Related papers: Simulating the dynamics of time-dependent Hamilton…

We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…

We present a quantum algorithm for the dynamical simulation of time-dependent Hamiltonians. Our method involves expanding the interaction-picture Hamiltonian as a sum of generalized permutations, which leads to an integral-free Dyson series…

We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians by transitioning to the interaction picture,…

We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…

Compared with time independent Hamiltonians, the dynamics of generic quantum Hamiltonians $H(t)$ are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty…

We present a numerical method to simulate the time evolution, according to a Hamiltonian made of local interactions, of quantum spin chains and systems alike. The efficiency of the scheme depends on the amount of the entanglement involved…

We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…

In this paper, we present a proof-of-concept quantum algorithm for simulating time-dependent Hamiltonian evolution by reducing the problem to simulating a time-independent Hamiltonian in a larger space using a discrete clock Hamiltonian…

We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…

In this paper, we present a method for the Hamiltonian simulation in the context of eigenvalue estimation problems which improves earlier results dealing with Hamiltonian simulation through the truncated Taylor series. In particular, we…

In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…

The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation…

Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterising quantum materials. Recently, a series of quantum algorithms employing block-encoding of Hamiltonians have succeeded in providing…

Efficient simulation of quantum dynamics with time-dependent Hamiltonians is important not only for time-varying systems but also for time-independent Hamiltonians in the interaction picture. Such simulations are more challenging than their…

Non-autonomous dynamical systems appear in a very wide range of interesting applications, both in classical and quantum dynamics, where in the latter case it corresponds to having a time-dependent Hamiltonian. However, the quantum…

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…

Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using…

The implementation of time-evolution operators $U(t)$, called Hamiltonian simulation, is one of the most promising usage of quantum computers. For time-independent Hamiltonians, qubitization has recently established efficient realization of…

We present an efficient quantum algorithm for simulating the dynamics of Markovian open quantum systems. The performance of our algorithm is similar to the previous state-of-the-art quantum algorithm, i.e., it scales linearly in evolution…

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…