Variational algorithms for linear algebra

• DOI: 10.1016/j.scib.2021.06.023
• Publication Date: 2021-06-26T07:31:30Z
• Authors: Xiaosi Xu; Jinzhao Sun; Suguru Endo; Ying Li; Simon C. Benjamin; Xiao Yuan
• Keywords: Linear algebra; Numerical Linear Algebra; Hamiltonian (control theory)

Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational tasks that are compatible with noisy intermediate-scale devices. We show the solutions of systems equations matrix-vector multiplications can be translated as ground states constructed Hamiltonians. Based on algorithms, introduce Hamiltonian morphing together an adaptive ansätz finding state, solution verification. Our especially suitable problems sparse matrices, wide applications in machine learning optimisation problems. The algorithm matrix also used simulation open system simulation. evaluate cost effectiveness our through numerical simulations equations. implement IBM cloud device a high fidelity 99.95%.