The equivalence between canonical and grand canonical constraints near a random fixed point in a critical disordered system is confirmed by means of Monte Carlo simulations. The slow approach to the asymptotic distribution for canonical averaging given by the ${L}^{(\ensuremath{\alpha}/\ensuremath{\nu}{)}_{\mathrm{random}}}$ term is overcome by simulating long range correlated diluted Ising systems with $(\ensuremath{\alpha}/\ensuremath{\nu}{)}_{\mathrm{random}}=(a\ensuremath{-}d)$ for the particular values $a=2$ (linear defects) and $d=3$ (three dimensional systems).The equivalence between canonical and grand canonical constraints near a random fixed point in a critical disordered system is confirmed by means of Monte Carlo simulations. The slow approach to the asymptotic distribution for canonical averaging given by the ${L}^{(\ensuremath{\alpha}/\ensuremath{\nu}{)}_{\mathrm{random}}}$ term is overcome by simulating long range correlated diluted Ising systems with $(\ensuremath{\alpha}/\ensuremath{\nu}{)}_{\mathrm{random}}=(a\ensuremath{-}d)$ for the particular values $a=2$ (linear defects) and $d=3$ (three dimensional systems).

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsMay 17, 20027 citations

Frozen Gaussian sampling algorithms for simulating Markovian open quantum systems in the semiclassical regime

Limin Xu, Zhen Huang, Zhennan Zhou

Simulating Markovian open quantum systems in the semiclassical regime poses a grand challenge for computational physics, as the highly oscillatory nature of the dynamics imposes prohibitive resolution requirements on traditional grid-based methods. To overcome this barrier, this paper introduces an efficient Frozen Gaussian Sampling (FGS) algorithm based on the Wigner-Fokker-Planck phase-space formulation. The proposed algorithm exhibits two transformative advantages. First, for the computation of physical observables, its sampling error is independent of the semiclassical parameter $\varepsilon$ , thus fundamentally breaking the prohibitive computational scaling faced by grid methods in the semiclassical limit. Second, its mesh-free nature entirely eliminates the boundary-induced instabilities that constrain long-time grid-based simulations. Leveraging these capabilities, the FGS algorithm serves as a powerful investigatory tool for exploring the long-time behavior of open quantum systems. Specifically, we provide compelling numerical evidence for the existence of steady states in strongly non-harmonic potentials-a regime where rigorous analytical results are currently lacking.Simulating Markovian open quantum systems in the semiclassical regime poses a grand challenge for computational physics, as the highly oscillatory nature of the dynamics imposes prohibitive resolution requirements on traditional grid-based methods. To overcome this barrier, this paper introduces an efficient Frozen Gaussian Sampling (FGS) algorithm based on the Wigner-Fokker-Planck phase-space formulation. The proposed algorithm exhibits two transformative advantages. First, for the computation of physical observables, its sampling error is independent of the semiclassical parameter $\varepsilon$, thus fundamentally breaking the prohibitive computational scaling faced by grid methods in the semiclassical limit. Second, its mesh-free nature entirely eliminates the boundary-induced instabilities that constrain long-time grid-based simulations. Leveraging these capabilities, the FGS algorithm serves as a powerful investigatory tool for exploring the long-time behavior of open quantum systems. Specifically, we provide compelling numerical evidence for the existence of steady states in strongly non-harmonic potentials-a regime where rigorous analytical results are currently lacking.

quant-pharXiv:2512.14015Dec 17, 20250 citations

Improving quantum computer simulations

G. W. Arnold, Binh Trieu, Hans A. De Raedt +3 more

Jan 1, 20081 citation

A perspective on quantum simulations

E. Solano

Proceedings of the International School of Physics "Enrico Fermi"Jan 1, 20180 citations

Theoretical Perspectives of Quantum Simulation

Changhyoup LEE, Changsuk Noh, Jaeyoon Cho

Simulation is a ubiquitous tool for understanding and predicting the behavior of complex systems, ranging from those in natural sciences to those in social studies. When it comes to quantum systems, however, conventional simulation methods encounter fundamental limitations imposed by quantum physics. To overcome this challenge, the concept of using quantum systems to simulate other quantum systems, namely, quantum simulation, has emerged as an indispensable paradigm. In this special issue, we explore the underlying concepts and theoretical frameworks that drive this rapidly developing field.Simulation is a ubiquitous tool for understanding and predicting the behavior of complex systems, ranging from those in natural sciences to those in social studies. When it comes to quantum systems, however, conventional simulation methods encounter fundamental limitations imposed by quantum physics. To overcome this challenge, the concept of using quantum systems to simulate other quantum systems, namely, quantum simulation, has emerged as an indispensable paradigm. In this special issue, we explore the underlying concepts and theoretical frameworks that drive this rapidly developing field.

Physics and High TechnologyJun 26, 20250 citations

a=2

(linear defects) and

d=3

(three dimensional systems).

\varepsilon

, thus fundamentally breaking the prohibitive computational scaling faced by grid methods in the semiclassical limit. Second, its mesh-free nature entirely eliminates the boundary-induced instabilities that constrain long-time grid-based simulations. Leveraging these capabilities, the FGS algorithm serves as a powerful investigatory tool for exploring the long-time behavior of open quantum systems. Specifically, we provide compelling numerical evidence for the existence of steady states in strongly non-harmonic potentials-a regime where rigorous analytical results are currently lacking.