VarSaw: Application-tailored Measurement Error Mitigation for Variational Quantum Algorithms

TL;DR

VarSaw is proposed, which improves JigSaw in an application-tailored manner, by identifying considerable redundancy in the JigSaw approach for VQAs: spatial redundancy across subsets from different VQA circuits and temporal redundancy across globals from different VQA iterations.

Abstract

For potential quantum advantage, Variational Quantum Algorithms (VQAs) need high accuracy beyond the capability of today's NISQ devices, and thus will benefit from error mitigation. In this work we are interested in mitigating measurement errors which occur during qubit measurements after circuit execution and tend to be the most error-prone operations, especially detrimental to VQAs. Prior work, JigSaw, has shown that measuring only small subsets of circuit qubits at a time and collecting results across all such subset circuits can reduce measurement errors. Then, running the entire (global) original circuit and extracting the qubit-qubit measurement correlations can be used in conjunction with the subsets to construct a high-fidelity output distribution of the original circuit. Unfortunately, the execution cost of JigSaw scales polynomially in the number of qubits in the circuit, and when compounded by the number of circuits and iterations in VQAs, the resulting execution cost quickly turns insurmountable. To combat this, we propose VarSaw, which improves JigSaw in an application-tailored manner, by identifying considerable redundancy in the JigSaw approach for VQAs: spatial redundancy across subsets from different VQA circuits and temporal redundancy across globals from different VQA iterations. VarSaw then eliminates these forms of redundancy by commuting the subset circuits and selectively executing the global circuits, reducing computational cost (in terms of the number of circuits executed) over naive JigSaw for VQA by 25x on average and up to 1000x, for the same VQA accuracy. Further, it can recover, on average, 45% of the infidelity from measurement errors in the noisy VQA baseline. Finally, it improves fidelity by 55%, on average, over JigSaw for a fixed computational budget. VarSaw can be accessed here: https://github.com/siddharthdangwal/VarSaw.

Figures (19)

• Figure 1: Traditional VQA is significantly impacted by measurement error. JigSaw combats measurement error but introduces high execution cost which is particularly harmful for VQA. VarSaw minimally achieves JigSaw's measurement error mitigation at an execution cost similar to traditional VQA. When measurement error is very high, its benefits in terms of both fidelity and computational cost is even greater.
• Figure 2: (a) Traditional VQA task run over multiple iterations. Each iteration executes multiple circuits corresponding to the different Pauli Strings in the problem Hamiltonian. (b) For every circuit in the original task, JigSaw runs multiple circuits - these are the Global circuits (same as original) and the Measurement Subsets (which scale linearly in the number of circuit qubits). These are run every iteration. (c) VarSaw optimizes JigSaw in a VQA-cognizant manner. It exploits spatial redundancy (repetitions and commutativity) to reduce the number of Subsets executed every iteration. Further, it exploits temporal redundancy (similarity in adjacent iterations' distributions) to reduce the number of iterations on which the Globals are executed.
• Figure 3: Overview of JigSaw (Adapted from jigsaw).
• Figure 4: VQA: a hybrid algorithm that alternates between classical optimization and quantum execution.
• Figure 5: Ansatz circuit measured on different Pauli bases (left: 'ZZZ', right: 'XZX'). Qubit commutativity allows for a set of Pauli strings to be measured on a single basis.