Solving Differential Equations via Continuous-Variable Quantum Computers

Understand

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.