Noisy intermediate-scale quantum simulation of the one-dimensional wave equation

Abstract

We design and implement quantum circuits for the simulation of the one-dimensional wave equation on the Quantinuum H1-1 quantum computer. The circuit depth of our approach scales as $O(n^2)$ for $n$ qubits representing the solution on $2^n$ grid points, and leads to infidelities of $O(2^{-4n}{t}^2)$ for simulation time $t$ assuming smooth initial conditions. By varying the qubit count we study the interplay between the algorithmic and physical gate errors to identify the optimal working point of minimum total error. Our approach to simulating the wave equation can be used with appropriate state preparation algorithms across different quantum processors and serve as an application-oriented benchmark.

11 pages, 8 figures, 1 table

References in corpus (25)

• Quantum Computing in the NISQ era and beyond
• Variational Quantum Algorithms
• Barren plateaus in quantum neural network training landscapes
• Quantum computational chemistry
• Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
• t$|$ket$⟩$ : A Retargetable Compiler for NISQ Devices
• Variational quantum algorithms for nonlinear problems
• High-order quantum algorithm for solving linear differential equations
• Efficient quantum algorithm for dissipative nonlinear differential equations
• Quantum algorithm for linear differential equations with exponentially improved dependence on precision
• Solving nonlinear differential equations with differentiable quantum circuits
• Quantum algorithm and circuit design solving the Poisson equation
• High-precision quantum algorithms for partial differential equations
• Quantum Algorithm for Simulating the Wave Equation
• Improved quantum algorithms for linear and nonlinear differential equations
• Variational Quantum Algorithms for Computational Fluid Dynamics
• Approximate Quantum Fourier Transform with $O(n\log (n))$ T gates
• Quantum algorithm for non-homogeneous linear partial differential equations
• Exponential quantum speedup in simulating coupled classical oscillators
• Multigrid Renormalization
• Practical Quantum Computing: solving the wave equation using a quantum approach
• Realization of quantum signal processing on a noisy quantum computer
• Quantum algorithms for approximate function loading
• Quantum simulation of real-space dynamics
• Depth analysis of variational quantum algorithms for heat equation

Cited by in corpus (17)

• Two quantum algorithms for solving the one-dimensional advection-diffusion equation
• Simulating unsteady fluid flows on a superconducting quantum processor
• Incompressible Navier-Stokes solve on noisy quantum hardware via a hybrid quantum-classical scheme
• Simulating fluid flows with quantum computing
• Scalable Quantum Simulations of Scattering in Scalar Field Theory on 120 Qubits
• Compact quantum algorithms for time-dependent differential equations
• Quantum state preparation for multivariate functions
• Numerical solution of nonlinear Schrödinger equation by a hybrid pseudospectral-variational quantum algorithm
• Benchmarking Quantum Computers: Towards a Standard Performance Evaluation Approach
• Towards Variational Quantum Algorithms for generalized linear and nonlinear transport phenomena
• Implementation of Quantum Fourier Transform and Quantum Hashing for a Quantum Device with Arbitrary Qubits Connection Graphs
• Quantum circuits for partial differential equations in Fourier space
• A Quantum-Inspired Algorithm for Wave Simulation Using Tensor Networks
• Spectral quantum algorithm for passive scalar transport in shear flows
• Quantum-assisted tracer dispersion in turbulent shear flow
• Quantum Framework for Simulating Linear PDEs with Robin Boundary Conditions
• Performance evaluation of variational quantum eigensolver and quantum dynamics algorithms on the advection-diffusion equation