Abstract Many current and near-future applications of quantum computing utilise parametric families of quantum circuits and variational methods that can suffer from obstacles including non-convergence to the global minimum due to local minima, critical slowing down, or exponential resource scaling. Here we show that quantum imaginary time evolution can overcome these obstacles if the underlying physical system satisfies a set of conditions. This includes many relevant applications such as ground state preparation for local theories in physics or chemistry, combinatorial optimisation problems, or quantum machine learning. In particular, we analyse the quantum imaginary time evolution showing convergence guarantees to the global minimum without critical slowing down and providing a priori estimates on the required evolution time which scale linearly in system size and inverse energy gap. Furthermore, a provided complexity analysis shows that quantum imaginary time evolution can be efficiently compiled into a parametric quantum circuit, finding the optimal parameters included, for a large class of physically relevant problems.Abstract Many current and near-future applications of quantum computing utilise parametric families of quantum circuits and variational methods that can suffer from obstacles including non-convergence to the global minimum due to local minima, critical slowing down, or exponential resource scaling. Here we show that quantum imaginary time evolution can overcome these obstacles if the underlying physical system satisfies a set of conditions. This includes many relevant applications such as ground state preparation for local theories in physics or chemistry, combinatorial optimisation problems, or quantum machine learning. In particular, we analyse the quantum imaginary time evolution showing convergence guarantees to the global minimum without critical slowing down and providing a priori estimates on the required evolution time which scale linearly in system size and inverse energy gap. Furthermore, a provided complexity analysis shows that quantum imaginary time evolution can be efficiently compiled into a parametric quantum circuit, finding the optimal parameters included, for a large class of physically relevant problems.

arXiv:2506.03014Communications PhysicsSep 8, 20260 citations

Probabilistic Approximation of the Evolution Operator

Il'dar Abdullovich Ibragimov, Nataliya V. Smorodina, Михаил Михайлович Фаддеев

Functional Analysis and Its ApplicationsApr 1, 20188 citations

A New Hybrid Quantum Evolutionary Algorithm

Zhen Zhuang

When quantum inspired evolution algorithm(QEA)is used for the optimization of continuous functions with many local optima,it's easy to be trapped into the local deceptive optima.In this paper,a new hybrid quantum evolution algorithm is proposed to overcome the shortcoming of the QEA.The new hybrid QEA combines the merits of classic GA and QEA by using double coding mechanism(classic binary coding and quantum probabilistic coding),and combining the classical crossover and quantum probabilistic search.It not only has the global searching capacity of classic GA,but also improves the local searching capacity of algorithm by using quantum probabilistic search.Experiments on 23 test functions of diverse complexities are implemented and compared with QEA in this paper.The result indicates that the new hybrid QEA is better than QEA in both quality of final result and the convergence rate.When quantum inspired evolution algorithm(QEA)is used for the optimization of continuous functions with many local optima,it's easy to be trapped into the local deceptive optima.In this paper,a new hybrid quantum evolution algorithm is proposed to overcome the shortcoming of the QEA.The new hybrid QEA combines the merits of classic GA and QEA by using double coding mechanism(classic binary coding and quantum probabilistic coding),and combining the classical crossover and quantum probabilistic search.It not only has the global searching capacity of classic GA,but also improves the local searching capacity of algorithm by using quantum probabilistic search.Experiments on 23 test functions of diverse complexities are implemented and compared with QEA in this paper.The result indicates that the new hybrid QEA is better than QEA in both quality of final result and the convergence rate.

