Related papers: A Rigorous Introduction to Hamiltonian Simulation …
Hamiltonian simulation is known to be one of the fundamental building blocks of a variety of quantum algorithms such as its most immediate application, that of simulating many-body systems to extract their physical properties. In this work,…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Quantum simulation has wide applications in quantum chemistry and physics. Recently, scientists have begun exploring the use of randomized methods for accelerating quantum simulation. Among them, a simple and powerful technique, called…
The product formula, commonly known as Trotter decomposition, is a central tool for digital quantum simulation, whose performance depends critically on how the Hamiltonian is partitioned into tractable blocks. Standard decompositions…
Advancing quantum technologies requires precise and robust coherent control of quantum systems. Robust higher-order Hamiltonian engineering is essential for high-precision control and for accessing effective dynamics absent at zeroth order.…
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…
Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near-term are the simplest, which use the Trotter…
Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…
Path integral-based simulation methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical…
We introduce a hybrid classical-quantum algorithm for simulating a Hamiltonian of the form $H= \sum_{i=1}^K H_i = \sum_{i=1}^K H_{i_1} \otimes H_{i_2} \otimes \cdots \otimes H_{i_M}$. Given that the entries of all $\{ H_{i_1}, H_{i_2} ,…
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…
This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…
In the present article, we review a continual effort on generalization of the Trotter formula to higher-order exponential product formulas. The exponential product formula is a good and useful approximant, particularly because it conserves…
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…
Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum…
Quantum computing promises transformative impacts in simulating Hamiltonian dynamics, essential for studying physical systems inaccessible by classical computing. However, existing compilation techniques for Hamiltonian simulation, in…
We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the…
The well-conditioned multi-product formula (MPF), proposed by [Low, Kliuchnikov, and Wiebe, 2019], is a simple high-order time-independent Hamiltonian simulation algorithm that implements a linear combination of standard product formulas of…
A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in…