Architecture of a Quantum Multicomputer
Rodney Van Meter1 ∗1W. J. Munro2 3 †Kae Nemoto3 ‡Faculty of Environment and Information Studies, Keio University
5322 Endo, Fujisawa, Kanagawa, 252-8520, Japan
2Hewlett-Packard Laboratories
Filton Road, Stoke Gifford, Bristol BS34 8QZ, United Kingdom
3
National Institute of Informatics
2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, JapanAbstract. We have created the architecture of a quantum multicomputer and analyzed its performance for running
Shor’s algorithm for factoring large numbers. In this paper, we combine fault-tolerance techniques with performancegoals for our architecture, which uses a linear interconnect and six logical qubits per node. Our performance targetof factoring a 1,024-bit number in one month requires teleporting 6.2 logical qubits per second on each link inthe system, which translates to 3,300 physical teleportations per second on each link. A qubus-based interconnect
generates Bell pairs of intermediate fidelity that must be purified. Starting from a Bell state with fidelity F = 0.638,
as a qubus-based cavity QED interconnect might generate with a qubit-to-qubit loss of 3.4dB, about 1.5 million
physical entanglement attempts per second are enough to reach this level of performance.
Keywords: distributed quantum computation, quantum computer architecture

1Introduction

Researchers have begun designing systems for distributed
quantum computation (DQC). The basic principle of distributed quantum computation has been known for adecade [1, 2]. A few uses for geographically distributed entanglement have been developed, but more recently, interest has
grown in the use of distributed quantum computation within
a single laboratory. We refer to such distributed-memory systems as quantum multicomputers.
The interest in DQC stems from the difficulty of scaling up
any individual quantum computer to hold the millions of physical qubits that may be necessary for some applications. Any
quantum computing technology will have a limit to the number of physical qubits that can be supported in a single device.
These limits are not yet well understood, but may range into
the low thousands for solid-state systems. Quantum error correction reduces the number available to applications to only
a handful of logical qubits. Thus, researchers are designingdevices to be connected into multicomputers [3, 4, 5].
In previous work, we have determined that a linear network of nodes will perform well on the addition subroutine,
and that the most efficient form of the algorithm on a quantum multicomputer teleports data qubits, rather than gates [6].
The mechanics of the original Vedral-Barenco-Ekert (VBE)
carry-ripple adder [7] work best for nodes that hold at least
four logical qubits. The links between nodes may be serial,
and two layers of the [[23,1,7]] Steane quantum error correction code will allow teleportation error rates of around onepercent. We have also established a performance goal of factoring a 1,024-bit number in one month of wall-clock time on
our system, which should exceed the performance of the bestclassical systems available [8].
In this paper, we establish performance requirements for theinterconnect links, increase the level of detail on the node re∗rdv@sfc.wide.ad.jp† bill.munro@hp.com‡ nemoto@nii.ac.jp

quirements and on QEC, and provide a more complete analysis of the application algorithm. We show that physical qubits
must be teleported between nodes at about 3,300 teleportations per second on each link in the system, and individual
nodes must contain about 10,000 physical qubits. Using thequbus scheme for the interconnect, initial fidelities are low,
and purification must be used. For a cavity QED system as
a candidate technology, the resulting requirement is about 1.5
million entanglement attempts per second on each link.

2 Multicomputer Architecture
Our quantum multicomputer (QMC) architecture consistsof a group of semi-autonomous nodes, connected by a quantum network and a real-time classical network, all controlledfrom a classical front-end computer that determines the program to be run and the role to be played by each node. Eachnode contains four logical qubits for the algorithmic data andtwo logical buffer qubits for communications, which are used
to send and receive data through a qubus entangling channel,
giving a total of six logical qubits per node. All quantum error correction is performed locally, within a single node. Our
complete system will consist of 1,024 nodes for the arithmeticunit, plus a few more for the control variables for the algorithm. An overview of the quantum components of the architecture is shown in Figure 1.
A computer system cannot be designed without an understanding of its target workload and expected performance.
Above, we suggested a goal of factoring a 1,024-bit number
in one month of wall-clock execution time. Next we show that
achieving this performance level will require 6.2 logical qubit
teleportations per second per node.
The computational core of Shor’s algorithm is the quantum
modular exponentiation. The modular exponentiation can beperformed in roughly 4n2 calls to the addition subroutine, orabout four million calls for a 1,024-bit number. The execution time of the adder can be optimized down to the time toteleport two logical qubits between a pair of nodes, when themulticomputer qubus
nodeconnection