Jan 1, 20083 citations

TIME EVOLUTION OF THE PROBABILITY DENSITY

WORLD SCIENTIFIC eBooksMar 1, 19870 citations

Lieb-Robinson Bounds and the Simulation of Time-Evolution of Local Observables in Lattice Systems

Martin Kliesch, Christian Gogolin, Jens Eisert

arXiv:1306.0716Mathematical physics studiesJan 1, 201458 citations

Fast convergence of propagation algorithms for open quantum systems

Giorgio Facelli, Hamza Fawzi, Omar Fawzi +3 more

We establish general conditions for the rapid convergence of propagation algorithms for computing expectation values of local observables in quantum many-body systems, covering both spin and fermionic systems. Our results apply to evolutions that are sufficiently contractive, providing a general mechanism by which contractivity controls the growth generated by local interactions and enables efficient classical simulation. As a first application, we consider noisy time evolution generated by local Hamiltonians on arbitrary interaction graphs. We show that the dynamics can be efficiently simulated when the noise strength $λ$ is sufficiently large compared to the degree of the interaction graph. More generally, for systems with an interaction strength $u$ , our bounds determine a time horizon $t_{\text{max}}$ as a function of the interaction strength $u$ , the noise strength $λ$ , and the interaction structure below which the algorithm is efficient. In the noiseless limit, $λ=0$ , our analysis extends the efficiently simulable time scale from $\log(1/u)$ proved in Facelli, Fawzi, and Fawzi (2026) to $t_{\text{max}} \sim 1/u$ matching the recent improvement by Zhao, Marvian and Tong (2026). As a second application, we apply the same framework to the computation of local observables in Gibbs states of local Hamiltonians. We consider a pseudo-Lindbladian whose steady state is the Gibbs state and show that, at sufficiently high temperature, its propagation algorithm converges rapidly. In particular, for weakly-interacting systems with interaction strength $u$ , our result applies up to inverse temperatures $β\sim\log(1/u)$ .We establish general conditions for the rapid convergence of propagation algorithms for computing expectation values of local observables in quantum many-body systems, covering both spin and fermionic systems. Our results apply to evolutions that are sufficiently contractive, providing a general mechanism by which contractivity controls the growth generated by local interactions and enables efficient classical simulation. As a first application, we consider noisy time evolution generated by local Hamiltonians on arbitrary interaction graphs. We show that the dynamics can be efficiently simulated when the noise strength $λ$ is sufficiently large compared to the degree of the interaction graph. More generally, for systems with an interaction strength $u$, our bounds determine a time horizon $t_{\text{max}}$ as a function of the interaction strength $u$, the noise strength $λ$, and the interaction structure below which the algorithm is efficient. In the noiseless limit, $λ=0$, our analysis extends the efficiently simulable time scale from $\log(1/u)$ proved in Facelli, Fawzi, and Fawzi (2026) to $t_{\text{max}} \sim 1/u$ matching the recent improvement by Zhao, Marvian and Tong (2026). As a second application, we apply the same framework to the computation of local observables in Gibbs states of local Hamiltonians. We consider a pseudo-Lindbladian whose steady state is the Gibbs state and show that, at sufficiently high temperature, its propagation algorithm converges rapidly. In particular, for weakly-interacting systems with interaction strength $u$, our result applies up to inverse temperatures $β\sim\log(1/u)$.

quant-pharXiv:2610.06769Oct 6, 20260 citations

λ

is sufficiently large compared to the degree of the interaction graph. More generally, for systems with an interaction strength

u

, our bounds determine a time horizon

t_{\text{max}}

as a function of the interaction strength

u

, the noise strength

λ

, and the interaction structure below which the algorithm is efficient. In the noiseless limit,

λ=0

, our analysis extends the efficiently simulable time scale from

\log(1/u)

proved in Facelli, Fawzi, and Fawzi (2026) to

t_{\text{max}} \sim 1/u

matching the recent improvement by Zhao, Marvian and Tong (2026). As a second application, we apply the same framework to the computation of local observables in Gibbs states of local Hamiltonians. We consider a pseudo-Lindbladian whose steady state is the Gibbs state and show that, at sufficiently high temperature, its propagation algorithm converges rapidly. In particular, for weakly-interacting systems with interaction strength

u

, our result applies up to inverse temperatures

β\sim\log(1/u)