Efficient Calculation of Equilibrium Correlation Functions
Abstract
A majority of measurable dynamic quantities of a physical system is described as an equilibrium correlation function of the form GAB(t−t') = <A(t)B(t')>, where t' represents the impact time and t represents the response time. Conventional quantum algorithms to compute such quantities via Hamiltonian simulation such as the Hadamard test, variational methods, or linear-response-based algorithms share one feature in common: each time point t−t' is calculated by a different quantum circuit, leading to at least O(Nt) total shots, and at least O(Nt2) total quantum gates. Here, we provide a different approach: utilizing O(log Nt) ancilla qubits to store time as a quantum variable, and effectively parallelize the computation of an equilibrium correlation function by requiring only a single quantum circuit for all time points. We show that this circuit needs to be run only O(log Nt) times, which in total requires O(Nt log Nt) quantum resources in the large system size limits. We prove that this scaling is optimal, and demonstrate our algorithm calculating the Green's function of a one-dimensional spinless Hubbard model.
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BibTeX
@misc{shen2026efficient,
title = {{Efficient Calculation of Equilibrium Correlation Functions}},
author = {Yizhi Shen and Roel Van Beeumen and Wibe A. de Jong and Efekan Kökcü},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40349},
eprint = {2609.40349},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40349},
}
RIS
TY - UNPB
TI - Efficient Calculation of Equilibrium Correlation Functions
AU - Yizhi Shen
AU - Roel Van Beeumen
AU - Wibe A. de Jong
AU - Efekan Kökcü
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40349
UR - https://arxiv.org/abs/2609.40349
AB - A majority of measurable dynamic quantities of a physical system is described as an equilibrium correlation function of the form G_AB(t−t') = <A(t)B(t')>, where t' represents the impact time and t represents the response time. Conventional quantum algorithms to compute such quantities via Hamiltonian simulation such as the Hadamard test, variational methods, or linear-response-based algorithms share one feature in common: each time point t−t' is calculated by a different quantum circuit, leading to at least O(N_t) total shots, and at least O(N_t^2) total quantum gates. Here, we provide a different approach: utilizing O(log N_t) ancilla qubits to store time as a quantum variable, and effectively parallelize the computation of an equilibrium correlation function by requiring only a single quantum circuit for all time points. We show that this circuit needs to be run only O(log N_t) times, which in total requires O(N_t log N_t) quantum resources in the large system size limits. We prove that this scaling is optimal, and demonstrate our algorithm calculating the Green's function of a one-dimensional spinless Hubbard model.
ER -