantages are made possible by the magic of quantum effects enabled by quantum mechanics.

QIS

The initialism QIS is commonly used as a shorthand for quantum information science.

What disciplines are involved with quantum information science?

Quantum information science is not yet its own distinct field. It encompasses a variety of disciplines, in an interdisciplinary manner:

Physics — especially quantum mechanics

Physical science — anything relying on quantum effects, such as chemistry

Materials science

Materials engineering

Mathematics

Computer science

Software development

Software engineering — in theory, eventually

Applications development

Electrical engineering

Computer engineering

Mechanical engineering

What is quantum?

Quantum is essentially a reference to quantum mechanics, which concerns itself with atomic and subatomic particles, their energy, their motion, and their interaction.

Larger accumulations of atoms and molecules behave in more of a statistical or aggregate manner, where the quantum mechanical properties (quantum effects) get averaged away. QIS and its subfields focus at the quantum mechanical level where the special features of quantum mechanics (quantum effects) are visible and can be exploited and manipulated.

Quantum mechanics

Quantum mechanics is the field of physics which is the theoretical foundation of quantum information science, but this paper won’t delve deeply into the concepts of quantum mechanics — see the Wikipedia Quantum mechanics article for more detail, but the key elements are what are known as quantum effects, summarized below.

Quantum physics

Quantum physics is sometimes used merely as a synonym for quantum mechanics, but technically quantum physics is the application to the principles of quantum mechanics to the many areas of physics at the subatomic, atomic, and molecular level, including the behavior of particles and waves in magnetic and electrical fields.

Quantum chemistry

Quantum chemistry is the application of quantum mechanics to chemistry, particularly for the behavior of electrons, including excited atoms, molecules, and chemical reactions.

Applying classical computing to quantum chemistry is referred to as computational chemistry.

Quantum computational chemistry

Applying quantum computing to quantum chemistry is referred to as quantum computational chemistry (and here).

Quantum biology

Quantum biology is the application of quantum mechanics to biology, particularly for the behavior of electrons in complex, organic molecules, such as how organic molecules form, how they can change, how they can decompose, and even how they can fold.

Quantum field theory

Quantum field theory is the part of quantum mechanics concerned with subatomic particles and their interactions, but it is not necessary to dive down to that level of detail to comprehend quantum information science. For more information, read the Wikipedia Quantum field theory article.

Quantum theory

Quantum theory is not technically a proper term. Used loosely, it commonly refers to quantum mechanics or possibly simply to quantum effects.

Quantum system

A quantum system or more properly an isolated quantum system is a particle or wave, or collection of particles and waves, which can be analyzed for its quantum effects as if it were a single, discrete object.

Isolated quantum system

Technically, any quantum system is an isolated quantum system. The emphasis is on the fact that the particles and waves within the system can be analyzed and modeled in isolation, without concern for particles and waves outside of the system. That’s the theory. In practice, no system is truly isolated (except maybe the entire universe), but the assumption of isolation dramatically simplifies understanding, modeling, and computation of the system. Without the concept of an isolated quantum system, the modeling and mathematics would be too complex to be tractable (workable.)

Each qubit of a quantum computer is an isolated quantum system, except when it is entangled with other qubits, in which case the entangled qubits collectively constitute a larger isolated quantum system.

Quantum effects

Quantum mechanics — and hence all of quantum information science and its subfields — is based on quantum effects. Quantum information science is based on any aspect of quantum effects which can be observed, measured, controlled, or communicated in some manner. Some quantum effects cannot be directly observed or measured, but can sometimes be indirectly inferred or at least have some ultimate effect on the results of manipulating a quantum system.

Quantum effects and their properties include:

Discrete rather than continuous values for physical quantities. Quanta for discrete values. The unit for discrete values. Technically, quantum is a singular unit and quanta is the plural of quantum (just as with data and datum.) Particle and wave duality. Particles have wave properties and behavior, and waves have particle properties and behavior. For example, a photon can act as a particle as well as a wave, and an electron can act as a wave as well as a particle. Probabilistic rather than strictly deterministic behavior. Uncertainty of exact value or measurement. More than just uncertainty of any measurement, there is uncertainty in the actual value of any property, as a fundamental principle of quantum mechanics. A given property of a given quantum system may have a range of values, even before the property is measured. For example, a particle or wave can be at two — or more — positions at the same moment of time. Superposition of states — can be in two states at the same time. Entanglement — the same quantum state can exist at two physically separated locations at the same time. Spooky action at a distance — popular reference to entanglement. Phase — the complex or imaginary part of the probability amplitude of a quantum state. The notion of cyclical or periodic behavior or a fraction of a single cycle of a wave or circle. Measured either in radians (two pi radians in a circle or cycle) or a fraction between 0.0 and 1.0, where 1.0 corresponds to a full, single cycle or circle (two pi radians.) Interference — cancellation or reinforcement of the complex or imaginary part of the probability amplitude of two quantum states (phases). Useful for quantum computing — it enables quantum parallelism. Not to be confused with environmental interference which disrupts the operation of a quantum system. Wave function is used to fully describe the state of a particle or wave (technically, an isolated quantum system) based on the probabilities of superposed and entangled states. The sum of the basis states of the quantum system, each weighted by its probability amplitude. Linear algebra is the notation used to express a wave function. Probability amplitude — a complex number with both real and imaginary parts. Square it and then take the square root to get the probability for a particular basis state. Basis state — the actual numeric value of a single quantum state, comparable to a binary 0 or 1. Computational basis state — the combined basis states of a collection of qubits. A collection of strings of 0’s and 1’s, each string having a probability amplitude as its weight in the wave function. Essentially each string is an n-bit binary value. Quantum state — the state of an isolated quantum system described by its wave function. Alternatively, a single basis state. Collapse of wave function on measurement, where the probabilities of superposed states will influence but not completely determine the observed value. Measurement always causes the wave function of a quantum system to collapse. Measurement — the process of observing a quantum system. By definition, measurement causes collapse of the wave function, and will always produce a single basis state (0 or 1) or computational basis state (string of 0’s and 1’s) regardless of any superposition or entanglement which may be defined by the wave function of the quantum system. Tunneling — the ability of a subatomic particle or wave such as an electron to appear to be able to move through a solid barrier as if it weren’t there. In actuality, quantum mechanics dictates that a particle or wave has a probability to be at any given location, so that a particle or wave can have a probability of being at either side of the barrier at a given moment, allowing the particle or wave to appear to skip over or through the barrier in the next moment. An example would be electrons and a Josephson junction used in a superconducting transmon qubit.

