Statistical Phase Estimation and Error Mitigation on a Superconducting Quantum Processor
Nick S. Blunt, Laura Caune, Róbert Izsák, Earl T. Campbell, Nicole Holzmann · PRX Quantum · 2023
Quantum phase estimation (QPE) is a key quantum algorithm, which has been widely studied as a method to perform chemistry and solid-state calculations on future fault-tolerant quantum computers.Recently, several authors have proposed statistical alternatives to QPE that have benefits on early faulttolerant devices, including shorter circuits and better suitability for error-mitigation techniques.However, experimental investigations of the algorithm on real quantum processors are lacking.Here, we implement statistical phase estimation on Rigetti's superconducting processors.Specifically, we use a modification of the Lin and Tong [PRX Quantum 3, 010318 (2022)] algorithm with the improved Fourier approximation of Wan et al. [Phys.Rev. Lett.129, 030503 (2022)] and apply a variational-compilation technique to reduce the circuit depth.We then incorporate error-mitigation strategies including zero-noise extrapolation and readout-error mitigation with bit-flip averaging.We propose a new method to estimate energies from the statistical phase estimation data, which is found to improve the accuracy in the final energy estimates by 1-2 orders of magnitude with respect to prior theoretical bounds, reducing the cost of performing accurate phase-estimation calculations.We apply these methods to chemistry problems for active spaces up to four electrons in four orbitals, including the application of a quantum embedding method, and use them to correctly estimate energies within chemical precision.Our work demonstrates that statistical phase estimation has a natural resilience to noise, particularly after mitigating coherent errors, and can achieve far higher accuracy than suggested by previous analysis, demonstrating its potential as a valuable quantum algorithm for early fault-tolerant devices.