O(N³) Measurement Cost for Variational Quantum Eigensolver on\n Molecular Hamiltonians

2019/08/30 by Pranav Gokhale, Frederic T. Chong, Gokhale, Pranav +1 · 6 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum and electron transport phenomena

paper · pdf · doi:10.48550/arxiv.1908.11857

openalex publication_date 2019/08/30 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

Variational Quantum Eigensolver (VQE) is a promising algorithm for near-term\nquantum machines. It can be used to estimate the ground state energy of a\nmolecule by performing separate measurements of O(N⁴) terms. Several recent\npapers observed that this scaling may be reducible to O(N³) by partitioning\nthe terms into linear-sized commuting families that can be measured\nsimultaneously. We confirm these empirical observations by studying the\nMIN-COMMUTING-PARTITION problem at the level of the fermionic Hamiltonian and\nits encoding into qubits. Moreover, we provide a fast, pre-computable procedure\nfor creating linearly-sized commuting partitions by solving a round-robin\nscheduling problem via flow networks.\n

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