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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…

Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes of quantum dynamics, including driven systems, has not been fully established. Here we introduce and study a notion of quantum…

We present a systematic construction of effective Hamiltonians of periodically driven quantum systems. Because of an equivalence between the time dependence of a Hamiltonian and an interaction in its Floquet operator, flow equations, that…

Many-mode Floquet theory [T.-S. Ho, S.-I. Chu, and J. V. Tietz, Chem. Phys. Lett., v. 96, 464 (1983)] is a technique for solving the time-dependent Schr\"odinger equation in the special case of multiple periodic fields, but its limitations…

Known as no fast-forwarding theorem in quantum computing, the simulation time for the Hamiltonian evolution needs to be $O(\|H\| t)$ in the worst case, which essentially states that one can not go across the multiple scales as the…

The inevitable accumulation of errors in near-future quantum devices represents a key obstacle in delivering practical quantum advantages, motivating the development of various quantum error-mitigation methods. Here, we derive fundamental…

We propose a Deep-Picard iteration framework for high-dimensional nonlinear space-time fractional diffusion equations.The method is based on a nonlinear fractional Feynman--Kac fixed-point formulation, which replaces direct discretization…

In order to realize fault-tolerant quantum computation, tight evaluation of error threshold under practical noise models is essential. While non-Clifford noise is ubiquitous in experiments, the error threshold under non-Clifford noise…

We investigate the computational complexity of the Local Hamiltonian (LH) problem and the approximation of the Quantum Partition Function (QPF), two central problems in quantum many-body physics and quantum complexity theory. Both problems…

This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms…

The time evolution of quantum many-body systems is one of the most promising applications for near-term quantum computers. However, the utility of current quantum devices is strongly hampered by the proliferation of hardware errors. The…

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…

The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly…

We present a method for describing the time evolution of many-body controlled quantum systems using matrix product operators (MPOs). Existing techniques for solving the time-dependent Schr\"odinger equation (TDSE) with an MPO Hamiltonian…

We propose a framework to design concurrently a frustration-free quantum many-body Hamiltonian and its numerically exact ground states on a sufficiently large finite-size cluster in one and two dimensions using an elementary matrix product…

Evolutions of local Hamiltonians in short times are expected to remain local and thus limited. In this paper, we validate this intuition by proving some limitations on short-time evolutions of local time-dependent Hamiltonians. We show that…

We consider the use of quantum error detecting codes, together with energy penalties against leaving the codespace, as a method for suppressing environmentally induced errors in Hamiltonian based quantum computation. This method was…

Trotter product formulas are a natural and powerful approach to perform quantum simulation. However, the error analysis of product formulas is challenging, and their cost is often overestimated. It is established that Trotter error can be…

Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…

For a closed system with periodic driving, Floquet theorem tells that the time evolution operator can be written as $ U(t,0)\equiv P(t)e^{\frac{-i}{\hbar}H_F t}$ with $P(t+T)=P(t)$, and $H_F$ is Hermitian and time-independent called Floquet…