Related papers: A Quantum Algorithm for Dynamic Mode Decomposition…
This work studies the variational quantum eigensolver algorithm, designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. Methods of reducing the number of required qubit…
Non-Markovian dynamics is ubiquitous in both quantum and classical systems, but the numerical computation of the time-delay dynamics is demanding. In this work, we propose an efficient quantum algorithm for solving linear distributed delay…
We investigate time complexities of finite difference methods for solving the high-dimensional linear heat equation, the high-dimensional linear hyperbolic equation and the multiscale hyperbolic heat system with quantum algorithms (hence…
We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how to obtain the corresponding eigenstate? The algorithm is based on the resonance phenomena. For a…
We investigate the quantum algorithms for dynamic programming by Ambainis et al. (SODA'19). While giving provable complexity speedups and applicable to a variety of NP-hard problems, these algorithms have a notable drawback: they require a…
The theoretical investigation of non-adiabatic processes is hampered by the complexity of the coupled electron-nuclear dynamics beyond the Born-Oppenheimer approximation. Classically, the simulation of such reactions is limited by the…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
We introduce a variational hybrid classical-quantum algorithm to simulate the Lindblad master equation and its adjoint for time-evolving Markovian open quantum systems and quantum observables. Our method is based on a direct representation…
We present an algorithm for measurement of $k$-local operators in a quantum state, which scales logarithmically both in the system size and the output accuracy. The key ingredients of the algorithm are a digital representation of the…
Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems…
To approximate solutions of complex nonlinear partial differential equations remains a computational challenge, especially for sets of equations relevant in industry, such as Euler or Navier-Stokes equations. Even the most sophisticated…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
We propose quantum methods for solving differential equations that are based on a gradual improvement of the solution via an iterative process, and are targeted at applications in fluid dynamics. First, we implement the Jacobi iteration on…
Using quantum algorithms to simulate complex physical processes and correlations in quantum matter has been a major direction of quantum computing research, towards the promise of a quantum advantage over classical approaches. In this work…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…
We propose a numerical homogenization method for scalar linear partial differential equations with rough coefficients, that integrates classical coarse-scale solvers with quantum subroutines for fine-scale corrections. Inspired by the…
As quantum hardware rapidly advances toward the early fault-tolerant era, a key challenge is to develop quantum algorithms that are not only theoretically sound but also hardware-friendly on near-term devices. In this work, we propose a…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
We present a polynomial-time quantum algorithm for obtaining the energy spectrum of a physical system, i.e. the differences between the eigenvalues of the system's Hamiltonian, provided that the spectrum of interest contains at most a…
This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…