Quantum algorithm and circuit design solving the Poisson equation

Cao, Yudong; Papageorgiou, Anargyros; Petras, Iasonas; Traub, Joseph F.; Kais, Sabre

doi:10.1088/1367-2630/15/1/013021

Cited by 146 publications

(171 citation statements)

References 41 publications

Supporting

Mentioning

170

Contrasting

Order By: Relevance

“…Recently Cao et al proposed a quantum algorithm for solving the d-dimensional 2 Poisson equation based on the HHL algorithm [11,17]16], which achieves an exponential speedup against any classical algorithms in terms of dimension of the Poisson equation. They presented in principle a scalable quantum circuit for the algorithm, of which the number of qubits and quantum operations used are proportional to, respectively, 1 1 2 22 max{ , log } (log ) d    and 1 1 3 22 max{ , log } (log ) d    within the error of ε.…”

Section: Introductionmentioning

confidence: 99%

Quantum fast Poisson solver: the algorithm and complete and modular circuit design

Wang

et al. 2020

Quantum Inf Process

View full text Add to dashboard Cite

The Poisson equation has applications across many areas of physics and engineering, such as the dynamic process simulation of ocean current. Here we present a quantum Fast Poisson Solver, including the algorithm and the complete and modular circuit design. The algorithm takes the HHL algorithm as the template. The controlled rotation is performed based on the arc cotangent function which is evaluated by the Plouffe's binary expansion method. And the same method is used to compute the cosine function for the eigenvalue approximation in phase estimation. Quantum algorithms for solving square root and reciprocal functions are developed based on the non-restoring digitrecurrence method. These advances make the algorithm's complexity lower and the circuit-design more modular. The number of the qubits and operations used by the circuit are O(dlog 2 (ε -1 )) and O(dlog 3 (ε -1 )), respectively. We demonstrate our circuits on a quantum virtual computing system installed on the Sunway TaihuLight supercomputer. This is an important step toward practical applications of quantum Fast Poisson Solver in the near-term hybrid classical/quantum devices.

show abstract

Section: Introductionmentioning

confidence: 99%

Quantum fast Poisson solver: the algorithm and complete and modular circuit design

Wang

et al. 2020

Quantum Inf Process

View full text Add to dashboard Cite

show abstract

“…However, any physical realization of the algorithm should account for that as well. There are cases where the implementation cost of the exponential is low, for example, when dealing with the Laplacian Δ [51], or other operators that can be diagonalized efficiently, as well as the terms of the electronic Hamiltonian (4) as shown in [17,50].…”

Section: General Considerations For Hamiltonian Simulationmentioning

confidence: 99%

Divide and conquer approach to quantum Hamiltonian simulation

Hadfield

Papageorgiou

2018

New J. Phys.

Self Cite

View full text Add to dashboard Cite

We show a divide and conquer approach for simulating quantum mechanical systems on quantum computers. We can obtain fast simulation algorithms using Hamiltonian structure. Considering a sum of Hamiltonians we split them into groups, simulate each group separately, and combine the partial results. Simulation is customized to take advantage of the properties of each group, and hence yield refined bounds to the overall simulation cost. We illustrate our results using the electronic structure problem of quantum chemistry, where we obtain significantly improved cost estimates under very mild assumptions.

show abstract

“…Further applications have been developed which take advantage of the unique capabilities of quantum computing platforms, e.g. methods for the solution of linear systems of equations [1], numerical gradient estimation [2] and the Poisson equation [3].…”

Section: Introductionmentioning

confidence: 99%

Parallel evaluation of quantum algorithms for computational fluid dynamics

Steijl

Barakos

2018

Computers & Fluids

View full text Add to dashboard Cite

The development and evaluation of quantum computing algorithms for computational fluid dynamics is described along with a detailed analysis of the parallel performance of a quantum computer simulator developed as part of the present work. The quantum computer simulator is used in the evaluation of the quantum algorithms on a conventional parallel computer, and is applied to quantum lattice-based algorithms as well as the Poisson equation. A key result is a demonstration of how the Poisson equation can be solved effeciently on a quantum computer, while its use within a larger algorithm representing a full CFD solver poses a number of significant challenges.

show abstract

Quantum algorithm and circuit design solving the Poisson equation

Cited by 146 publications

References 41 publications

Quantum fast Poisson solver: the algorithm and complete and modular circuit design

Quantum fast Poisson solver: the algorithm and complete and modular circuit design

Divide and conquer approach to quantum Hamiltonian simulation

Parallel evaluation of quantum algorithms for computational fluid dynamics

Contact Info

Product

Resources

About