Quantum resource

A quantum resource is any quantum effect which has some utility in quantum information science, such as for computation in quantum computing or representing quantum information in quantum communication.

It’s an odd term, but sometimes you see it used. Oddly, a qubit would not technically be considered a quantum resource, but superposition, entanglement, and interference would. See the list of quantum effects above.

Quantum state

Quantum state is the unit of quantum information.

A particle or wave — referred to as an isolated quantum system — has a quantum state for each physical quality which can be observed.

The quantum state is described by a wave function. The individual possible states are known as basis states. Such as a 0 and a 1. Each basis state in a wave function occurs with some probability. A basis state can also have a complex or imaginary component, known as a phase, which is periodic or cyclical. This is exploited in quantum computing to enable quantum parallelism using interference of the phase of a potentially large number of quantum states. The probability and phase are combined into a single, complex value, called the probability amplitude, where the probability is the square root of the absolute value (or modulus) of the complex number. The basis states and their probability amplitudes are combined to form the wave function. If the probability of a basis state is other than 0.0 or 1.0, the two basis states are superposed. The quantum states of two separate particles or waves — two isolated quantum systems — can be shared or entangled.

The concept of quantum state applies across all subfields of QIS, not just quantum computing and quantum communication.

See the preceding section on quantum effects for more detail.

Wave function

Each qubit or collection of entangled qubits has a quantum state which is described by a wave function using linear algebra to detail each of the basis states and its probability amplitude.

Linear algebra

Linear algebra is the notation used to express a wave function in terms of basis states and probability amplitudes. It’s complex math (figuratively and literally), and not for the faint of heart.

Quantum information

Classical information (a sequence or collection of bits) is represented as quantum information in the form of a quantum state, one quantum state for each classical bit.

Quantum state is the unit of quantum information.

A quantum bit or qubit is the unit of storage and manipulation of quantum information (quantum states).

To be clear, quantum information can represent more than just a 0 or 1 classical bit. Since it is a quantum state, it may include a superposition of both a 0 and a 1. The probabilities of 0 and 1 may differ (but they have to add up to 1.0). The probability can include a phase component, and a quantum state may be entangled or shared between two separate, otherwise-isolated quantum systems (particles or waves.)

The concept of quantum information applies across all subfields of QIS, not just quantum computing and quantum communication.

Measurement

Quantum state is not directly observable or directly measurable using normal, non-quantum methods or devices. We can indeed measure any quantum information we want, but measuring a quantum state has the effect of collapsing the wave function of that quantum state, eliminating the truly quantum-ness of the state (e.g., superposition, entanglement, and interference), leaving the quantum information in a purely classical state, such as the 0 and 1 of classical information.

These aspects of measurement apply across all of the subfields of quantum information science — quantum computing, quantum communication, and quantum metrology and sensing.

Qubit

Qubit is short for quantum bit.

Bit is actually short for binary digit — a 0 or 1.

Quantum bit

A quantum bit, commonly referred to as a qubit, is a device or a particle or wave (e.g., photon) — an isolated quantum system — used for the purpose of holding and manipulating a single bit of quantum information in the form of quantum state.

People commonly say that a qubit is the quantum analog of a classical bit, but this is somewhat of a misnomer since a qubit is a device which holds quantum information rather than the quantum information itself. So it is quantum information which is the quantum analog of the classical bit.

Generally we can say that a quantum bit is the unit of quantum information, except that a quantum bit is really the unit of storage and manipulation of quantum information. To be more technically correct, we should say that a quantum state is the unit of quantum information.

As with quantum state, a qubit can be either a 0 or a 1, a superposition of both a 0 and a 1, or an entanglement of the quantum states of two qubits.

