Improved amplitude amplification strategies for the quantum simulation of classical transport problems

Abstract

The quantum simulation of classical fluids often involves the use of probabilistic algorithms that encode the result of the dynamics in the form of the amplitude of the selected quantum state. In most cases, however, the amplitude probability is too low to allow an efficient use of these algorithms, thereby hindering the practical viability of the quantum simulation. The oblivious amplitude amplification algorithm is often presented as a solution to this problem, but to no avail for most classical problems, since its applicability is limited to unitary dynamics. In this paper, we show analytically that oblivious amplitude amplification when applied to non-unitary dynamics leads to a distortion of the quantum state and to an accompanying error in the quantum update. We provide an analytical upper bound of such error as a function of the degree of non-unitarity of the dynamics and we test it against a quantum simulation of an advection-diffusion-reaction equation, a transport problem of major relevance in science and engineering. Finally, we also propose an amplification strategy that helps mitigate the distortion error, while still securing an enhanced success probability.

References in corpus (9)

• Simulating Hamiltonian dynamics with a truncated Taylor series
• Fixed-point quantum search with an optimal number of queries
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• Quantum computing with Qiskit
• Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
• Variable time amplitude amplification and a faster quantum algorithm for solving systems of linear equations
• Three Carleman routes to the quantum simulation of classical fluids
• Potential quantum advantage for simulation of fluid dynamics
• Explicit Quantum Circuit for Simulating the Advection-Diffusion-Reaction Dynamics

Cited by in corpus (4)

• Quantum Iterative Methods for Solving Differential Equations with Application to Computational Fluid Dynamics
• A time-marching quantum algorithm for simulation of the nonlinear Lorenz dynamics
• Stochastic Schrödinger Equations for Quantum Reverse Diffusion
• Performance evaluation of variational quantum eigensolver and quantum dynamics algorithms on the advection-diffusion equation