Leveraging commuting groups for an efficient variational Hamiltonian ansatz

TL;DR

This paper presents a novel quantum circuit design that leverages commuting groups within Hamiltonians to reduce circuit complexity and improve the efficiency of calculating low-lying eigenvalues in quantum computing.

Contribution

It introduces a new ansatz using commuting clusters and Clifford unitaries, enhancing circuit efficiency for Hamiltonian eigenvalue problems.

Findings

Effective in accurately determining ground state energies

Reduces circuit complexity compared to existing methods

Applicable to various quantum chemistry Hamiltonians

Abstract

Efficiently calculating the low-lying eigenvalues of Hamiltonians, written as sums of Pauli operators, is a fundamental challenge in quantum computing. While various methods have been proposed to reduce the complexity of quantum circuits for this task, there remains room for further improvement. In this article, we introduce a new circuit design using commuting groups within the Hamiltonian to further reduce the circuit complexity of Hamiltonian-based quantum circuits. Our approach involves partitioning the Pauli operators into mutually commuting clusters and finding Clifford unitaries that diagonalize each cluster. We then design an ansatz that uses these Clifford unitaries for efficient switching between the clusters, complemented by a layer of parameterized single qubit rotations for each individual cluster. By conducting numerical simulations, we demonstrate the effectiveness of our method in accurately determining the ground state energy of different quantum chemistry Hamiltonians. Our results highlight the applicability and potential of our approach for designing problem-inspired ansatz for various quantum computing applications.