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We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a…

While rigorous quantum dynamical simulations of many-body systems are extremely difficult (or impossible) due to the exponential scaling with dimensionality, corresponding classical simulations completely ignore quantum effects.…

The past few years have witnessed the concrete and fast spreading of quantum technologies for practical computation and simulation. In particular, quantum computing platforms based on either trapped ions or superconducting qubits have…

Quantum simulation can help us study poorly understood topics such as high-temperature superconductivity and drug design. However, existing quantum simulation algorithms for current quantum computers often have drawbacks that impede their…

Tracking the behaviour of stochastic systems is a crucial task in the statistical sciences. It has recently been shown that quantum models can faithfully simulate such processes whilst retaining less information about the past behaviour of…

Quantum computing promises the possibility of studying the real-time dynamics of nonperturbative quantum field theories while avoiding the sign problem that obstructs conventional lattice approaches. Current and near-future quantum devices…

In recent years quantum simulation has made great strides culminating in experiments that operate in a regime that existing supercomputers cannot easily simulate. Although this raises the possibility that special purpose analog quantum…

Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient…

We present a recursive formula for the computation of the static effective Hamiltonian of a system under a fast-oscillating drive. Our analytical result is well-suited to symbolic calculations performed by a computer and can be implemented…

Genetic algorithms are heuristic optimization techniques inspired by Darwinian evolution. Quantum computation is a new computational paradigm which exploits quantum resources to speed up information processing tasks. Therefore, it is…

Quantum coherence allows for reduced-memory simulators of classical processes. Using recent results in single-shot quantum thermodynamics, we derive a minimal work cost rate for quantum simulators that is quasistatically attainable in the…

In computer simulations, quantum delocalization of atomic nuclei can be modeled making use of the Path Integral (PI) formulation of quantum statistical mechanics. This approach, however, comes with a large computational cost. By restricting…

Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been…

As a milestone for general-purpose computing machines, we demonstrate that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. Moreover, on noisy devices without error correction, we…

The computational complexity of simulating the dynamics of physical quantum systems is a central question at the interface of quantum physics and computer science. In this work, we address this question for the simulation of exponentially…

Quantum computing promises to revolutionize several scientific and technological domains through fundamentally new ways of processing information. Among its most compelling applications is digital quantum simulation, where quantum computers…

Recently, the entanglement dynamics of two harmonic oscillators initially prepared in a separable-coherent state was demonstrated to offer a pathway for prime number identification. This article presents a generalized approach and outlines…

Digital-analog is a quantum computational paradigm that employs the natural interaction Hamiltonian of a system as the entangling resource, combined with single qubit gates, to implement universal quantum operations. As in the case of its…

We show on the example of the Arnold cat map that classical chaotic systems can be simulated with exponential efficiency on a quantum computer. Although classical computer errors grow exponentially with time, the quantum algorithm with…

Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement…