Solving Differential Equations via Continuous-Variable Quantum Computers

• URL: http://arxiv.org/abs/2012.12220v1
• Date: Tue, 22 Dec 2020 18:06:12 GMT
• Title: Solving Differential Equations via Continuous-Variable Quantum Computers
• Authors: Martin Knudsen and Christian B. Mendl
• Abstract summary: We explore how a continuous-dimensional (CV) quantum computer could solve a classic differential equation, making use of its innate capability to represent real numbers in qumodes. Our simulations and parameter optimization using the PennyLane / Strawberry Fields framework demonstrate good both linear and non-linear ODEs.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We explore how a continuous-variable (CV) quantum computer could solve a classic differential equation, making use of its innate capability to represent real numbers in qumodes. Specifically, we construct variational CV quantum circuits [Killoran et al., Phys.~Rev.~Research 1, 033063 (2019)] to approximate the solution of one-dimensional ordinary differential equations (ODEs), with input encoding based on displacement gates and output via measurement averages. Our simulations and parameter optimization using the PennyLane / Strawberry Fields framework demonstrate good convergence for both linear and non-linear ODEs.

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