Related papers: Optimal-order Trotter-Suzuki decomposition for qua…
In this study, we investigate Trotter evolution in the Gross-Neveu and hyperbolic Ising models in two spacetime dimensions, using quantum computers. We identify different sources of errors prevalent in various quantum processing units and…
Universal quantum simulation may provide insights into those many-body systems that cannot be described classically, and that cannot be efficiently simulated with current technology. The Trotter formula, which decomposes a desired unitary…
Suzuki-Trotter decompositions of exponential operators like $\exp(Ht)$ are required in almost every branch of numerical physics. Often the exponent under consideration has to be split into more than two operators $H=\sum_k A_k$, for…
Hamiltonian simulation represents an important module in a large class of quantum algorithms and simulations such as quantum machine learning, quantum linear algebra methods, and modeling for physics, material science and chemistry. One of…
Lie-Trotter-Suzuki decompositions are an efficient way to approximate operator exponentials $\exp(t H)$ when $H$ is a sum of $n$ (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution…
Quantum simulation is a promising way toward practical quantum advantage, but noise in current quantum hardware poses a significant obstacle. We prove that not only the physical error but also the algorithmic error in a single Trotter step…
Quantum simulation is a promising application for quantum computing. Quantum simulation algorithms may require the ability to control the time evolution unitary. Naive techniques to control a unitary can substantially increase the required…
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…
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…
Trotterization is the most common and convenient approximation method for Hamiltonian simulations on digital quantum computers, but estimating its error accurately is computationally difficult for large quantum systems. Here, we develop a…
Hamiltonian simulation, i.e., simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful…
Trotterization is a standard approach for simulating quantum time evolution on quantum computers, where the Hamiltonian is split into local terms and each term is applied in sequence. The order of these terms affects the fidelity of the…
We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…
As present day quantum hardware is limited by various noise mechanisms, quantum advantage can only be reached in the near-term by designing noise-resilient quantum algorithms. In this work, we employ state-of-the-art quantum process…
Simulation of continuous time evolution requires time discretization on both classical and quantum computers. A finer time step improves simulation precision, but it inevitably leads to increased computational efforts. This is particularly…
This work presented a perturbational decomposition method for simulating quantum evolution under the one-dimensional Ising model with both longitudinal and transverse fields. By treating the transverse field terms as perturbations in the…
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…
Digital quantum computers are potentially an ideal platform for simulating open quantum many-body systems beyond the digital classical computers. Many studies have focused on obtaining the ground state by simulating time dynamics or…
Quantum computers open the possibility of performing real-time calculations for quantum field theory scattering processes. We propose to use an index averaging the absolute value of the difference between the accurately calculated Trotter…
We consider the extent to which a Trotterized time evolution implemented on a quantum computer is altered by the presence of decoherence. Given a specific set of assumptions regarding the manner in which noise processes acting on such a…