Related papers: The first-order Trotter decomposition in the dynam…
Efficiently simulating many-body quantum systems with Coulomb interactions is a fundamental question in quantum physics, quantum chemistry, and quantum computing, yet it presents unique challenges: the Hamiltonian is an unbounded operator…
Solving the electronic structure problem via unitary evolution of the electronic Hamiltonian is one of the promising applications of digital quantum computers. One of the practical strategies to implement the unitary evolution is via…
The accuracy of quantum dynamics simulation is usually measured by the error of the unitary evolution operator in the operator norm, which in turn depends on certain norm of the Hamiltonian. For unbounded operators, after suitable…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
Trotter errors in digitized quantum dynamics arise from approximating time-ordered evolution under noncommuting Hamiltonian terms with a product formula. In the adiabatic regime, such errors are known to exhibit long-time self-healing…
Digital quantum simulation of many-body dynamics relies on Trotterization to decompose the target time evolution into elementary quantum gates operating at a fixed equidistant time discretization. Recent advances have outlined protocols…
Efficient error estimates for the Trotter product formula are central in quantum computing, mathematical physics, and numerical simulations. However, the Trotter error's dependency on the input state and its application to unbounded…
The Trotter-Suzuki decomposition is an important tool for the simulation and control of physical systems. We provide evidence for the stability of the Trotter-Suzuki decomposition. We model the error in the decomposition and determine…
Compiling time-evolution operators of the form $U(t)=e^{-iHt}$ into hardware-native gate sequences is a central bottleneck for digital quantum simulation on noisy intermediate-scale quantum (NISQ) devices. Generic transpilation treats…
We derive higher-order error bounds with small prefactors for a general Trotter product formula, generalizing a result of Childs et al. [Phys. Rev. X 11, 011020 (2021)]. We then apply these bounds to the real-time quantum time evolution…
A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…
We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting commutativity of the target Hamiltonian, sparsity of interactions, and…
The potential of employing higher orders of the Trotter-Suzuki decomposition of the evolution operator for more effective simulations of quantum systems on a noisy quantum computer is explored. By examining the transverse-field Ising model…
Trotter and linear-combination-of-unitary (LCU) are two popular Hamiltonian simulation methods. We propose Hamiltonian simulation algorithms using LCU to compensate Trotter error, which enjoy both of their advantages. By adding few gates…
Accurately simulating long-time dynamics of many-body systems is a challenge in both classical and quantum computing due to the accumulation of Trotter errors. While low-order Trotter-Suzuki decompositions are straightforward to implement,…
Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably…
We develop a general technique for proving convergence of repeated quantum interactions to the solution of a quantum stochastic differential equation. The wide applicability of the method is illustrated in a variety of examples. Our main…
Efficient simulation of many-body quantum systems is central to advances in physics, chemistry, and quantum computing, with a key question being whether the simulation cost scales polynomially with the system size. In this work, we analyze…
We study several aspects of the regular deformations of completely integrable systems. Namely, we prove the existence of a Hamiltonian normal form for these deformations and we show the necessary and sufficient conditions a perturbation has…
In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the…