Error mitigation for variational quantum algorithms through mid-circuit measurements

TL;DR

This paper introduces mid-circuit post-selection techniques for error mitigation in variational quantum algorithms, leveraging known state structures to detect and filter errors without requiring extensive qubits or classical control, suitable for current hardware.

Contribution

It proposes novel mid-circuit post-selection schemes for specific encodings, including a space compression method for one-hot states, enhancing error mitigation on NISQ devices.

Findings

Effective error filtering demonstrated on Quantum Alternating Operator Ansatz

Method works without ancilla qubits, suitable for hardware with measurement and reset capabilities

Improves noise robustness by exploiting state structure and mid-circuit measurements

Abstract

Noisy Intermediate-Scale Quantum (NISQ) algorithms require novel paradigms of error mitigation. To obtain noise-robust quantum computers, each logical qubit is equipped with hundreds or thousands of physical qubits. However, it is not possible to use memory-consuming techniques for current quantum devices having at most hundreds or at best thousands of physical qubits on their own. For specific problems, valid quantum states have a unique structure as in the case of Fock states and W-states where the Hamming weight is fixed, and the evolution takes place in a smaller subspace of the full Hilbert space. With this pre-knowledge, some errors can be detected in the course of the evolution of the circuit, by filtering the states not obeying the pattern through post-selection. In this paper, we present mid-circuit post-selection schemes for frequently used encodings such as one-hot, binary, gray, and domain-wall encoding. For the particular subspace of one-hot states, we propose a method that works by compressing the full Hilbert space to a smaller subspace, allowing projecting to the desired subspace without using any ancilla qubits. We demonstrate the effectiveness of the approach for the Quantum Alternating Operator Ansatz algorithm. Our method is particularly suitable for the currently available hardware, where measuring and resetting is possible, but classical control conditional operators are not.