@article{@misc{knudsen2020solving, title={Solving Differential Equations via Continuous-Variable Quantum Computers}, author={Martin Knudsen and Christian B. Mendl}, year={2020}, eprint={2012.12220}, archivePrefix={arXiv}, primaryClass={quant-ph} }, author = {Knudsen, Martin and Mendl, Christian}, title = {Neural Network Continuous-Variable Quantum Computing}, journal = {arXiv}, year = {2020}, month = {Dec}, language = {en}, 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.}, note = {Archive-ID: 2020_12_22_SolvingDifferentialEquationsviaContinuous-VariableQuantumComputers}, url = {https://arxiv.org/abs/2012.12220}, }