Related papers: Simulating Time-dependent Hamiltonian Based On Hig…
The time evolution operator plays a crucial role in the precise computation of chemical experiments on quantum computers and holds immense promise for advancing the fields of physical and computer sciences, with applications spanning…
We exactly solve a quantum Fermi accelerator model consisting of a time-independent non-Hermitian Hamiltonian with time-dependent Dirichlet boundary conditions. A Hilbert space for such systems can be defined in two equivalent ways, either…
It is shown how to construct a time-independent Hamiltonian having only one degree of freedom from which an arbitrary linear constant-coefficient evolution equation of any order can be derived.
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…
We study the problem of learning an unknown quantum many-body Hamiltonian $H$ from black-box queries to its time evolution $e^{-\mathrm{i} H t}$. Prior proposals for solving this task either impose some assumptions on $H$, such as its…
In this paper we propose a systematic method to solve the inverse dynamical problem for a quantum system governed by the von Neumann equation: to find a class of Hamiltonians reproducing a prescribed time evolution of a pure or mixed state…
We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body…
Chau et al. [New J. Phys. 20, 073003 (2018)] presented a new and straight-forward derivation of a fourth-order approximation '$U_7$' of the time-evolution operator and hinted at its potential value as a symplectic integrator. $U_7$ is based…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
Variational compression can significantly lower implementation overheads for encoding the time evolution of Hamiltonians into quantum circuits. However, they usually lack global convergence guarantees and well-established scaling behavior.…
We propose an approach to factorize the time-evolution operator of a quantum system through a (finite) sequence of elementary operations that are time-ordered. Our proposal borrows from previous approaches based on Lie algebra techniques…
We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation…
A fast and stable method is formulated to compute the time evolution of a wavefunction by numerically solving the time-dependent Schr{\"o}dinger equation. This method is a real space/real time evolution method implemented by several…
The dynamics of classical and quantum systems which are driven by a high frequency ($\omega$) field is investigated. For classical systems the motion is separated into a slow part and a fast part. The motion for the slow part is computed…
An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the…
Many significant quantum physical systems are characterized by Hamiltonians expressible as a linear combination of time-independent generators of a closed Lie algebra, $\hat{H}(t)=\sum_{l=1}^{L}\eta_{l}(t)\hat{g}_{l}$. The Wei-Norman method…
In this paper, we introduce classically time-controlled quantum automata or CTQA, which is a reasonable modification of Moore-Crutchfield quantum finite automata that uses time-dependent evolution and a "scheduler" defining how long each…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
We construct a Hamiltonian whose dynamics simulate the dynamics of every other Hamiltonian up to exponentially long times in the system size. The Hamiltonian is time-independent, local, one-dimensional, and translation invariant. As a…
We develop a general optimization strategy for performing a chosen unitary or non-unitary task on an open quantum system. The goal is to design a controlled time-dependent system Hamiltonian by variationally minimizing or maximizing a…