Related papers: Adaptive Trotterization for time-dependent Hamilto…
Digital quantum simulation has broad applications in approximating unitary evolution of Hamiltonians. In practice, many simulation tasks for quantum systems focus on quantum states in the low-energy subspace instead of the entire Hilbert…
Quantum simulation is one of the most promising scientific applications of quantum computers. Due to decoherence and noise in current devices, it is however challenging to perform digital quantum simulation in a regime that is intractable…
We present a quantum computational framework using Hamiltonian Truncation (HT) for simulating real-time scattering processes in $(1+1)$-dimensional scalar $\phi^4$ theory. Unlike traditional lattice discretisation methods, HT approximates…
A higher-order Suzuki-Trotter decomposition or Trotterization can be exploited to mitigate the Trotter error in digital quantum simulation. This work revisits the second-order symmetric Trotterization in terms of the Trotter error, where…
We discuss a general procedure to construct an integrable real-time trotterization of interacting lattice models. As an illustrative example we consider a spin-$1/2$ chain, with continuous time dynamics described by the isotropic ($XXX$)…
Randomized compilation protocols have recently attracted attention as alternatives to traditional deterministic Trotter-Suzuki methods, potentially reducing circuit depth and resource overhead. These protocols determine gate application…
Understanding the intricate quantum spin dynamics of radical pair reactions is crucial for unraveling the underlying nature of chemical processes across diverse scientific domains. In this work, we leverage Trotterization to map coherent…
Quantum computers can efficiently simulate the dynamics of quantum systems. In this paper, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product formula algorithm. We…
We describe methods to construct digital quantum simulation algorithms for quantum spin systems on a regular lattice with local interactions. In addition to tools such as the Trotter-Suzuki expansion and graph coloring, we also discuss the…
We present several improvements to the standard Trotter-Suzuki based algorithms used in the simulation of quantum chemistry on a quantum computer. First, we modify how Jordan-Wigner transformations are implemented to reduce their cost from…
We introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…
Trotterization is one of the central approaches for simulating quantum many-body dynamics on quantum computers or tensor networks. In addition to its simple implementation, recent studies have revealed that its error and cost can be reduced…
Trotter product formulas constitute a cornerstone quantum Hamiltonian simulation technique. However, the efficient implementation of Hamiltonian evolution of nested commutators remains an under explored area. In this work, we construct…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
Hamiltonian formulations of lattice field theories provide access to real-time dynamics, but their simulation is difficult to implement efficiently. Trotter-Suzuki decompositions are at the center of time evolution computation, either on…
Operator scrambling, which governs the spread of quantum information in many-body systems, is a central concept in both condensed matter and high-energy physics. Accurately capturing the emergent properties of these systems remains a…
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…
Digital simulation of quantum dynamics by evaluating the time evolution of a Hamiltonian is the initially proposed application of quantum computing. The large number of quantum gates required for emulating the complete second quantization…
Simulating real-time dynamics under a Hamiltonian is a central goal of quantum information science. While numerous Hamiltonian-simulation quantum algorithms have been proposed, the effects of physical noise have rarely been incorporated…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…