Single-shot error mitigation by coherent Pauli checks Article Swipe

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E. van den Berg , Sergey Bravyi , Jay Gambetta , Petar Jurcevic , Dmitri Maslov , Kristan Temme · YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2212.03937

Generating samples from the output distribution of a quantum circuit is a ubiquitous task used as a building block of many quantum algorithms. Here we show how to accomplish this task on a noisy quantum processor lacking full-blown error correction for a special class of quantum circuits dominated by Clifford gates. Our approach is based on Coherent Pauli Checks (CPCs) that detect errors in a Clifford circuit by verifying commutation rules between random Pauli-type check operators and the considered circuit. Our main contributions are as follows. First, we derive a simple formula for the probability that a Clifford circuit protected by CPCs contains a logical error. In the limit of a large number of checks, the logical error probability is shown to approach the value ${\approx}7εn/5$, where $n$ is the number of qubits and $ε$ is the depolarizing error rate. Our formula agrees nearly perfectly with the numerical simulation results. Second, we show that CPCs are well-suited for quantum processors with a limited qubit connectivity. For example, the difference between all-to-all and linear qubit connectivity is only a 3X increase in the number of CNOT gates required to implement CPCs. Third, we describe simplified one-sided CPCs which are well-suited for mitigating measurement errors in the single-shot settings. Finally, we report an experimental demonstration of CPCs with up to 10 logical qubits and more than 100 logical CNOT gates. Our experimental results show that CPCs provide a marked improvement in the logical error probability for the considered task of sampling the output distribution of quantum circuits.

Type

preprint

Language

en

Landing Page

http://arxiv.org/abs/2212.03937

PDF

https://arxiv.org/pdf/2212.03937

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green

Cited By

1

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10

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https://openalex.org/W4310997712

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https://openalex.org/W4310997712

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DOI

https://doi.org/10.48550/arxiv.2212.03937

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Title

Single-shot error mitigation by coherent Pauli checks

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Type

preprint

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Language

en

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Publication year

2022

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Publication date

2022-12-07

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E. van den Berg, Sergey Bravyi, Jay Gambetta, Petar Jurcevic, Dmitri Maslov, Kristan Temme

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https://arxiv.org/abs/2212.03937

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https://arxiv.org/pdf/2212.03937

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Yes

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green

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https://arxiv.org/pdf/2212.03937

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Concepts

Pauli exclusion principle, Qubit, Controlled NOT gate, Quantum circuit, Quantum error correction, Quantum gate, Computer science, Algorithm, Quantum algorithm, Topology (electrical circuits), Quantum, Quantum mechanics, Mathematics, Arithmetic, Physics, Combinatorics

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Cited by

1

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2023: 1

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10

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