Related papers: Simulating Hamiltonian dynamics with a truncated T…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series…
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…
We propose the use of quantum optical systems to perform universal simulation of quantum dynamics. Two specific implementations that require present technology are put forward for illustrative purposes. The first scheme consists of neutral…
Simulating the time evolution of a physical system at quantum mechanical levels of detail -- known as Hamiltonian Simulation (HS) -- is an important and interesting problem across physics and chemistry. For this task, algorithms that run on…
Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications of quantum systems. It is highly desired to design quantum algorithms that can speedup Hamiltonian diagonalization, especially those…
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…
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…
Building on recent advances in quantum algorithms which measure and reuse qubits and in efficient classical simulation leveraging projective measurements, we extend these frameworks to real-time dynamics of quantum many-body systems…
We show that it is possible to uniquely reconstruct a generic many-body local Hamiltonian from a single pair of initial and final states related by time evolution with the Hamiltonian. We then propose a practical version of the protocol…
We examine the problem of simulating lattice gauge theories on a universal quantum computer. The basic strategy of our approach is to transcribe lattice gauge theories in the Hamiltonian formulation into a Hamiltonian involving only Pauli…
This work provides a rigorous and self-contained introduction to numerical methods for Hamiltonian simulation in quantum computing, with a focus on high-order product formulas for efficiently approximating the time evolution of quantum…
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…
Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized…
Characterizing noisy quantum devices requires methods for learning the underlying quantum Hamiltonian which governs their dynamics. Often, such methods compare measurements to simulations of candidate Hamiltonians, a task which requires…
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…
IBM quantum computers are used to simulate the dynamics of small systems of interacting quantum spins. For time-independent systems with fewer than three spins, we compute the exact time evolution at arbitrary times and measure spin…
How well can quantum computers simulate classical dynamical systems? There is increasing effort in developing quantum algorithms to efficiently simulate dynamics beyond Hamiltonian simulation, but so far exact resource estimates are not…
We show that the time evolution of the wave function of a quantum mechanical many particle system can be implemented very efficiently on a quantum computer. The computational cost of such a simulation is comparable to the cost of a…
The most widely used approach for simulating the dynamics of time-dependent Hamiltonians via quantum computation depends on the quantum-classical hybrid variational quantum time evolution algorithm, in which ordinary differential equations…