Distributed Quantum Error Correction
First International Conference on Quantum Error Correction
December 19, 2007

Rodney Van Meter (Keio) rdv@sfc.wide.ad.jp
Jacob M. Taylor (MIT),
Liang Jiang (Harvard)
Copyright © 2006 Keio
University

I don’t care about quantum error
correction.
I care about quantum computer
system architectures.
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A Quantum Multicomputer Nodequantum network

waveguideclassical control & measurement
to next
node

coherent
microwave
sourcetransceiver
qubit
qubit
node
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dilutionrefrigerator

One Like This?

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A Quantum Multicomputer

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Multicomputer Research• Architecture:# of nodes? Qubits/node?
Network topology? Link design?
• Software: applications, language design• Error management:
Quantum Error Correction (QEC),
purification for teleportation• Performance analysis
rdv, KMI, PRA 71(5), 2005; rdv, KMI, TDL, MS+S2006;
rdv, WJM, KN, KMI, Proc. Int. Symp. Computer Architecture (ISCA) (2006)
J. Emerging Tech. in Computing Systems (2007)6

Link Design7Link Design• Two levels of [[23,1,7]] code allow 1%
physical teleportation failure when factoring a1024-bit number• Serial links work well when memory error
rate 100x better than teleportation– Preferable for engineering reasons• Creating and using distributed logical zeros ispainful and unlikely to work well.
rdv, KN, WJM, IEEE Trans. on Computers, 56(12), 20078

Small NodesOi, Devitt, Hollenberg, PRA 74

14 qubits/node,
one level of [[5,1,3]]

95 qubits/node,
only 1 for data
(1 measurement,2 purification,Jiang1ettransceiver)al., quant-ph/0703029

Kim & Kim, arxiv:0711.3866

a few hundred
qubits/nodeSmall Nodes• Many technologies support small nodes, notthe 3-5 thousand physical qubits we want• At first glance, teleportation failure rates mustmeet standard threshold arguments

10Partial Bell Measurement11[[9,1,3]] Shor Code Stabilizer
X X X X X X I I I I I I
X X X
X X X
I I I
X X X

Z Z I II IZ IZ I II II I I I I I I I I I I
I I I I I I Z Z I I Z Z I I I I I I
I I I I I I I I I I I I Z Z I I Z Z
12Shor Stabilizer in 3 Nodes

Z Z I
I I I
I I I
13PBM+ 2 Bell pairs = 4 Bell pairs
for oneI I I
round ofX X Xlevel one
X X X
QEC
PBM uses one |000000>+|111111>,
built & verified using two Bell pairs
PBM

2 Bell pairs
X X XX X X
I I IZero Bell pairs consumed!
I Z Z I I I I I I I I I I I I
I I I Z Z I I Z Z I I I I I I
I I I I I I I I I Z Z I I Z Z

PBM = Partial Bell Measurement

Concatenation
FTM 9x2 Bell pairs x6
Z Z I
I I I
I I I

FTM

27x2 Bell pairs x2
I I I
X X XX X X
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FTM = Full Transversal Measurement

[[9,1,3]]x[[9,1,3]]• Single-data-qubit (5 phy qubit) nodes require(5+6)x2x9 + 9x2x6 + 27x2x2 = 414
physical Bell pairs• 3-data-qubit nodes (9 phy) require
4x9 + 9x2x6 + 27x2x2 = 252
physical Bell pairs– ~1.6x for scaleup 5-->9 physical qubits/node• 9-data-qubit nodes (20 phy) require
9x2x6 + 27x2x2 = 216
physical Bell pairs– but first level QEC will cycle faster•
15 Plus 81 Bell pairs per logical gate or teleportation

Observations• All codes require entanglement btw nodes– Some syndromes purely local, some “hard”• Mitigation approaches:– match to error type (biased error model)– reduce frequency in “hard” direction– relax constraints: Bacon-Shor?
• For detailed performance calculation,need to separate Bell pair creation from
actual teleportation
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Conclusions• Small nodes not ideal, but usable– full logical qubits/node much better(how much depends on ratio of logical
gates to QEC)
• At second level and above, the interconnect
remains teleportation

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AQUA: Advancing QuantumArchitecture
What will you build your
http://www.sfc.wide.ad.jp/aqua/
computer out of?
with thanks toKohei M. Itoh, Kae Nemoto,
Bill Munro, Thaddeus Ladd,
Austin Fowler
and MEXT for funding18

Keio?

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