Sustained growth of quantum circuit complexity in many-body Hamiltonian dynamics
Abstract
The quantum circuit complexity of an evolving many-body quantum system is believed to exhibit a sustained growth, maintained for timescales much longer than the onset of thermalization. Most previous works have focused on models which violate energy conservation, such as random unitary circuits. Here we study generic, local time-independent Hamiltonian dynamics. We unconditionally prove that for generic local Hamiltonians and typical initial product states at high effective temperature, the robust quantum circuit complexity must grow over a very long period of time, attaining an exponentially large value at late times. Our approach relies on two structural properties that we prove rigorously: (i) generic local Hamiltonians satisfy generalized spectral no-resonance conditions of arbitrary order, and (ii) typical high-temperature product states are effectively supported in exponentially many energy eigenstates. These properties have been widely assumed without proof in prior works. As corollaries of this result, we show the late-time state displays robust volume-law entanglement that is irremovable by polynomial-size circuits, and we establish a no fast-forwarding result for generic local Hamiltonians. We also lower bound the complexity of preparing sufficiently large subsystems with local quantum channels, in contrast with sufficiently small thermalizing regions which we show retain low complexity at late times.
Related
- Elementary modal logics and circuit complexity
- Dynamics of Stochastic Hamiltonian systems I - Wong-Zakai Variational integrators
- Hamiltonian dynamics with nonconservative forces on extended phase space: An analytical mechanics derivation
- Hamiltonian Lift of Bures--Wasserstein Covariance Dynamics with a Spectral Floor
- Symplectic filtering of Hamiltonian dynamics with moving sensors
BibTeX
@misc{lee2026sustained,
title = {{Sustained growth of quantum circuit complexity in many-body Hamiltonian dynamics}},
author = {Wonjun Lee and Saúl Pilatowsky-Cameo and Soonwon Choi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26885},
eprint = {2609.26885},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26885},
}
RIS
TY - UNPB
TI - Sustained growth of quantum circuit complexity in many-body Hamiltonian dynamics
AU - Wonjun Lee
AU - Saúl Pilatowsky-Cameo
AU - Soonwon Choi
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.26885
UR - https://arxiv.org/abs/2609.26885
AB - The quantum circuit complexity of an evolving many-body quantum system is believed to exhibit a sustained growth, maintained for timescales much longer than the onset of thermalization. Most previous works have focused on models which violate energy conservation, such as random unitary circuits. Here we study generic, local time-independent Hamiltonian dynamics. We unconditionally prove that for generic local Hamiltonians and typical initial product states at high effective temperature, the robust quantum circuit complexity must grow over a very long period of time, attaining an exponentially large value at late times. Our approach relies on two structural properties that we prove rigorously: (i) generic local Hamiltonians satisfy generalized spectral no-resonance conditions of arbitrary order, and (ii) typical high-temperature product states are effectively supported in exponentially many energy eigenstates. These properties have been widely assumed without proof in prior works. As corollaries of this result, we show the late-time state displays robust volume-law entanglement that is irremovable by polynomial-size circuits, and we establish a no fast-forwarding result for generic local Hamiltonians. We also lower bound the complexity of preparing sufficiently large subsystems with local quantum channels, in contrast with sufficiently small thermalizing regions which we show retain low complexity at late times.
ER -