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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…
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…
Large-scale classical simulation of quantum computers is crucial for benchmarking quantum algorithms, establishing boundaries of quantum advantage and exploring heuristic quantum algorithms. We present a full-state vector simulation…
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…
Quantum dynamics can be simulated on a quantum computer by exponentiating elementary terms from the Hamiltonian in a sequential manner. However, such an implementation of Trotter steps has gate complexity depending on the total Hamiltonian…
We present an empirical analysis of the scaling of the minimal quantum circuit depth required for a variational quantum simulation (VQS) method to obtain a solution to the time evolution of a quantum system within a predefined error…
In order to evaluate, validate, and refine the design of new quantum algorithms or quantum computers, researchers and developers need methods to assess their correctness and fidelity. This requires the capabilities of quantum circuit…
Realistic simulation of quantum materials is a central goal of quantum computation. Although quantum processors have advanced rapidly in scale and fidelity, it has remained unclear whether pre-fault-tolerant devices can perform…
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…
We estimate the resource requirements, the total number of physical qubits and computational time, required to compute the ground state energy of a 1-D quantum Transverse Ising Model (TIM) of N spin-1/2 particles, as a function of the…
We report experimental digital quantum simulation of the one-dimensional Fermi-Hubbard model on a superconducting quantum processor at a scale beyond the reach of exact statevector simulation and challenging for state-of-the-art…
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…
The hope of the quantum computing field is that quantum architectures are able to scale up and realize fault-tolerant quantum computing. Due to engineering challenges, such ''cheap'' error correction may be decades away. In the meantime, we…
The quantum simulation of quantum chemistry is a promising application of quantum computers. However, for N molecular orbitals, the $\mathcal{O}(N^4)$ gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes…
We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve…
Fault-tolerant schemes can use error correction to make a quantum computation arbitrarily ac- curate, provided that errors per physical component are smaller than a certain threshold and in- dependent of the computer size. However in…
We investigate the sampling efficiency for the simulations of quantum many-body systems at finite temperatures when initial sampling states are generated by applying Trotter gates to random phase product states (RPPSs). We restrict the…
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…
Digital quantum simulators provide a diversified tool for solving the evolution of quantum systems with complicated Hamiltonians and hold great potential for a wide range of applications. Although much attention is paid to the unitary…
Simulating quantum systems is believed to be one of the first applications for which quantum computers may demonstrate a useful advantage. For many problems in physics, we are interested in studying the evolution of the electron-phonon…