Constant Overhead Quantum Fault-Tolerance with Quantum Expander Codes

We prove that quantum expander codes can be combined with quantum fault-tolerance techniques to achieve constant overhead: the ratio between the total number of physical qubits required for a quantum computation with faulty hardware and the number of logical qubits involved in the ideal computation...

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Vydané v:2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS) s. 743 - 754
Hlavní autori: Fawzi, Omar, Grospellier, Antoine, Leverrier, Anthony
Médium: Konferenčný príspevok..
Jazyk:English
Vydavateľské údaje: IEEE 01.10.2018
Predmet:
Decoding
decoding algorithm
expander codes
Fault tolerance
Fault tolerant systems
Graph theory
Noise measurement
percolation
single-shot quantum error correction
ISSN:2575-8454
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Popis
Shrnutí:We prove that quantum expander codes can be combined with quantum fault-tolerance techniques to achieve constant overhead: the ratio between the total number of physical qubits required for a quantum computation with faulty hardware and the number of logical qubits involved in the ideal computation is asymptotically constant, and can even be taken arbitrarily close to 1 in the limit o small physical error rate. This improves on the polylogarithmic overhead promised by the standard threshold theorem. To achieve this, we exploit a framework introduced by Gottesman together with a family of constant rate quantum codes, quantum expander codes. Our main technical contribution is to analyze an efficient decoding algorithm for these codes and prove that it remains robust in the presence of noisy syndrome measurements, a property which is crucial for fault-tolerant circuits. We also establish two additional features of the decoding algorithm that make it attractive for quantum computation: it can be parallelized to run in logarithmic depth, and is single-shot, meaning that it only requires a single round of noisy syndrome measurement.
ISSN:2575-8454
DOI:10.1109/FOCS.2018.00076