First-quantized quantum simulation with non-local potentials by matrix-product-state encoding
Abstract
Quantum simulations based on first-quantized approaches can offer lower space and gate complexities than second-quantized approaches. The gate requirements for these simulations can be further reduced by employing pseudopotentials, a technique widely used in classical quantum chemistry calculations to decrease the number of simulated electrons. However, implementing pseudopotentials in quantum circuits remains challenging due to their non-local nature. In this study, we proposed a method to efficiently implement non-local potentials using matrix product state (MPS) encoding. MPS encoding allows us to efficiently implement a Trotter step operator with a circuit depth of O(deg(Vloc) ndeg(Vloc) + 8Lnnatomχ2 + 2n2), where deg(Vloc) is the degree of the polynomial local potential, natom is the number of atoms in the system, L is the maximum number of projector functions across all atoms, and n is the number of qubits used to represent the binary-encoded wave function in one-dimensional space. We demonstrated the effectiveness of this approach by applying it to a model of the ionization of a one-dimensional hydrogen atom driven by an ultrashort laser pulse. Our results showed that MPS encoding significantly reduces the required circuit depth compared to a direct unitary decomposition, providing a pathway for practical first-quantized simulations.
Related
- Encoding universal quantum computation into quantized Berry phases: Hardness results and classical algorithms
- Quantum simulation of wave optics in weakly inhomogeneous media using block encoding
- Quantum lattice Boltzmann method via density-matrix encoding for fluid simulation with wall boundary conditions
- Transformer fault diagnosis using an efficient simulation-driven variational quantum classifier with domain-aware feature encoding
- From sparse quantum-computing data to atomistic simulation with universal machine-learning interatomic potentials
BibTeX
@misc{tsuoka2026firstquantized,
title = {{First-quantized quantum simulation with non-local potentials by matrix-product-state encoding}},
author = {Kazuki Tsuoka and Taichi Kosugi and Masari Watanabe and Hirofumi Nishi and Yu-ichiro Matsushita},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00521},
eprint = {2610.00521},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00521},
}
RIS
TY - UNPB
TI - First-quantized quantum simulation with non-local potentials by matrix-product-state encoding
AU - Kazuki Tsuoka
AU - Taichi Kosugi
AU - Masari Watanabe
AU - Hirofumi Nishi
AU - Yu-ichiro Matsushita
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00521
UR - https://arxiv.org/abs/2610.00521
AB - Quantum simulations based on first-quantized approaches can offer lower space and gate complexities than second-quantized approaches. The gate requirements for these simulations can be further reduced by employing pseudopotentials, a technique widely used in classical quantum chemistry calculations to decrease the number of simulated electrons. However, implementing pseudopotentials in quantum circuits remains challenging due to their non-local nature. In this study, we proposed a method to efficiently implement non-local potentials using matrix product state (MPS) encoding. MPS encoding allows us to efficiently implement a Trotter step operator with a circuit depth of O(deg(V_loc) n^deg(V_loc) + 8Lnn_atomχ^2 + 2n^2), where deg(V_loc) is the degree of the polynomial local potential, n_atom is the number of atoms in the system, L is the maximum number of projector functions across all atoms, and n is the number of qubits used to represent the binary-encoded wave function in one-dimensional space. We demonstrated the effectiveness of this approach by applying it to a model of the ionization of a one-dimensional hydrogen atom driven by an ultrashort laser pulse. Our results showed that MPS encoding significantly reduces the required circuit depth compared to a direct unitary decomposition, providing a pathway for practical first-quantized simulations.
ER -