A hard-constraint, parameter-shift quantum circuit model is fitted to first-order ODEs, but its input-derivative formula omits a chain-rule factor and the validation uses the same reference data it trains on.
Solving Differential Equations via Continuous-Variable Quantum Computers
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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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Physics-Informed Quantum Machine Learning with Hard Constraint Embedding for Nonlinear Differential Equations of the First Order
A hard-constraint, parameter-shift quantum circuit model is fitted to first-order ODEs, but its input-derivative formula omits a chain-rule factor and the validation uses the same reference data it trains on.