Quantum advantage for differential equation analysis

Abstract

Quantum algorithms for both differential equation solving and for machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in useful problem instances. The essential obstacle for quantum differential equation solving is that outputting useful information may require difficult post-processing, and the essential obstacle for quantum machine learning is that inputting the training set is a difficult task just by itself. In this paper, we demonstrate, when combined, these difficulties solve one another. We show how the output of quantum differential equation solving can serve as the input for quantum machine learning, allowing dynamical analysis in terms of principal components, power spectra, and wavelet decompositions. To illustrate this, we consider continuous time Markov processes on epidemiological and social networks. These quantum algorithms provide an exponential advantage over existing classical Monte Carlo methods.

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Cited by in corpus (8)

• Quantum Machine Learning: from physics to software engineering
• Quantum Variational Solving of Nonlinear and Multi-Dimensional Partial Differential Equations
• Towards Cosmological Simulations of Dark Matter on Quantum Computers
• Parallel Quantum Algorithm for Hamiltonian Simulation
• Quantum algorithms for group convolution, cross-correlation, and equivariant transformations
• A Quantum Algorithm for Dynamic Mode Decomposition Integrated with a Quantum Differential Equation Solver
• Alternatives to a nonhomogeneous partial differential equation quantum algorithm
• A time-marching quantum algorithm for simulation of the nonlinear Lorenz dynamics