Qutrits, qudits, and qumodes

There are also qutrits where are three-valued quantum bits, qudits which are ten-valued quantum bits, and qumodes which are continuous-valued quantum bits used in photonic quantum computers, but these are beyond the scope of this paper.

Phase

In addition to representing a classical bit, or a superposition of two classical bits, a qubit can also have a phase, which is simply a fraction of one cycle of a periodic wave. When two classical bits are superposed, each may have its own distinct phase.

A phase is represented as the imaginary part of the complex number which represents the probability amplitude for either a zero or one bit.

As would waves in general, two phases can cancel or reinforce the complex or imaginary part of the probability amplitude of two quantum states. This is useful for quantum computing, to enable quantum parallelism.

The value of phase can be represented as either a real value between zero and two pi (pi is approximately 3.14159…), representing an angle or fraction of a circle measured in radians, or a real value between zero and 1.0, representing a fraction of a full circle. Two pi radians and 1.0 would be equivalent, as would pi radians and 0.5, as would pi/2 radians and 0.25.

Interference

The phase of the quantum state of two qubits can interfere, either cancelling or reinforcing the complex or imaginary part of the probability amplitude of the quantum states (phases) of the two qubits.

Interference is useful for quantum computing — it enables quantum parallelism.

Not to be confused with environmental interference which disrupts the operation of a quantum system.

Environmental interference

Magnetic fields, electrical fields, or electromagnetic radiation in the physical environment surrounding a quantum system (such as a quantum computer) can disrupt or interfere with the proper operation of the quantum system.

When people speak of current quantum computers as being NISQ devices — Noisy Intermediate-Scale Devices, environmental interference is a large part of the source of such noise.

Shielding and other measures can be used to eliminate or at least partially mitigate such environmental interference, but generally it is an ongoing struggle which cannot be completely won.

Some of the environmental interference can arise from the internal components of the quantum system itself, with a variety of magnetic fields, electrical fields, and electromagnetic radiation being generated as a side effect of normal operation of the system itself. Again, measures can be taken to minimize or mitigate for such internal environmental interference, but it is generally an ongoing struggle with no absolute victory in sight.

Not to be confused with interference between the phases of two quantum states, which is actually a beneficial feature and used to implement quantum parallelism.

Stationary qubits and flying qubits

Quantum computing and quantum communication make use of qubits differently — qubits are stationary for quantum computing, but qubits can be flying qubits for quantum communication — two qubits (say, photons) can be entangled and then physically separated, potentially over an extended distance, and still maintain their entangled quantum state.

Quantum error correction (QEC)

Quantum states and qubits are very sensitive to environmental interference, which can cause errors. Quantum error correction (QEC) is a method for using redundancy to detect and even correct errors which can occur in qubits and operations on qubits (called quantum logic gates.)

QEC is seen as essential for more advanced quantum computers and quantum algorithms, where errors for many qubits and many gates would quickly (or gradually) reduce or eliminate the ability to compute correct or acceptable values.

There are no current implementations of quantum error correction — QEC is more of a theoretical concept for the future. It may not be practical for five or even ten years.

See also: fault-tolerant quantum computer.

Logical and physical qubits

There are a variety of strategies that can be employed to implement quantum error correction (QEC). One approach is the use of logical qubits.

When multiple physical qubits are used to provide the needed redundancy for a qubit, they are collectively referred to as a logical qubit. Algorithms operate on logical qubits.

Quantum programs, quantum logic gates, and quantum circuits

Quantum programs for quantum computers are also known as quantum circuits, which consist of sequences of quantum logic gates, each gate of a circuit being the basic operation of a quantum computer.

Unlike classical computers, a quantum logic gate is a software instruction, not a hardware device. Qubits are the hardware devices of a quantum computer.

Unitary transforms

Each quantum logic gate implements what is known in quantum mechanics as a unitary transform or unitary transformation, which is any of the fundamental ways in which the quantum state of a quantum system (e.g., a qubit) can change. Any further detail is far beyond the scope and intended audience of this informal paper.

Quantum algorithms

An algorithm is more of an abstract, high-level plan for how to solve a problem, while code or a program is the translation of an algorithm (the plan) into the implementation details needed to execute the algorithm on a computer. This is true for both classical and quantum computers.

There is some added complexity required for quantum algorithms since quantum computers do not have all of the features of a classical computer. Generally, a quantum programmer will write a classical computer program which dynamically generates the quantum circuits (sequences of quantum logic gates) representing the implementation of the quantum algorithm, and then requests that the generated circuits be executed on the quantum computer, after which the state of the quantum computer (measurement of the qubits) will be returned to the developer’s classical program for analysis and further processing.

Algorithmic building blocks

As noted, the low-level quantum logic gates of a quantum circuit are commonly dynamically generated by a classical computer program. This is a very tedious and error-prone process.

An alternative approach is to develop pre-coded libraries of the classical code needed to generate common forms of quantum circuits. Quantum developers can then invoke these library components to generate quantum circuits rather than developing the code fresh for each new quantum program.

Unfortunately, there currently aren’t many such rich libraries available, and the ones which are available are fairly primitive — or are proprietary and not available to everyone for free.