qubit
fiber orwave guidecentimeters
to meters

microns
to millimeters
serial connection transceiver qubitnode−internalqubit
qubus−qubit qubit−qubit
coupling
coupling

Figure 1: Quantum portions of our quantum multicomputer

cavity wave guide

~2dB

~2dB

fiber

wave guide cavity

0.17dB/km ~2dB

~2dB

Figure 2: Qubit-to-qubit losses in a cavity QED systemtime to generate a high-fidelity Bell pair is long compared to
the local gate time [6]. To compose a series of additions intoa multiplication, a control variable must be used to set oneof the operands. We must teleport the control variable into
the node before each addition, and again to clear the operand
after the addition. Thus, we use a total of four teleportation
operations per addition, half for algorithm control and half for
the arithmetic itself. Sixteen million logical qubit teleportations can be accomplished in one month if the rate of logicalteleportations is 6.2 per second.
For two levels of the [[23,1,7]] Steane error correcting code,teleporting a logical qubit requires 232 = 529 physical qubit
teleportations. Because we are using serial links between themulticomputer nodes, each link must support 6.2 × 529 =3300 physical teleportations per second.
Teleportation consumes Bell pairs. The interconnect subsystem is tasked with creating the high-fidelity Bell pairs that
we need. The qubus system is one candidate for the interconnect [9]. Simulations of a cavity QED form of qubus for quantum repeaters reveal an upper bound of about 5dB loss qubitto-qubit, beyond which entanglement fidelity is too low forpurification to operate [10]. For a more practical limit, a lossof 3.4dB will give an initial fidelity F = 0.638. The entanglement attempts succeed about 40% of the time, and purification itself is a probabilistic process, so using purification toreach a final fidelity F = 0.98 or better requires an average ofabout 450 qubus entanglement attempts. To execute 6.2 logical teleportations per second requires 450 × 3300 = 1.5 × 106
physical entanglement attempts per second.
Figure 2 shows approximate, somewhat optimistic signal
strength losses from qubit to qubit for a cavity QED system.
For a multicomputer configuration, with a fiber length of only
a few meters, the loss is clearly dominated by the couplings in
the system. To reach our preferred loss level of three to fourdB, modest improvement in coupling efficiency is needed.
Switching or demultiplexing of incoming signals to multiple
transceiver qubits seems desirable, but switch losses are often

several dB. This figure makes it clear that avoiding any unnecessary losses is an important goal when designing qubusbased interconnects.
Single-qubit rotations on logical qubits are difficult, andfault tolerance demands that direct data qubit-to-data qubit interactions be minimized. Fowler therefore recommends using
three registers for each logical qubit [11], boosting the numberof qubits per node to 6 × 3 × 232 = 9522 physical qubits. Including transceiver qubits for the interconnect and purificationbuffering, we require about 10,000 physical qubits per node.

3 Conclusion
In this paper, we have described a quantum multicomputer built from about ten million physical qubits packaged
in a thousand separate nodes, connected by a qubus-based interconnect. We believe such a multicomputer structure canbe developed more easily than a large-scale monolithic system, allowing a variety of physical qubit technologies to scale
quickly beyond currently-perceived limits. Thus, the multicomputer has the potential to dramatically accelerate the arrival of quantum computers that generate results beyond thereach of classical systems.
Acknowledgments. The authors thank MEXT for partial
support for this research, and Kohei M. Itoh, Thaddeus D.
Ladd, and Austin Fowler for technical guidance.

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