Error mitigation techniques

Abstract

A method of mitigating errors in quantum computing, wherein the method comprises: performing (S) an operation on the state of a qubit in a group of qubits a plurality of times, wherein the operation has a first error rate, and wherein each performance of the operation comprises: performing a first operation comprising: a gate operation, a symmetry operation, and a first basis operation; or performing a second operation comprising: the gate operation, the symmetry operation, and a second basis operation; wherein the first and second basis operations are different basis operations selected from a set of basis operations; and measuring the state of the qubit; wherein the probability of performing the first operation is a first probability, and the probability of performing the second operation is a second probability; obtaining (S) a symmetry measurement for the group of qubits after each performance of the operation using the symmetry operation, wherein the group of qubits comprises a plurality of qubits; wherein the symmetry measurement is a first symmetry outcome if the number of errors is even or a second symmetry outcome if the number of errors is odd; obtaining (S) a first state measurement by determining the average state of the qubit for the first symmetry outcome; obtaining (S) a second state measurement by determining the average state of the qubit for the second symmetry outcome; fitting (S) the first state measurement to a first curve having the form (I); fitting the second state measurement to a second curve having the form (II); wherein n is an error rate and A and γ are fitting parameters; and extrapolating (S) the average state of the qubit at a second error rate using the first and second fitted curves; wherein the second error rate is lower than the first error rate.