Variational quantum Hamiltonian engineering

Estimating the expectation value of a Hamiltonian and performing a Hamiltonian simulation are two fundamental tasks in quantum computation, with their efficiency heavily dependent on the Pauli norm of the Hamiltonian, which sums the absolute values of its Pauli coefficients. In this work, we propose...

Full description

Saved in:
Bibliographic Details
Main Authors: Benchi Zhao, Keisuke Fujii
Format: Article
Language:English
Published: American Physical Society 2025-05-01
Series:Physical Review Research
Online Access:http://doi.org/10.1103/PhysRevResearch.7.023123
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850187394029977600
author Benchi Zhao
Keisuke Fujii
author_facet Benchi Zhao
Keisuke Fujii
author_sort Benchi Zhao
collection DOAJ
description Estimating the expectation value of a Hamiltonian and performing a Hamiltonian simulation are two fundamental tasks in quantum computation, with their efficiency heavily dependent on the Pauli norm of the Hamiltonian, which sums the absolute values of its Pauli coefficients. In this work, we propose a variational quantum algorithm called variational quantum Hamiltonian engineering (VQHE) to minimize the Pauli norm of a Hamiltonian, thereby reducing the overhead for expectation value estimation and Hamiltonian simulation. We first develop a theoretical framework that transforms the Pauli norm minimization problem into a vector l_{1}-norm minimization problem. We then design an appropriate cost function and employ parametrized quantum circuits to variationally minimize this cost function. Numerical experiments demonstrate the effectiveness of VQHE in reducing the Pauli norm for both the Ising Hamiltonian and molecular Hamiltonians. Furthermore, we show that VQHE is compatible with grouping strategies, enabling further reductions in measurement complexity for expectation value estimation. Our results highlight the potential of VQHE to enhance the efficiency of quantum algorithms in near-term quantum devices, offering a promising approach for practical quantum computing applications.
format Article
id doaj-art-dc3f8c371842401f85eb3f6bb97c608f
institution OA Journals
issn 2643-1564
language English
publishDate 2025-05-01
publisher American Physical Society
record_format Article
series Physical Review Research
spelling doaj-art-dc3f8c371842401f85eb3f6bb97c608f2025-08-20T02:16:06ZengAmerican Physical SocietyPhysical Review Research2643-15642025-05-017202312310.1103/PhysRevResearch.7.023123Variational quantum Hamiltonian engineeringBenchi ZhaoKeisuke FujiiEstimating the expectation value of a Hamiltonian and performing a Hamiltonian simulation are two fundamental tasks in quantum computation, with their efficiency heavily dependent on the Pauli norm of the Hamiltonian, which sums the absolute values of its Pauli coefficients. In this work, we propose a variational quantum algorithm called variational quantum Hamiltonian engineering (VQHE) to minimize the Pauli norm of a Hamiltonian, thereby reducing the overhead for expectation value estimation and Hamiltonian simulation. We first develop a theoretical framework that transforms the Pauli norm minimization problem into a vector l_{1}-norm minimization problem. We then design an appropriate cost function and employ parametrized quantum circuits to variationally minimize this cost function. Numerical experiments demonstrate the effectiveness of VQHE in reducing the Pauli norm for both the Ising Hamiltonian and molecular Hamiltonians. Furthermore, we show that VQHE is compatible with grouping strategies, enabling further reductions in measurement complexity for expectation value estimation. Our results highlight the potential of VQHE to enhance the efficiency of quantum algorithms in near-term quantum devices, offering a promising approach for practical quantum computing applications.http://doi.org/10.1103/PhysRevResearch.7.023123
spellingShingle Benchi Zhao
Keisuke Fujii
Variational quantum Hamiltonian engineering
Physical Review Research
title Variational quantum Hamiltonian engineering
title_full Variational quantum Hamiltonian engineering
title_fullStr Variational quantum Hamiltonian engineering
title_full_unstemmed Variational quantum Hamiltonian engineering
title_short Variational quantum Hamiltonian engineering
title_sort variational quantum hamiltonian engineering
url http://doi.org/10.1103/PhysRevResearch.7.023123
work_keys_str_mv AT benchizhao variationalquantumhamiltonianengineering
AT keisukefujii variationalquantumhamiltonianengineering