Dynamical quantum Ansatz tree approach for the heat equation

TL;DR

This paper introduces a variational quantum tree approach for solving the time-dependent heat equation, leveraging probabilistic circuits and a specialized ansatz structure to achieve potential exponential speedup over classical methods.

Contribution

The paper extends the variational Ansatz tree approach to the full time-dependent heat equation, incorporating probabilistic circuits and a novel ansatz structure for quantum advantage.

Findings

Proposes a quantum algorithm with exponential speedup potential.

Utilizes a probabilistic quantum circuit to model heat sources.

Employs a specialized ansatz tree structure for efficient state preparation.

Abstract

Quantum computers can be used for the solution of various problems of mathematical physics. In the present paper, we consider a discretized version of the heat equation and address its solution on quantum computer using variational Anzats tree approach (ATA). We extend this method originally proposed for the system of linear equations to tackle full time dependent heat equation. The key ingredients of our method are (i) special probabilistic quantum circuit in order to add heat sources to temperature distribution, (ii) limiting auxiliary register in the preparation of quantum state, (iii) utilizing a robust cluster of repetitive nodes in the anzats tree structure. We suggest that our procedure provides an exponential speedup compared to the classical algorithms in the case of time dependent heat equation.