This state of affairs will likely change, but it is not clear how long it may take before the available libraries are rich enough to satisfy the needs of most quantum applications.

Significant additional research is needed in this area before development of sophisticated quantum applications can become widespread.

Hybrid quantum/classical algorithms

Although quantum computers are quite powerful, their operations are very simple and lack the capabilities for conditional execution, looping, function calls, rich data types, I/O, database access, and network access. Also, quantum devices are very sensitive to environmental interference so that quantum algorithms must be very short. As a result many algorithms are designed as hybrid algorithms, with some parts being quantum and some parts being classical — hybrid quantum/classical algorithms, so that the quantum parts can be kept relatively small.

Variational quantum algorithms

An important class of hybrid quantum/classical algorithms are variational quantum algorithms, which iterate one or more parameters based on the results of a quantum algorithm until acceptable values are reached.

Quantum computer as a coprocessor

As mentioned above, a quantum computer lacks many of the basic capabilities of a classical computer. In essence, a quantum computer complements the capabilities of a classical computer. Put another way, a quantum computer is effectively a coprocessor for a classical computer.

An application would in general be coded as a program on a classical computer, with I/O, database access, network access, and use of rich data types, with occasional invocations of quantum circuits for portions of algorithms which can exploit the quantum parallelism of the quantum computer, as if it were a coprocessor.

Quantum advantage and quantum supremacy

Quantum advantage indicates the degree of performance advantage of a quantum computer or quantum application over an equivalent classical computer or classical application.

Quantum supremacy indicates that a quantum algorithm or quantum application can accomplish a task which simply isn’t possible on even the most powerful classical supercomputer.

Some people use these two terms as if they were synonyms, so you have to examine the context carefully to determine the intended meaning.

The quantum advantage is frequently due to an exponential speedup, described below.

For more on quantum advantage and quantum supremacy read this informal paper:

In 2019 Google claimed to have achieved quantum supremacy. This informal paper offers my thoughts on that effort:

Exponential speedup

The performance of a quantum algorithm may increase exponentially as the size of the input grows. This is known as an exponential speedup. For example, if the input grew in size by a factor of k, the speedup over a classical algorithm would be a factor of 2^k rather than only some constant factor.

Exponential speedup is what gives a quantum algorithm or quantum application a quantum advantage.

And if the quantum advantage is large enough, it turns into quantum supremacy.

See more about quantum advantage and quantum supremacy in the preceding section.

The source of exponential speedup is quantum parallelism, described below.

Quantum parallelism

Although limited to only quantum computing, the concept of quantum parallelism is the key computational advantage of a quantum computer over a classical computer.

Quantum parallelism is the ability to perform a calculation over the full range of all possible values of a parameter, all in parallel, at the same time, as if it really were a single calculation.

By setting a collection of qubits into a superposition of both 0 and 1, a quantum program can execute a computation over the entire range of values (quantum states) of those qubits.

If there are k qubits it the collection, there are 2^k quantum states.

That’s not a lot of quantum states for smaller values of k — 2¹⁰ is 1,024, but for larger values of k it is a potentially very large number of states — 2³⁰ is a billion distinct quantum states, 2⁴⁰ is a trillion distinct quantum states, and anything over about 2⁵⁵ is far greater than the number of bits that even the largest conceivable classical supercomputer cluster could hold.

The real trick is that after executing a computation over a large number of quantum states, clever tricks must be used to extract values (quantum states) of interest from the large number of values — to select single tree from a vast forest. This is where the phase of quantum state comes in and interference is used to trick the quantum computer into divulging selected information. It may seem odd to have to resort to such tricks for such obvious operations, but that’s the nature of the quantum world.

Quantum communication

The whole point of quantum communication is to enable direct and secure communication of classical information with neither the complexity nor the risk of traditional encryption. Any attempt to eavesdrop or disrupt a quantum communication link will disrupt the quantum state, which cannot be read directly, but only inferred through the use of quantum entanglement.

The focus and purpose of quantum communication is that it is secure by design.

Quantum communication is between stations and may involve repeaters for longer distances, and quantum storage as well.

A couple of terms also associated with quantum communication:

Quantum networking

Quantum networking may sometimes merely be used as a synonym for quantum communication, but it is more properly related to communication between quantum computers, which is more of a theoretical field which will have significant future applications, but at present is limited to theory and research rather than practice or commercial applications.

While quantum communication focuses on transmitting classical data (bits) in a secure manner, quantum networking focuses on transmitting quantum information. Two classical computers could communicate or network using quantum communication, but quantum networking is required for two quantum computers to communicate or share quantum information or quantum state.

Current quantum computers have no capabilities for I/O, let alone at the level of quantum information, so the concept of quantum networking remains a speculative, theoretical research topic.

There is also hope that quantum networking could lead to the development of the quantum internet.

Whether quantum networking should ultimately be a separate subfield or considered under quantum communication is not completely clear and may evolve with the field. For now, it is a distinct research field — or an ambiguous term, take your choice.

Quantum internet

The quantum internet is a research concept for using quantum networking to implement a network with a level of features comparable to what we have in the Internet, but based on transmitting quantum information rather than only classical bits.

