Related papers: Full-quantum variational dynamics simulation for t…
We describe a simple quantum algorithm to simulate time-dependent Hamiltonian, extending the methodology of quantum signal processing. The framework achieves optimal scaling up to some factor with respect to other parameters, and nearly…
A numerical scheme for solving the time-evolution of wave functions under the time dependent Kohn-Sham equation has been developed. Since the effective Hamiltonian depends on the wave functions, the wave functions and the effective…
Imaginary time evolution is a powerful tool for studying quantum systems. While it is possible to simulate with a classical computer, the time and memory requirements generally scale exponentially with the system size. Conversely, quantum…
Utilizing quantum computer to investigate quantum chemistry is an important research field nowadays. In addition to the ground-state problems that have been widely studied, the determination of excited-states plays a crucial role in the…
The recent literature on near-term applications for quantum computers contains several examples of the applications of hybrid quantum/classical variational approaches. This methodology can be applied to a variety of optimization problems,…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real-time using higher-order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this…
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process.…
Solving non-Hermitian quantum many-body systems on a quantum computer by minimizing the variational energy is challenging as the energy can be complex. Here, based on energy variance, we propose a variational method for solving the…
Stochastic differential equations (SDEs), which models uncertain phenomena as the time evolution of random variables, are exploited in various fields of natural and social sciences such as finance. Since SDEs rarely admit analytical…
From weather to neural networks, modeling is not only useful for understanding various phenomena, but also has a wide range of potential applications. Although nonlinear differential equations are extremely useful tools in modeling, their…
The optimal control problem for open quantum systems can be formulated as a time-dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the…
The simulation of ion-atom collisions remains a formidable challenge due to the complex interplay between electronic and nuclear degrees of freedom. We present a hybrid quantum-classical computing framework for simulating time-dependent…
Variational quantum eigensolver~(VQE) typically optimizes variational parameters in a quantum circuit to prepare eigenstates for a quantum system. Its applications to many problems may involve a group of Hamiltonians, e.g., Hamiltonian of a…
We propose an explicit algorithm based on the Linear Combination of Hamiltonian Simulations technique to simulate both the advection-diffusion equation and a nonunitary discretized version of the Koopman-von Neumann formulation of nonlinear…
We present a framework for efficient extraction of the viscosity solutions of nonlinear Hamilton-Jacobi equations with convex Hamiltonians. These viscosity solutions play a central role in areas such as front propagation, mean-field games,…
Hamiltonian simulation is a fundamental algorithm in quantum computing that has attracted considerable interest owing to its potential to efficiently solve the governing equations of large-scale classical systems. Exponential speedup…
Quantum simulation is known to be capable of simulating certain dynamical systems in continuous time -- Schrodinger's equations being the most direct and well-known -- more efficiently than classical simulation. Any linear dynamical system…
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly…
The theoretical analysis of the Adiabatic Quantum Computation protocol presents several challenges resulting from the difficulty of simulating, with classical resources, the unitary dynamics of a large quantum device. We present here a…