Non-unitary Coupled Cluster Enabled by Mid-circuit Measurements on Quantum Computers

TL;DR

This paper introduces a novel quantum state preparation method for quantum chemistry that leverages mid-circuit measurements to implement non-unitary coupled cluster states, reducing gate counts and classical overhead.

Contribution

It presents a new approach combining coupled cluster theory with mid-circuit measurements to improve quantum state preparation efficiency in quantum chemistry applications.

Findings

Achieves accurate energy evaluation and state overlap for small molecules.

Reduces CNOT and T gate counts by 28% and 57% respectively compared to standard methods.

Demonstrates potential for lowering classical computational overhead in quantum algorithms.

Abstract

Many quantum algorithms rely on a quality initial state for optimal performance. Preparing an initial state for specific applications can considerably reduce the cost of probabilistic algorithms such as the well studied quantum phase estimation (QPE). Fortunately, in the application space of quantum chemistry, generating approximate wave functions for molecular systems is well studied, and quantum computing algorithms stand to benefit from importing these classical methods directly into a quantum circuit. In this work, we propose a state preparation method based on coupled cluster (CC) theory, which is a pillar of quantum chemistry on classical computers, by incorporating mid-circuit measurements into the circuit construction. Currently, the most well studied state preparation method for quantum chemistry on quantum computers is the variational quantum eigensolver (VQE) with a unitary-CC with single- and double-electron excitation terms (UCCSD) ansatz whose operations are limited to unitary gates. We verify the accuracy of our state preparation protocol using mid-circuit measurements by performing energy evaluation and state overlap computation for a set of small chemical systems. We further demonstrate that our approach leads to a reduction of the classical computation overhead, and the number of CNOT and T gates by 28% and 57% on average when compared against the standard VQE-UCCSD protocol.