Related papers: Quantum Algorithm for Simulating the Wave Equation
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…
The simulation of open quantum dynamics on quantum circuits has attracted wide interests recently with a variety of quantum algorithms developed and demonstrated. Among these, one particular design of a unitary-dilation-based quantum…
Estimating the overlap between an approximate wavefunction and a target eigenstate of the system Hamiltonian is essential for the efficiency of quantum phase estimation. In this work, we derive upper and lower bounds on this overlap using…
Quantum simulation is a prominent application of quantum computers. While there is extensive previous work on simulating finite-dimensional systems, less is known about quantum algorithms for real-space dynamics. We conduct a systematic…
Many physical and chemical processes in the condensed phase environment exhibit non-Markovian quantum dynamics. As such simulations are challenging on classical computers, we developed a variational quantum algorithm that is capable of…
We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…
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…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare…
We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The…
Simulating physical systems has been an important application of classical and quantum computers. In this article we present an efficient classical algorithm for simulating time-dependent quantum mechanical Hamiltonians over constant…
Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. Here, we propose a variational quantum algorithm for solving a general evolution equation through…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
We solve the one-dimensional Helmholtz equation in several scenarios using the quantum annealer provided by the D-Wave systems within a pseudospectral scheme, where its solution is encoded into certain set of suitable basis functions. We…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
Quantum simulation is a promising pathway toward practical quantum advantage by simulating large-scale quantum systems. In this work, we propose communication-efficient distributed quantum simulation protocols by exploring three quantum…
In the future, ab initio quantum simulations of heavy ion collisions may become possible with large-scale fault-tolerant quantum computers. We propose a quantum algorithm for studying these collisions by looking at a class of observables…
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…