At present, no current quantum computers have any type of I/O capability, so no networking is possible at the level of quantum information. Eventually this may change, but not in the near future.

Quantum channel

Quantum channel is an ambiguous term — it may refer to quantum communication where classical information (raw bits) is being transferred, or it may refer to quantum networking where quantum information (quantum state), including superposition, probability amplitudes, and phase is being transferred.

Quantum teleportation

Quantum teleportation is a reference to the use of a quantum channel where full quantum state is being transferred, not merely classical bits alone.

Quantum key distribution (QKD)

Quantum key distribution is a secure method for two parties to produce an encryption key that only these two parties can use to communicate with each other.

Alice and Bob

Alice and Bob are fictional names for the two parties at either end of a communication channel. Typically one of them encrypts a message and the other decrypts the encrypted message.

Alice and Bob are used to describe cryptography and quantum cryptography in general.

Quantum storage

At present in quantum computing, there is no concept of storage for quantum information analogous to classical storage (disk, tape, flash drives) — other than the qubits themselves, which are more like registers than storage.

Whether this state of affairs may change in the future is a matter of pure speculation.

The concept of quantum storage applies to quantum communication as well, such as a quantum repeater, where entangled qubits may be kept temporarily before they are sent on to another station.

Quantum metrology and quantum sensing

Quantum metrology is the study of making high-precision measurement of physical quantities using quantum effects.

Physical quantities include:

Time Distance Acceleration Momentum Angular velocity Mass Energy Electromagnetic radiation — frequency, intensity Gas concentration Magnetic fields Electric fields, charge Temperature Pressure Gravity, gravity waves

There is no great clarity as to the distinction between quantum metrology and quantum sensing. They are frequently used together or even as synonyms.

The simple distinction that I would draw is that quantum metrology focuses more on the theory (science) of the physical quantities being measured, while quantum sensing focuses more on the practical aspects and applications of that science.

Applications of quantum sensing include biosensing, neuroimaging, and object detection.

Quantum sensors

The term quantum sensors is used to refer to the actual, practical, physical devices used to implement quantum sensing.

There is no analogous term for quantum metrology, although experimental work in quantum metrology would obviously require quantum sensors in the lab.

Quantum-enabled sensors

Alternative term for quantum sensors — sensors which utilize quantum effects.

Quantum detection

Quantum detection is covered by quantum sensing but focuses on the specific task of filtering signals from noise, with the goal of detecting the presence or absence of specific signals or objects. It may be less about accurately measuring a physical quantity than about detecting that a designated signal is present or not.

Quantum sensing and detection

Quantum sensing and detection are sometimes combined. They are closely related but not identical. I surmise that the combination is intended to emphasize applications, where both capabilities are needed to be developed and deployed in unison.

Quantum simulators

Not to be confused with quantum simulation which will be described in a subsequent section, a quantum simulator is an application running on a classical computer which simulates the operation of a quantum computer.

This is useful for several possible reasons:

The desired quantum computer is not readily available due to scheduling, demand, or cost. It is not yet practical to design and build the desired quantum computer. Debugging of quantum programs is needed, which is not possible on a real physical quantum computer. An audit log of the operations of a quantum program are needed, which is not possible on a real physical quantum computer. It is desirable to do many runs of a quantum program during development and testing, without the overhead of gaining access to a real physical quantum computer for each run.

In general, it may simply be more convenient to experiment with a quantum algorithm on a quantum simulator than to deal with the formality of a real physical quantum computer.

Quantum-inspired computing

Although not listed on the common enumerations of the subfields of QIS, quantum-inspired computing is still an important subfield.

Rather than running on a real physical quantum computer or a quantum simulator running on a classical computer, a quantum-inspired algorithm or quantum-inspired application is a classical algorithm or classical application running on a classical computer in which the algorithm is modeled on the principles of quantum computing, particularly quantum parallelism.

Generally, one starts with a pure, optimal quantum algorithm, and then represents it in an intermediate language which can be compiled into classical code. A quantum-inspired algorithm then decomposes the problem to be solved so that it can be executed as efficiently as possible on a classical computer, taking full advantage of any classical parallel computing features, such as multitasking, multiple processors, and even massively distributed clusters of high-performance classical computers.

Specialized hardware, such as GPUs, FPGAs, and even full-custom digital hardware could be adapted to focus on the needs of quantum-inspired algorithms.

Granted, in the general case, a quantum-inspired algorithm would not be able to compete with a real quantum computer, but in many specialized cases it may do well enough to satisfy application needs.

The intention is that a quantum-inspired algorithm would dramatically outperform a pure quantum algorithm running on a quantum simulator — if it doesn’t then the original quantum algorithm can be run as-is on a quantum simulator.

Think of quantum-inspired computing as a poor-man’s quantum computer.

Theory and practice

Traditionally, science refers more to theory and research experimentation, while practice refers more to engineering, development of applications, and real-world deployment of applications.

Unfortunately, quantum information science combines both traditional notions of science and practice under one umbrella.

Science and engineering

Traditionally, science is more associated with theory, while engineering is more associated with practice and development and deployment of practical applications.

