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Fermionic quantum processors are a promising platform for quantum simulation of correlated fermionic matter. In this work, we study a hardware-efficient protocol for measuring complex expectation values of the time-evolution operator,…
Phase-space representations are of increasing importance as a viable and successful means to study exponentially complex quantum many-body systems from first principles. This review traces the background of these methods, starting from the…
We recently showed that the Dephasing Representation (DR) provides an efficient tool for computing ultrafast electronic spectra and that further acceleration is possible with cellularization [M. \v{S}ulc and J. Van\'i\v{c}ek, Mol. Phys.…
Simulating the real-time dynamics of lattice gauge theories, underlying the Standard Model of particle physics, is a notoriously difficult problem where quantum simulators can provide a practical advantage over classical approaches. In this…
We describe a numerical method which allows us to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent…
We introduce a new class of quantum Monte Carlo methods, based on a Gaussian quantum operator representation of fermionic states. The methods enable first-principles dynamical or equilibrium calculations in many-body Fermi systems, and,…
We represent the method of dynamic diffusion for the approximate solution of Shroedinger equation with decoherence. Decoherence shows as the divergency of exact solution from the dynamics of diffusion swarm, which arises when the total…
Computing dynamical properties of strongly interacting quantum many-body systems poses a major challenge to theoretical approaches. Usually, one has to resort to numerical analytic continuation of results on imaginary frequencies, which is…
We develop and analyze a numerical method for stochastic time-fractional diffusion driven by additive fractionally integrated Gaussian noise. The model involves two nonlocal terms in time, i.e., a Caputo fractional derivative of order…
Lattice gauge theories describe fundamental phenomena in nature, but calculating their real-time dynamics on classical computers is notoriously difficult. In a recent publication [Nature 534, 516 (2016)], we proposed and experimentally…
We present a neural flow wavefunction, Gauge-Fermion FlowNet, and use it to simulate 2+1D lattice compact quantum electrodynamics with finite density dynamical fermions. The gauge field is represented by a neural network which parameterizes…
We propose efficient algorithms for classically simulating fermionic linear optics operations applied to non-Gaussian initial states. By gadget constructions, this provides algorithms for fermionic linear optics with non-Gaussian…
Quantum simulation of synthetic dynamic gauge field has attracted much attentions in recent years. There are two traditional ways to simulate gauge theories. One is to directly simulate the full Hamiltonian of gauge theories with local…
Many-mode interacting Bose gases (1D,2D,3D) are simulated from first principles. The model uses a second-quantized Hamiltonian with two-particle interactions (possibly ranged), external potential, and interactions with an environment, with…
First principles simulations of the quantum dynamics of interacting Bose gases using the stochastic gauge representation are analyzed. In a companion paper, we showed how the positive P representation can be applied to these problems using…
Simulating quantum many-body systems is a highly demanding task since the required resources grow exponentially with the dimension of the system. In the case of fermionic systems, this is even harder since nonlocal interactions emerge due…
A variety of simulation methodologies have been used for modeling reaction-diffusion dynamics -- including approaches based on Differential Equations (DE), the Stochastic Simulation Algorithm (SSA), Brownian Dynamics (BD), Green's Function…
Simulating quantum dynamics is one of the most important applications of quantum computers. Traditional approaches for quantum simulation involve preparing the full evolved state of the system and then measuring some physical quantity.…
To overcome the fast oscillatory behavior of correlation functions for extracting scattering phase shift in real-time quantum simulations encountered in Ref.\cite{Guo:2026qkx}, we propose and test two solutions in the present work. One is…
We review recent developments in the theory of quantum dynamics in ultra-cold atomic physics, including exact techniques, but focusing on methods based on phase-space mappings that are appli- cable when the complexity becomes exponentially…