Single-shot error mitigation by coherent Pauli checks

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