Unfortunately, quantum information science blurs the distinction, including both the traditional sense of science and engineering under the same umbrella.

Hardware and software

Both hardware (physical devices) and software are included under quantum information science.

Both hardware and software traditionally have a split between science and practical applications.

Hardware has its basis in theoretical and experimental physics and practical electrical engineering and computer engineering.

Software has its basis in mathematics and computer science and practical software development and software engineering.

Device

A device or physical device is generally some form of hardware, such as:

An electronic component. A computer. A digital electronic component such as a gate or flip flop. A quantum computer. Such as a so-called NISQ device. A qubit. A sensor. A quantum sensor.

NISQ device

NISQ device is short for noisy intermediate-scale quantum device. It is a quantum computer that either currently exists or might likely be designed and built in the next few years using either current quantum computing technology or modest evolution of current technology. Such a computer does not have the redundancy or fault-tolerance to fully compensate for the variety of errors which can occur in a quantum computer.

In contrast to a fault-tolerant quantum computer.

One practical effect is that quantum programs must be relatively short so that they can fully execute before errors accumulate to an unacceptable degree.

Another practical effect is to encourage hybrid quantum/classical algorithms so that a much larger quantum algorithm can be decomposed into smaller pieces, with classical code to handle the transitions between the quantum pieces. Variational quantum algorithms are an example.

Fault-tolerant quantum computer

A fault-tolerant quantum computer (FTQC) has a combination of more robust components and quantum error correction so that correct results will achieved for most computations, regardless of what errors may occur at the lower hardware levels in the quantum computer.

Put simply, in theory, logical qubits will be guaranteed to return correct results even as the underlying physical qubits may encounter relatively frequent errors.

FTQC is an active area of research, but there are no current or near-term prospects for practical quantum computers.

Noisy intermediate-scale quantum (NISQ) computers are the alternative to FTQC. All current and near-term quantum computers are NISQ devices.

Applications

Just another call out to highlight the importance of focusing attention on quantum applications — applications of quantum information science, especially since the headline term, quantum information science, leaves it unclear whether applications are really included.

But applications are definitely included under quantum information science and technology.

For an overview of applications for quantum computing:

Algorithms

Quantum algorithms are a crossover between the science aspects of QIS and the applications aspects of quantum information science. Researchers (scientists) are needed to develop advanced algorithms, while software developers and application developers are needed to put those algorithms into practice.

Quantum simulation

Technically, quantum simulation is simply an application of quantum computing, but it is a fairly special form of application since it cuts to the heart of physics, quantum physics and quantum chemistry, and it was the application which got the ball rolling to pursue quantum computing when Prof. Richard Feynman pointed out back in 1982 that quantum physics would be needed to simulate quantum physics.

Put simply quantum simulation is the application of quantum computing to the task of simulating real, physical systems at the quantum mechanical level — the level of physical reality where quantum effects and the laws of quantum mechanics prevail over classical mechanics.

Be careful not to confuse quantum simulation with quantum simulators (simulating a quantum computer on a classical computer.)

Natural sciences and quantum simulation

Any of the fields or subfields of the natural sciences which use the adjective quantum and are based on the principles of quantum mechanics can benefit from quantum simulation, including:

Quantum physics. Quantum chemistry. Known also as quantum computational chemistry. Quantum biology. Any process which involves chemical reactions and the exchange or transfer of energy.

What are the biggest factors holding back quantum computing?

This informal paper highlights the hardware and algorithm issues that are holding back advances in quantum computing:

When will quantum computing finally take off for practical applications?

This informal paper addresses the question of when quantum computing will finally be ready for mainstream applications — When will quantum computing hardware and algorithms reach the stage where real-world, practical, production-quality, production-capacity applications can be readily produced without heroic levels of effort?:

Quantum cryptography and post-quantum cryptography

Quantum cryptography includes both the use of quantum communication to securely transmit classical data using quantum entanglement, as well as post-quantum cryptography which is the use of more advanced encryption schemes which are not crackable using even powerful quantum computers.

Some consider post-quantum cryptography to be categorically distinct from quantum cryptography.

QIST — Quantum information science and technology

The initialism QIST is sometimes used as a shorthand to refer to quantum information science and technology, presumably to treat the practice and applications of quantum information science somewhat separately from the more theoretical aspects of quantum information science. In other words, to treat practice as distinct from theory.

Experimentation and prototyping vs. development and production

People are now saying that quantum computing is transitioning from the lab to practice, but that’s a little misleading. There are four distinct phases in practice:

Experimentation. Staff are simply familiarizing themselves with the new technology, software, and tools. Staff may actually be using the new technology, but not for actual production deployment — or anything even close. Prototyping and mockups. Staff are doing preliminary implementations of capabilities to see how well they work, how users respond to them, and what issues crop up, but nothing suitable for production. Development. Having identified all issues and having come up with proposed solutions, staff is now executing the engineering tasks needed to develop full-scale, production-ready solutions. Including testing, well before actual deployment. Deployment and production. The development of solutions has been completed, but rolling solutions out to users, testing with real users, training users on the new technology, and transitioning from existing solutions to the new solutions can be a tedious, difficult, and time-consuming array of tasks. Parallel use of the old and the new solutions may be necessary for an extended period until the new solutions have proved themselves in the full range of production scenarios, including peak periods and outages which could impact the new solutions.

