Single-shot error mitigation by coherent Pauli checks

• URL: http://arxiv.org/abs/2212.03937v1
• Date: Wed, 7 Dec 2022 20:03:07 GMT
• Title: Single-shot error mitigation by coherent Pauli checks
• Authors: Ewout van den Berg, Sergey Bravyi, Jay M. Gambetta, Petar Jurcevic, Dmitri Maslov, Kristan Temme
• Abstract summary: We show how to generate samples from the output distribution of a quantum circuit without full-blown error correction. Our approach is based on Coherent Pauli Checks that detect errors in a Clifford circuit.
• Score: 6.992823294269743
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 ${\approx}7\epsilon n/5$, where $n$ is the number of qubits and $\epsilon$ 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.

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