Constrained Quantum Imaginary Time in Krylov Space
Abstract
We introduce constrained quantum imaginary time evolution (CQITE), extending quantum imaginary time evolution (QITE) to constrained-search dynamics for ground-state preparation with prescribed expectation-value constraints. A central challenge in practical QITE is constructing a compact unitary representation of the imaginary-time evolution while maintaining accuracy and controlling the approximation error. We resolve this challenge by deriving an exact characterization of the imaginary-time evolution from the Krylov space generated by repeated applications of the Hamiltonian to the initial state. This characterization induces a hierarchy of operator directions expressed through nested anti-commutators. Truncating the hierarchy produces a systematic static operator pool, with polynomial size in the system size at any fixed truncation order. The resulting construction provides a principled route to compact unitary approximations of imaginary-time dynamics. Numerical tests on spin models show close agreement with exact constrained imaginary-time evolution and small constraint deviations, while a fermionic example yields energies close to the analytic constrained-search reference.
Related
- Krylov Complexity and Quantum Many-body Scars in Non-Hermitian Kinetically Constrained Models
- Mirror subspace diagonalization: a real-time quantum Krylov algorithm with near-optimal sampling cost
- Imaginary-time-enhanced feedback-based quantum algorithms for ground-state preparation
- Quantum Imaginary Time Evolution on an Infinite 1D Chain
- Quantum chaos and late-time equipartition of symmetry-resolved Krylov complexity
BibTeX
@misc{cuomo2026constrained,
title = {{Constrained Quantum Imaginary Time in Krylov Space}},
author = {Daniele Cuomo and Luis Cort Barrada and Michał Studziński and Robert van Leeuwen},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07800},
eprint = {2611.07800},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07800},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Constrained Quantum Imaginary Time in Krylov Space
AU - Daniele Cuomo
AU - Luis Cort Barrada
AU - Michał Studziński
AU - Robert van Leeuwen
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07800
UR - https://arxiv.org/abs/2611.07800
AB - We introduce constrained quantum imaginary time evolution (CQITE), extending quantum imaginary time evolution (QITE) to constrained-search dynamics for ground-state preparation with prescribed expectation-value constraints. A central challenge in practical QITE is constructing a compact unitary representation of the imaginary-time evolution while maintaining accuracy and controlling the approximation error. We resolve this challenge by deriving an exact characterization of the imaginary-time evolution from the Krylov space generated by repeated applications of the Hamiltonian to the initial state. This characterization induces a hierarchy of operator directions expressed through nested anti-commutators. Truncating the hierarchy produces a systematic static operator pool, with polynomial size in the system size at any fixed truncation order. The resulting construction provides a principled route to compact unitary approximations of imaginary-time dynamics. Numerical tests on spin models show close agreement with exact constrained imaginary-time evolution and small constraint deviations, while a fermionic example yields energies close to the analytic constrained-search reference.
ER -