Quantum Error Mitigation by Pauli Check Sandwiching

We introduce an error mitigation technique that uses multiple pairs of parity checks to mitigate errors. Each pair of checks uses one ancilla qubit to detect a component of the error operator and represents one layer of the technique. We prove that our technique can recover the noiseless state under the assumption of noise not affecting the checks. Our method is inspired by the parity checks present in stabilizer codes. Our error mitigation scheme does not incur any encoding overhead. Instead, we choose the checks based on the input circuit. We develop an algorithm for obtaining such checks for an arbitrary target circuit. Since our method applies to any circuit and input state, it can be easily combined with other error mitigation techniques. We evaluate the performance of the proposed methods using extensive numerical simulations on 1,850 random input circuits composed of Clifford gates and non-Clifford single-qubit rotations, a class of circuits encompassing most commonly considered variational algorithm circuits. We observe average improvements in fidelity of 34 percentage points with six layers of checks.