Related papers: First-Order Trotter Error from a Second-Order Pers…
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…
Product formulae are a popular class of digital quantum simulation algorithms due to their conceptual simplicity, low overhead, and performance which often exceeds theoretical expectations. Recently, Richardson extrapolation and polynomial…
The Trotter decomposition is a basic approach to Hamiltonian simulation (digital quantum simulation). The first-order Trotter decomposition is the simplest one, whose deviations from target dynamics are of the first order of a small…
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…
Trotter-Suzuki decompositions are frequently used in the quantum simulation of quantum chemistry. They transform the evolution operator into a form implementable on a quantum device, while incurring an error---the Trotter error. The Trotter…
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…
In previous work, we proposed a method for leveraging efficient classical simulation algorithms to aid in the analysis of large-scale fault tolerant circuits implemented on hypothetical quantum information processors. Here, we extend those…
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…
A complex but important challenge in understanding quantum mechanical phenomena is the simulation of quantum many-body dynamics. Although quantum computers offer significant potential to accelerate these simulations, their practical…
Analog quantum simulation is emerging as a powerful tool for uncovering classically unreachable physics such as many-body real-time dynamics. A complete quantification of uncertainties is necessary in order to make precise predictions using…
Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that, compared to…
The Schwinger model, which describes lattice quantum electrodynamics in $1+1$ space-time dimensions, provides a valuable framework to investigate fundamental aspects of quantum field theory, and a stepping stone towards non-Abelian gauge…
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…
Variational quantum algorithms have become the de facto model for current quantum computations. A prominent example of such algorithms -- the quantum approximate optimization algorithm (QAOA) -- was originally designed for combinatorial…
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…
We propose a quantum algorithm to simulate the dynamics in quantum chemistry problems. It is based on adding fresh qubits at each Trotter step, which enables a simpler implementation of the dynamics in the extended system. After each step,…
Understanding the impact of gate errors on quantum circuits is crucial to determining the potential applications of quantum computers, especially in the absence of large-scale error-corrected hardware. We put forward analytical arguments,…
In designing quantum control, it is generally required to simulate the controlled system evolution with a classical computer. However, computing the time evolution operator can be quite resource-consuming since the total Hamiltonian is…
Trotterization-based, iterative approaches to quantum simulation are restricted to simulation times less than the coherence time of the quantum computer, which limits their utility in the near term. Here, we present a hybrid…
Simulating the dynamic evolutions of physical and molecular systems in a quantum computer is of fundamental interest in many applications. Its implementation requires efficient quantum simulation algorithms. The Lie-Trotter-Suzuki…