Quantum algorithm for simulating the wave equation

Costa, Pedro C. S.; Jordan, Stephen P.; Ostrander, Aaron

doi:10.1103/physreva.99.012323

Cited by 116 publications

(75 citation statements)

References 20 publications

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“…And a number of potentially useful applications have been suggested. For example, we can use this matrix inversion algorithm to find approximate solutions to classical linear field equations [41,42,43] (after discretizing the field on a spatial lattice, and applying a suitable preconditioner). This procedure could be used, say, to solve the equations of electromagnetism in a complex three-dimensional geometry, for the purpose of optimizing the performance of an antenna.…”

Section: Quantum Matrix Inversionmentioning

confidence: 99%

Quantum Computing in the NISQ era and beyond

Preskill

2018

Quantum

5,949

3,402

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Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today's classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably. NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away -we should regard it as a significant step toward the more powerful quantum technologies of the future. Quantum technologists should continue to strive for more accurate quantum gates and, eventually, fully fault-tolerant quantum computing.

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Section: Quantum Matrix Inversionmentioning

confidence: 99%

Quantum Computing in the NISQ era and beyond

Preskill

2018

Quantum

5,949

3,402

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“…Since quantum computers can only perform linear unitary operations, it is not clear how nonlinear nonunitary simulations can be performed efficiently. While efficient quantum algorithms for linear ordinary differential equations (ODEs) are known [6,7], an attempt to simulate nonlinear dynamics by measuring the full state at each time step and feeding this information into the next time step would require an exponential amount of resources. The method of Ref.…”

Section: A Motivationmentioning

confidence: 99%

“…It is already known that there are quantum algorithms that can speed up the solution of a linear system of ordinary differential equations [6] and linear partial differential equations, such as wave equations [7]. Can this be extended to nonlinear systems?…”

Section: Complexity Estimatesmentioning

confidence: 99%

Koopman–von Neumann approach to quantum simulation of nonlinear classical dynamics

Joseph

2020

Phys. Rev. Research

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Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman-von Neumann formulation of classical mechanics. The Koopman-von Neumann formulation implies that the conservation of the probability distribution function on phase space, as expressed by the Liouville equation, can be recast as an equivalent Schrödinger equation on Hilbert space with a Hermitian Hamiltonian operator and a unitary propagator. This Schrödinger equation is linear in the momenta because it derives from a constrained Hamiltonian system with twice the classical phase-space dimension. A quantum computer with finite resources can be used to simulate a finite-dimensional approximation of this unitary evolution operator. Quantum simulation of classical dynamics is exponentially more efficient than a deterministic Eulerian discretization of the Liouville equation if the Koopman-von Neumann Hamiltonian is sparse. Utilizing quantum walk techniques for state preparation and amplitude estimation for the calculation of observables leads to a quadratic improvement over classical probabilistic Monte Carlo algorithms.

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“…The initial theoretical success in applying quantum computing to cryptanalysis was quickly replicated in other fields, such as computational chemistry and optimization research. With respect to the electromagnetic field modeling, a quantum algorithm was already developed that simulates the wave equation [102]. That led to the proposal of a quantum based TLM algorithm [103] for the simulations of electromagnetic structures.…”

Section: Prospects Of Quantum Computingmentioning

confidence: 99%

Viability of Numerical Full-Wave Techniques in Telecommunication Channel Modelling

Novak

2020

J. commun. softw. syst. (Online)

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In telecommunication channel modelling the wavelength is small compared to the physical features of interest, therefore deterministic ray tracing techniques provide solutions that are more efficient, faster and still within time constraints than current numerical full-wave techniques. Solving fundamental Maxwell's equations is at the core of computational electrodynamics and best suited for modelling electrical field interactions with physical objects where characteristic dimensions of a computing domain is on the order of a few wavelengths in size. However, extreme communication speeds, wireless access points closer to the user and smaller pico and femto cells will require increased accuracy in predicting and planning wireless signals, testing the accuracy limits of the ray tracing methods. The increased computing capabilities and the demand for better characterization of communication channels that span smaller geographical areas make numerical full-wave techniques attractive alternative even for larger problems. The paper surveys ways of overcoming excessive time requirements of numerical full-wave techniques while providing acceptable channel modelling accuracy for the smallest radio cells and possibly wider. We identify several research paths that could lead to improved channel modelling, including numerical algorithm adaptations for large-scale problems, alternative finite-difference approaches, such as meshless methods, and dedicated parallel hardware, possibly as a realization of a dataflow machine.

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Quantum algorithm for simulating the wave equation

Cited by 116 publications

References 20 publications

Quantum Computing in the NISQ era and beyond

Quantum Computing in the NISQ era and beyond

Koopman–von Neumann approach to quantum simulation of nonlinear classical dynamics

Viability of Numerical Full-Wave Techniques in Telecommunication Channel Modelling

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