Mid-circuit measurement as an algorithmic primitive

TL;DR

This paper investigates how mid-circuit measurements can serve as an algorithmic primitive to improve quantum algorithms, specifically enhancing the Quantum Approximate Optimization Algorithm (QAOA) by acting as a low-energy filter and amplifying ground states.

Contribution

It introduces the use of mid-circuit measurements as a novel technique to improve quantum algorithm performance, demonstrated on QAOA and validated on real hardware.

Findings

Mid-circuit measurement acts as a low-energy filter.

The method amplifies the ground state in simulations.

Validation on IBM Quantum hardware confirms effectiveness.

Abstract

We explore the usefulness of mid-circuit measurements to enhance quantum algorithmics. Specifically, we assess how quantum phase estimation (QPE) and mid-circuit measurements can improve the performance of variational quantum algorithms. Our focus is on the single-qubit version of QPE namely, the Hadamard test applied to the Quantum Approximate Optimization Algorithm (QAOA) ansatz. We demonstrate that a mid-circuit measurement acts as a low-energy filter when the desired outcome is obtained. When the other outcome is measured we heuristically rely on the mixer to repopulate the low energy states. Numerical simulations show that this method effectively amplifies the ground state. We validate our approach on real quantum hardware namely the IBM Quantum system one ibm_quebec.