Incompressible Navier-Stokes solve on noisy quantum hardware via a hybrid quantum-classical scheme

Abstract

Partial differential equation solvers are required to solve the Navier-Stokes equations for fluid flow. Recently, algorithms have been proposed to simulate fluid dynamics on quantum computers. Fault-tolerant quantum devices might enable exponential speedups over algorithms on classical computers. However, current and foreseeable quantum hardware introduce noise into computations, requiring algorithms that make judicious use of quantum resources: shallower circuit depths and fewer qubits. Under these restrictions, variational algorithms are more appropriate and robust. This work presents a hybrid quantum-classical algorithm for the incompressible Navier--Stokes equations. A classical device performs nonlinear computations, and a quantum one uses a variational solver for the pressure Poisson equation. A lid-driven cavity problem benchmarks the method. We verify the algorithm via noise-free simulation and test it on noisy IBM superconducting quantum hardware. Results show that high-fidelity results can be achieved via this approach, even on current quantum devices. Multigrid preconditioning of the Poisson problem helps avoid local minima and reduces resource requirements for the quantum device. A quantum state readout technique called HTree is used for the first time on a physical problem. Htree is appropriate for real-valued problems and achieves linear complexity in the qubit count, making the Navier-Stokes solve further tractable on current quantum devices. We compare the quantum resources required for near-term and fault-tolerant solvers to determine quantum hardware requirements for fluid simulations with complexity improvements.

arXiv comment26 pages, 10 figures, 5 tables

References in corpus (45)

• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Quantum algorithm for solving linear systems of equations
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Noisy intermediate-scale quantum (NISQ) algorithms
• Suppressing quantum errors by scaling a surface code logical qubit
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Logical quantum processor based on reconfigurable atom arrays
• The Variational Quantum Eigensolver: a review of methods and best practices
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
• Global entanglement in multiparticle systems
• A Race Track Trapped-Ion Quantum Processor
• Variational quantum algorithms for nonlinear problems
• Preconditioned quantum linear system algorithm
• Maximum Likelihood, Minimum Effort
• Efficient quantum algorithm for dissipative nonlinear differential equations
• A quantum linear system algorithm for dense matrices
• Quantum algorithm for linear differential equations with exponentially improved dependence on precision
• Variational Quantum Linear Solver
• Quantum algorithms and the finite element method
• Quantum algorithm and circuit design solving the Poisson equation
• Quantum algorithms for systems of linear equations inspired by adiabatic quantum computing
• High-precision quantum algorithms for partial differential equations
• Suppression of crosstalk in superconducting qubits using dynamical decoupling
• Dynamical decoupling for superconducting qubits: a performance survey
• Expressibility of the alternating layered ansatz for quantum computation
• Variational Quantum Algorithms for Computational Fluid Dynamics
• ADAPT: Mitigating Idling Errors in Qubits via Adaptive Dynamical Decoupling
• Quantum Fast Poisson Solver: the algorithm and modular circuit design
• Variational Quantum Solutions to the Advection-Diffusion Equation for Applications in Fluid Dynamics
• Effects of Dynamical Decoupling and Pulse-level Optimizations on IBM Quantum Computers
• Quantum algorithm for the Navier Stokes equations by using the streamfunction vorticity formulation and the lattice Boltzmann method
• Hybrid quantum algorithms for flow problems
• Lattice Boltzmann-Carleman quantum algorithm and circuit for fluid flows at moderate Reynolds number
• Three Carleman routes to the quantum simulation of classical fluids
• Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data
• Nonlinear dynamics as a ground-state solution on quantum computers
• Noisy intermediate-scale quantum simulation of the one-dimensional wave equation
• A Performance Study of Variational Quantum Algorithms for Solving the Poisson Equation on a Quantum Computer
• Compact quantum algorithms for time-dependent differential equations
• A Hybrid Quantum-Classical CFD Methodology with Benchmark HHL Solutions
• Preconditioning for a Variational Quantum Linear Solver

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• Performance evaluation of variational quantum eigensolver and quantum dynamics algorithms on the advection-diffusion equation