So, while organizations are indeed beginning the experimentation phase, and in limited cases even the prototyping phase, there’s no robust body of experience with full-scale development, let alone deployment and production.

Absent full-scale development, deployment, and production, it is not appropriate to say that quantum computing has transitioned to practice.

In fact, it could be two to five years — or longer — before we see much in the way of serious efforts to move beyond the prototyping stage. There could be some niches where production might be possible, but not on any broad basis.

Quantum computer science

At present, there is no clearly defined subset of quantum information science which can be seen as a quantum analog to classical computer science.

Quantum software engineering

At present, there is no clearly defined subset of quantum information science which can be seen as a quantum analog to classical software engineering.

Standardization

Over time, de jure standardization (formal standards) for quantum information science and its subfields will become more common, more formal, and more rigorous, but for now, the field is too dynamic and changing too rapidly for de jure standardization to have much appeal or traction.

Instead, we will likely see at least some degree of de facto standardization, where organizations tend towards using similar if not identical approaches to particular issues as other organizations which are similarly situated.

On the flip side, as quickly as de facto standards crop up, they may just as quickly be rendered obsolete by advances in technology.

Education and training

This paper won’t delve deeply into education and training for quantum information science, but simply provide a high-level view. Education and training are essential, for any new field of any significant complexity.

Some key points:

Both formal education and informal education, which is sometimes referred to as simply training. Undergraduate. Both minor and major in quantum information science or one or more of its subfields, especially quantum computing. Graduate. Both focus on quantum information science or one or more of its subfields, especially quantum computing, and some degree of exposure to quantum information science for degrees in other fields. PhD. Same as for graduate, but with a greater degree of specialization. Certificate programs for professionals who already have degrees, but not in quantum information science. May range from one-month to six-week to one-year programs. May include summer programs and summer schools. Seminars and boot camps on various aspects of quantum information science. May range from one hour to half a day, two days, three days, to a full week, or maybe two. On-the-job training. By the employer, possibly outsourced. Vender-specific training. Lifelong learning. The field is evolving rapidly and continuously, so there is literally no end to either education or training. Retraining of displaced workers. High school. Exposure to basic quantum information science concepts in math, science, and computer science or other STEM courses, including some hands-on use. Interdisciplinary. Especially for applications in areas where technical expertise is not as deep as required for quantum information science.

It is an open question as to what role the federal government (of the U.S. or other countries, or the EU) should play, or whether individual academic institutions, with input from the commercial sector and government agencies, can be expected to pick up the slack.

It remains to be seen whether at some point we experience a Sputnik moment and then people clamor for a quantum equivalent of the National Defense Education Act of 1958 to dramatically increase funding for scholarships, research programs, and hiring of teachers and professors.

We already have the National Quantum Initiative Act of 2018 which provides at least some increase in funding targeted at research and education, but not to the degree listed above — it’s more at the graduate and postdoctoral level, as opposed to say, high school teachers, interdisciplinary, or corporate training, let alone lifelong learning and retraining.

History

For historical reference, a workshop on quantum information science was held by the National Science Foundation (NSF) over twenty years ago, on October 28–29, 1999 in Arlington, Virginia:

Again for historical reference, from the Executive Summary of the workshop:

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.

Believe it or not, the U.S. Congress recently passed legislation (signed into law on December 21, 2018 by the President) — the National Quantum Initiative Act — which explicitly defines quantum information science:

The term “quantum information science” means the use of the laws of quantum physics for the storage, transmission, manipulation, computing, or measurement of information.

The Act refers to “the fields of:

(A) quantum information theory;

(B) quantum physics;

© quantum computational science;

(D) applied mathematics and algorithm development;

(E) quantum networking;

(F) quantum sensing and detection; and

(G) materials science and engineering;

Quantum communication is not explicitly listed there or even mentioned in the Act, but I believe that it is covered within quantum networking. I consider them separate, but that’s the confused nature of some of these new terms.

Quantum metrology is not explicitly listed there or even mentioned in the Act, but I believe that it is intended to be covered by quantum sensing.

Quantum information science is a misnomer

Quantum information science is a misnomer on many levels.

The major difficulties:

