It is vital to minimize the impact of errors for near-future quantum devices that will lack the resources for full fault tolerance. Two quantum error mitigation (QEM) techniques have been introduced recently, namely, error extrapolation [Y. Li and S. C. Benjamin, Phys. Rev. X 7, 021050 (2017)PRXHAE2160-330810.1103/PhysRevX.7.021050; K. Temme et al., Phys. Rev. Lett. 119, 180509 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.180509] and quasiprobability decomposition [K. Temme et al., Phys. Rev. Lett. 119, 180509 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.180509]. To enable practical implementation of these ideas, here we account for the inevitable imperfections in the experimentalist's knowledge of the error model itself. We describe a protocol for systematically measuring the effect of errors so as to design efficient QEM circuits. We find that the effect of localized Markovian errors can be fully eliminated by inserting or replacing some gates with certain single-qubit Clifford gates and measurements. Finally, having introduced an exponential variant of the extrapolation method we contrast the QEM techniques using exact numerical simulation of up to 19 qubits in the context of a "swap" test circuit. Our optimized methods dramatically reduce the circuit's output error without increasing the qubit count.
Endo, S., Benjamin, S. C., & Li, Y. (2018). Practical Quantum Error Mitigation for Near-Future Applications. Physical Review X, 8(3). https://doi.org/10.1103/PhysRevX.8.031027