Related papers: A quantum computing concept for 1-D elastic wave simulation with exponential speedup

A quantum computing concept for 1-D elastic wave simulation with exponential speedup

URL: http://arxiv.org/abs/2312.14747v2
Date: Tue, 7 May 2024 12:27:13 GMT
Title: A quantum computing concept for 1-D elastic wave simulation with exponential speedup
Authors: Malte Schade, Cyrill Boesch, Vaclav Hapla, Andreas Fichtner,
Abstract summary: We present a quantum computing concept for 1-D elastic wave propagation in heterogeneous media. The method rests on a finite-difference approximation, followed by a sparsity-preserving transformation of the discrete elastic wave equation to a Schr"odinger equation. An implementation on an error-free quantum simulator verifies our approach and forms the basis of numerical experiments.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Quantum computing has attracted considerable attention in recent years because it promises speed-ups that conventional supercomputers cannot offer, at least for some applications. Though existing quantum computers are, in most cases, still too small to solve significant problems, their future impact on domain sciences is already being explored now. Within this context, we present a quantum computing concept for 1-D elastic wave propagation in heterogeneous media with two components: a theoretical formulation and an implementation on a real quantum computer. The method rests on a finite-difference approximation, followed by a sparsity-preserving transformation of the discrete elastic wave equation to a Schr\"{o}dinger equation, which can be simulated directly on a gate-based quantum computer. An implementation on an error-free quantum simulator verifies our approach and forms the basis of numerical experiments with small problems on the real quantum computer IBM Brisbane. The latter produce simulation results that qualitatively agree with the error-free version but are contaminated by quantum decoherence and noise effects. Complementing the discrete transformation to the Schr\"{o}dinger equation by a continuous version allows the replacement of finite differences by other spatial discretisation schemes, such as the spectral-element method. Anticipating the emergence of error-corrected quantum chips, an analogy between our method and analyses of coupled mass-spring systems suggests that our quantum computing approach may lead to wave field simulations that run exponentially faster than simulations on classical computers.

Related papers

Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
arXiv Detail & Related papers (2024-08-22T08:21:28Z)
Quantum computing of reacting flows via Hamiltonian simulation [13.377719901871027]
We develop the quantum spectral and finite difference methods for simulating reacting flows in periodic and general conditions. The present quantum computing algorithms offer a one-shot'' solution for a given time without temporal discretization.
arXiv Detail & Related papers (2023-12-13T04:31:49Z)
Characterizing a non-equilibrium phase transition on a quantum computer [0.0]
We use the Quantinuum H1-1 quantum computer to realize a quantum extension of a simple classical disease spreading process. We are able to implement large instances of the model with $73$ sites and up to $72$ circuit layers. This work demonstrates how quantum computers capable of mid-circuit resets, measurements, and conditional logic enable the study of difficult problems in quantum many-body physics.
arXiv Detail & Related papers (2022-09-26T17:59:06Z)
Recompilation-enhanced simulation of electron-phonon dynamics on IBM Quantum computers [62.997667081978825]
We consider the absolute resource cost for gate-based quantum simulation of small electron-phonon systems. We perform experiments on IBM quantum hardware for both weak and strong electron-phonon coupling. Despite significant device noise, through the use of approximate circuit recompilation we obtain electron-phonon dynamics on current quantum computers comparable to exact diagonalisation.
arXiv Detail & Related papers (2022-02-16T19:00:00Z)
Quantum simulation of dissipative collective effects on noisy quantum computers [0.0]
We put forward the first fully quantum simulation of dissipative collective phenomena on a real quantum computer. The quantum simulation is based on the recently introduced multipartite collision model. We implement the algorithm on some IBM quantum computers to simulate superradiance and subradiance between a pair of qubits.
arXiv Detail & Related papers (2022-01-27T15:50:58Z)
Solving hadron structures using the basis light-front quantization approach on quantum computers [0.8726465590483234]
We show that quantum computing can be used to solve for the structure of hadrons governed by strongly-interacting quantum field theory. We present the numerical calculations on simulated quantum devices using the basis light-front quantization approach.
arXiv Detail & Related papers (2021-12-03T14:28:18Z)
Towards Quantum Simulations in Particle Physics and Beyond on Noisy Intermediate-Scale Quantum Devices [1.7242431149740054]
We review two algorithmic advances that bring us closer to reliable quantum simulations of model systems in high energy physics. The first method is the dimensional expressivity analysis of quantum circuits, which allows for constructing minimal but maximally expressive quantum circuits. The second method is an efficient mitigation of readout errors on quantum devices.
arXiv Detail & Related papers (2021-10-07T22:13:37Z)
Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
arXiv Detail & Related papers (2021-08-09T18:00:05Z)
An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation [55.41644538483948]
Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in chip size and error rates. We derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions. The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond $mathcalO(103)$ spins.
arXiv Detail & Related papers (2021-08-06T19:38:03Z)
Imaginary Time Propagation on a Quantum Chip [50.591267188664666]
Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems. We propose an algorithm to implement imaginary time propagation on a quantum computer.
arXiv Detail & Related papers (2021-02-24T12:48:00Z)
An Application of Quantum Annealing Computing to Seismic Inversion [55.41644538483948]
We apply a quantum algorithm to a D-Wave quantum annealer to solve a small scale seismic inversions problem. The accuracy achieved by the quantum computer is at least as good as that of the classical computer.
arXiv Detail & Related papers (2020-05-06T14:18:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.