Science and engineering are usually treated separately in the classical world, but are merged in quantum information science. The hardware engineering of quantum devices is included under quantum information science. In the classical world, electrical engineering and computer engineering are treated as separate from computer science, while in the quantum world the notion of engineering is subsumed under science — under quantum information science, that is. There is no quantum computer science as a direct analog to the computer science of the classical world. Any notion of quantum computer science is nebulously covered under the broad umbrella of quantum computing, which includes hardware, unlike the classical world where computer engineering is considered a specialized field of engineering rather than being covered by computer science. Quantum information science suggests a strong parallel with classical information science, but that is far from true. Information science classically is about information alone in an abstract sense, divorced from hardware and the physical means by which information is represented and transmitted. But quantum information science includes the hardware and physical aspects of capturing, storing, organizing, accessing, analyzing, manipulating, and communicating information. As of this moment there is no accepted umbrella term under quantum information science that serves as the analog to classical information science. All of quantum computing is included under quantum information science, while the vast bulk of classical computing is NOT included under classical information science. Quantum communication is covered by quantum information science, whereas the physical aspects of communication are covered under engineering and information theory in the classical world. Quantum information theory, the direct analog of classical information theory (ala Claude Shannon) is covered by quantum information science, while classical information theory is NOT considered part of information science in the classical world. All of quantum metrology and quantum sensing are covered by quantum information science, and while portions are indeed under science (physics) in the classical world, a substantial fraction belongs more properly under engineering. Quantum information is an ill-defined, vague, and ambiguous term. Granted, I do offer my own, clear definition in this paper, but my definition is not binding on others, and in fact is not fully representative of current usage by others. Sure, quantum information is the quantum analog of information in the classical world, but that is too vague. Does it refer to qubits, alone? Unclear. Does it refer to quantum state, alone? Again, unclear. Does it refer to superposition and entanglement of qubits, alone? Does it refer to wave functions, alone? Still unclear. Does it refer to basis states, alone? No clarity. And what about phase (imaginary part of probability amplitude)? No clarity. Does it refer to computational basis states, alone? No clarity at all. Is quantum information discrete as in the classical world, or continuous (rotations of the three-dimensional Bloch sphere)? So confusing. Given superposition and entanglement, is there actually a unit of quantum information? Not so clear. And then there are qutrits and qudits as well. And then photonic quantum computing introduces are qumodes. And squeezed states. Some combination of all of the above? Okay, sure, I guess, but that hardly seems like a sound basis for something worthy of being called a science. The hardware devices for holding, storing, and manipulating quantum information — qubits — are fully covered by quantum information science, while the hardware devices for holding, storing, and manipulating classical information — flip flops, logic gates, memory cells, and storage media — are NOT considered under classical information science, since they are covered by electrical engineering and computer engineering. There’s no notion of software engineering (or quantum software engineering) included under quantum information science. You could argue that it is or should be under quantum computing, but that belies its significance and importance. There is no notion of whether applications are included under quantum information science, or whether quantum information science is simply the raw underlying technology, the platform, and applications are built on top of quantum information science. Again, clarity is needed. Numerous entities refer to quantum information science and technology as if there are some aspects which are not considered directly under the main umbrella of quantum information science. I surmise that some writers are excluding applications and commercial products and services, trying to treat quantum information science as more of an R&D research effort. For example, the National Quantum Initiative Act of Congress: “The purpose of this Act is to ensure the continued leadership of the United States in quantum information science and its technology applications by… supporting research, development, demonstration, and application of quantum information science and technology…”. And, USC: “Quantum information science and technology is an emerging interdisciplinary academic discipline concerned with the study of the new possibilities quantum mechanics offers for the acquisition, transmission, and processing of information.” And, Japan: “we have witnessed the growing interest and rapid progress of quantum information science and technology around the world. In Japan, the early basic research in this field has mainly been supported by a unique program…” And, Berkeley: “CS C191. Quantum Information Science and Technology… This multidisciplinary course provides an introduction to fundamental conceptual aspects of quantum mechanics from a computational and informational theoretic perspective, as well as physical implementations and technological applications of quantum information science.” And, the White House: “The SCQIS assesses the national portfolio using seven broad categories: four in fundamental science (S1-S4) and three in technological development (T1-T3). … These seven areas represent the broad foundation necessary to support a full industrial and Governmental effort in quantum information science and technology.” And, University of Illinois Urbana-Champaign: “Illinois Quantum Information Science and Technology Center”. And, Princeton: “The initiative comes at a time of national momentum for quantum sciences at the University, government and industry level. In 2018, the federal government established the National Quantum Initiative to energize research and training in quantum information science and technology.” And, Los Alamos National Laboratory: “This roadmap has been formulated and written by the members of a Technology Experts Panel… whose membership of internationally recognized researchers … in quantum information science and technology (QIST) held a kick-off meeting…” And, University of Cologne: “In the scope of the Cluster of Excellence “ML4Q”, courses in Bonn and Cologne from the following list can be taken to be acknowledged in the area of “Quantum Information Science and Technology”.” And, National Academies of Sciences, Engineering, and Medicine: “Foundations of Quantum Information Science and Technology”. Just to mention a few. It is ambiguous whether quantum applications are included under quantum information science, or more properly belong under QIST — quantum information science and technology, unlike classical computer science which does NOT include applications.

That said, it’s the term people have used and nobody has suggested a better term.

And who’s to say that the terminology of classical computing, classical communication, and classical science and engineering in general is really so much better.

Still, mediocre and confusing terminology makes it incrementally more difficult to communicate ideas clearly, especially exceedingly complex ideas such as those derived from quantum mechanics.

And since classical computing and communication are not going away any time soon, it’s problematic to have two parallel but inconsistent sets of terminology.

Glossary

My own glossary of quantum computing terms includes many of the terms related to the other subfields of quantum information science as well:

What’s next?

More work is needed: