Advanced Methods for Quasiprobabilistic Quantum Error Mitigation
Christophe Piveteau · Repository for Publications and Research Data (ETH Zurich) · 2020
Current quantum computers are plagued by prohibitive amounts of noise, which complicates the experimental realization of useful quantum algorithms that outperform classical computers.Quantum error mitigation techniques could constitute a potential avenue to demonstrate this feat without the need for fault-tolerant quantum error correction.One method in this family of mitigation techniques is the quasiprobability method introduced by Temme et al. [1].It simulates a noise-free quantum computer with a noisy one, with the caveat of only producing the correct expected values of measurement observables.The cost of a quasiprobability simulation manifests as a sampling overhead which scales exponentially in the number of error-mitigated gates in the circuit.In this thesis we aim to reduce the exponential basis of that overhead, which in turn allows the application of the quasiprobability method to deeper quantum circuits.A central result is the introduction of a novel scheme, which we call Stinespring algorithm, that aims to choose the quasiprobability decomposition in a noise-aware manner.Along the way, we introduce a generalization of the quasiprobability method, which we denote approximate quasiprobability method, that allows for a tradeoff between an approximation error and the sampling overhead.This method is already interesting on its own and we present a few potential applications.Finally, we present some ideas how quantum error correction can benefit from the quasiprobability method.This final part is separate to the other topics of the master thesis and gives a rough overview of a new research project that started towards the end of the thesis and that we will continue to pursue in the future.i Overview of ContributionsWe summarize the novel contributions from this thesis:• Many details in the presentation of Chapter 2 have not been stated in such precision in previous literature.However, we estimate that many of these contributions are evident for someone knowledgeable in the domain.• The channel difference decomposition (Section 2.6).• The approximate QPD and its applications (Chapter 3).• The Stinespring algorithm (Chapter 4).