2020/11/17 by Daniel Gunlycke, Gunlycke, Daniel, Mark C. Palenik +5 · 2 citations
Computer Science · #Computational Physics and Python Applications #FOS: Physical sciences #Matrix Theory and Algorithms #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2011.08942
openalex publication_date 2020/11/17 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28
Several linear algebra routines for quantum computing use a basis of tensor products of identity and Pauli operators to describe linear operators, and obtaining the coordinates for any given linear operator from its matrix representation requires a basis transformation, which for an \mathrm N×\mathrm N matrix generally involves \mathcal O(\mathrm N4) arithmetic operations. Herein, we present an efficient algorithm that for our particular basis transformation only involves \mathcal O(\mathrm N2log2\mathrm N) operations. Because this algorithm requires fewer than \mathcal O(\mathrm N3) operations, for large \mathrm N, it could be used as a preprocessing step for quantum computing algorithms for certain applications. As a demonstration, we apply our algorithm to a Hamiltonian describing a system of relativistic interacting spin-zero bosons and calculate the ground-state energy using the variational quantum eigensolver algorithm on a quantum computer.