Short Shor-style syndrome sequences

Delfosse, Nicolas; Reichardt, Ben W.

doi:10.48550/arxiv.2008.05051

Cited by 8 publications

(15 citation statements)

References 17 publications

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“…The resource savings we have demonstrated may be further enhanced with other recent developments, such as reducing time overhead using Pauli-Y stabilizer measurements [21] (see also Ref. [48]). We also expect that we can reduce the resource cost of color-code quantum computing further by tailoring architectures to common types of structured noise [9,[49][50][51][52].…”

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confidence: 77%

Low-overhead quantum computing with the color code

Thomsen¹,

Kesselring²,

Bartlett³

et al. 2022

Preprint

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Fault-tolerant quantum computation demands significant resources: large numbers of physical qubits must be checked for errors repeatedly to protect quantum data as logic gates are implemented in the presence of noise. We demonstrate that an approach based on the color code can lead to considerable reductions in the resource overheads compared with conventional methods, while remaining compatible with a two-dimensional layout. We propose a lattice surgery scheme that exploits the color code's rich structure to perform arbitrary pairs of commuting logical Pauli measurements in parallel while keeping the space cost low. Compared to lattice surgery schemes based on the surface code with the same code distance, our approach yields about a 3× improvement in the space-time overhead. Even when taking into account the color code's lower error threshold using current decoders, the overhead is reduced by 10% at a physical error rate of 10 −3 and by 50% at 10 −4 .

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confidence: 77%

Low-overhead quantum computing with the color code

Thomsen¹,

Kesselring²,

Bartlett³

et al. 2022

Preprint

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“…Furthermore, it will be worthwhile to investigate the time-overhead of fault-tolerant gates. The discovery of ancilla systems that enable code deformations by single-shot error correction [43,76,77] would permit measurement-based gates in constant time, leaving open the tantalising prospect of fault-tolerant quantum computing with constant-space and constant-time overhead.…”

Section: Discussionmentioning

confidence: 99%

Low-overhead fault-tolerant quantum computing using long-range connectivity

Cohen,

Kim,

Bartlett

et al. 2021

Preprint

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Vast numbers of qubits will be needed for large-scale quantum computing using today's faulttolerant architectures due to the overheads associated with quantum error correction. We present a scheme for low-overhead fault-tolerant quantum computation based on quantum low-density paritycheck (LDPC) codes, where the capability of performing long-range entangling interactions allows a large number of logical qubits to be encoded with a modest number of physical qubits. In our approach, quantum logic gates operate via logical Pauli measurements that preserve both the protection of the LDPC codes as well as the low overheads in terms of required number of additional ancilla qubits. Compared with the surface code architecture, resource estimates for our scheme indicate order-of-magnitude improvements in the overheads for encoding and processing around one hundred logical qubits, meaning fault-tolerant quantum computation at this scale may be achievable with a few thousand physical qubits at achievable error rates.

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“…2, we choose distance-four codes whose stabilizer generators are fairly local, with short Shor-style stabilizer measurement sequences that do not require any SWAP gates. We consider two block codes and a color code that encode multiple qubits [DR20], and the rotated surface code [BMD07] as a benchmark for postselection. In contrast, before the advent of topological codes, block codes were used for the simulation of 2D local error correction [SDT07, SR09, LPSB14].…”

Section: Physical Layoutmentioning

confidence: 99%

“…These self-dual CSS (Calderbank-Shor-Steane) codes were first considered in Ref. [DR20], to show examples of codes that can be constructed to have single-shot sequences of stabilizer measurements. By fixing some of the logical operators, the k = 6 code can be transformed into the k = 4 and k = 2 codes.…”

Section: Codesmentioning

confidence: 99%

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Distance-four quantum codes with combined postselection and error correction

Prabhu¹,

Reichardt²

2021

Preprint

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When storing encoded qubits, if single faults can be corrected and double faults postselected against, logical errors only occur due to at least three faults. At current noise rates, having to restart when two errors are detected prevents very long-term storage, but this should not be an issue for low-depth computations. We consider distance-four, efficient encodings of multiple qubits into a modified planar patch of the 16-qubit surface code. We simulate postselected error correction for up to 12000 rounds of parallel stabilizer measurements, and subsequently estimate the cumulative probability of logical error for up to twelve encoded qubits.Our results demonstrate a combination of low logical error rate and low physical overhead. For example, the distance-four surface code, using postselection, accumulates 25 times less error than its distance-five counterpart. For six encoded qubits, a distance-four code using 25 qubits protects as well as the distance-five surface code using 246 qubits.Hence distance-four codes, using postselection and in a planar geometry, are qubit-efficient candidates for fault-tolerant, moderate-depth computations.

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Short Shor-style syndrome sequences

Cited by 8 publications

References 17 publications

Low-overhead quantum computing with the color code

Low-overhead quantum computing with the color code

Low-overhead fault-tolerant quantum computing using long-range connectivity

Distance-four quantum codes with combined postselection and error correction

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