Variationally Optimized Imaginary-time Polynomial Filters for Ground State Projection
Abstract
In this work, we develop a variational imaginary-time evolution (ITE) framework based on polynomial filtering, derived from an operator-level action principle, which yields an optimized non-unitary projector expressed as a polynomial in the Hamiltonian. Starting from a single-ancilla, first-order imaginary-time update defined by a Taylor expansion and Trotter-Suzuki (TS) decompositions, we show that replacing these approximations with alternative variational formulas substantially improves both accuracy and stability at larger time steps, leading to up to an order-of-magnitude enhancement in the final success probability. We further derive rigorous error bounds that depend only on static properties of the Hamiltonian, providing practical guidance for selecting the simulation time step. Benchmarks on the transverse-field Ising model demonstrate faster convergence to the ground-state energy and improved robustness compared to standard TS--Taylor ITE, highlighting variational polynomial filtering as a practical route to higher-fidelity ground-state preparation on near-term quantum devices.
Related
- Sampling Noise and Optimized Measurement Distribution in Imaginary-Time Quantum Dynamics Simulations
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- svPITE: A Python package for the state-vector-based probabilistic imaginary-time evolution algorithm
BibTeX
@misc{seifi2026variationally,
title = {{Variationally Optimized Imaginary-time Polynomial Filters for Ground State Projection}},
author = {Bahman Seifi and Ibsal Assi and J. P. F. LeBlanc},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28357},
eprint = {2608.28357},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28357},
note = {CC0},
}
RIS
TY - UNPB
TI - Variationally Optimized Imaginary-time Polynomial Filters for Ground State Projection
AU - Bahman Seifi
AU - Ibsal Assi
AU - J. P. F. LeBlanc
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28357
UR - https://arxiv.org/abs/2608.28357
AB - In this work, we develop a variational imaginary-time evolution (ITE) framework based on polynomial filtering, derived from an operator-level action principle, which yields an optimized non-unitary projector expressed as a polynomial in the Hamiltonian. Starting from a single-ancilla, first-order imaginary-time update defined by a Taylor expansion and Trotter-Suzuki (TS) decompositions, we show that replacing these approximations with alternative variational formulas substantially improves both accuracy and stability at larger time steps, leading to up to an order-of-magnitude enhancement in the final success probability. We further derive rigorous error bounds that depend only on static properties of the Hamiltonian, providing practical guidance for selecting the simulation time step. Benchmarks on the transverse-field Ising model demonstrate faster convergence to the ground-state energy and improved robustness compared to standard TS--Taylor ITE, highlighting variational polynomial filtering as a practical route to higher-fidelity ground-state preparation on near-term quantum devices.
ER -