Small Sampling Overhead Error Mitigation for Quantum Circuits

Probabilistic error cancellation (PEC) is a promising error mitigation technique that reduces the error rate without auxiliary quantum bits. However, PEC has two problems that need to be resolved: 1) there is no good PEC technique for parameterized gates and 2) sampling overhead (SO) grows exponentially with the number of PEC mitigated gates. We first propose a parameterized gate PEC (PGPEC) that mitigates the error without fully characterizing the gates, as the original PEC requires. The result shows that the number of gates requiring characterization for a thousand random circuits can be reduced by 97% or more. We next propose two novel approaches to solving the second problem. We propose a macro gate PEC (MGPEC) technique that aggregates multiple gates as a single macro gate to reduce the exponent of the SO. MGPEC reduces the SO by 49% on the QFT7 under the IBMQ noise model, which simulates real operation conditions of quantum circuits. We propose a design diversity PEC (DDPEC) technique to reduce the exponential basis of the SO. The results show that our DDPEC with design diversity check reduces overall SO by 13% on the QFT7 circuit under the IBM Q noise model. Combining the DDPEC with the MGPEC, we can reduce overall SO by 73%.