Related papers: Time-dependent Hamiltonian Simulation via Magnus E…
Reliable quantum technology requires knowledge of the dynamics governing the underlying system. This problem of characterizing and benchmarking quantum devices or experiments in continuous time is referred to as the Hamiltonian learning…
The Floquet-Magnus expansion is a widely used tool to derive effective descriptions of time-periodic quantum systems by approximating their dynamics with a time-independent Hamiltonian. However, its standard formulation is, strictly…
We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement nor classical communication. We characterize notions of simulation, and proceed to focus on…
The quantum circuit model is the de-facto way of designing quantum algorithms. Yet any level of abstraction away from the underlying hardware incurs overhead. In the era of near-term, noisy, intermediate-scale quantum (NISQ) hardware with…
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical tradeoff between improved accuracy for finer…
Hamiltonian simulation is one of the most important problems in the field of quantum computing. There have been extended efforts on designing algorithms for faster simulation, and the evolution time $T$ for the simulation turns out to…
A novel expansion of the evolution operator associated with a -- in general, time-dependent -- perturbed quantum Hamiltonian is presented. It is shown that it has a wide range of possible realizations that can be fitted according to…
Non-smooth optimization models play a fundamental role in various disciplines, including engineering, science, management, and finance. However, classical algorithms for solving such models often struggle with convergence speed,…
We present a time-dependent perturbative approach adapted to the treatment of intense pulsed interactions. We show there is a freedom in choosing secular terms and use it to optimize the accuracy of the approximation. We apply this…
We propose time-dependent Darboux (supersymmetric) transformations that provide a scheme for the calculation of explicitly time-dependent solvable non-Hermitian partner Hamiltonians. Together with two Hermitian Hamilitonians the latter form…
The problem of simulating sparse Hamiltonians on quantum computers is well studied. The evolution of a sparse N x N Hamiltonian H for time t can be simulated using O(||Ht||poly(log N)) operations, which is essentially optimal due to a…
The problem of finding superintegrable Hamiltonians and their integrals of motion can be reduced to solving a series of compatibility equations that result from the overdetermination of the commutator or Poisson bracket relations. The…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series…
We consider the problem of learning the Hamiltonian of a quantum system from estimates of Gibbs-state expectation values. Various methods for achieving this task were proposed recently, both from a practical and theoretical point of view.…
The controls enacting logical operations on quantum systems are described by time-dependent Hamiltonians that often include rapid oscillations. In order to accurately capture the resulting time dynamics in numerical simulations, a very…
We consider the manifold of all quantum many-body states that can be generated by arbitrary time-dependent local Hamiltonians in a time that scales polynomially in the system size, and show that it occupies an exponentially small volume in…
We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a…
This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
With rapid advancements in machine learning, first-order algorithms have emerged as the backbone of modern optimization techniques, owing to their computational efficiency and low memory requirements. Recently, the connection between…