Tensor-Programmable Quantum Circuits for Solving Differential Equations

Abstract

We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of unitary operators. Hence, it allows for the direct implementation of a broad class of differential equations governing the dynamics of classical and quantum systems. The capabilities of the framework are demonstrated for linear and non-linear partial differential equations using the example of the linearized Euler equations with absorbing boundaries and the nonlinear Burgers' equation. For a turbulence data set, we demonstrate potential advantages of the quantum tensor scheme over its classical counterparts.