Title: Variational quantum state diagonalization

Abstract

Abstract Variational hybrid quantum-classical algorithms are promising candidates for near-term implementation on quantum computers. In these algorithms, a quantum computer evaluates the cost of a gate sequence (with speedup over classical cost evaluation), and a classical computer uses this information to adjust the parameters of the gate sequence. Here we present such an algorithm for quantum state diagonalization. State diagonalization has applications in condensed matter physics (e.g., entanglement spectroscopy) as well as in machine learning (e.g., principal component analysis). For a quantum state ρ and gate sequence U , our cost function quantifies how far $$$$U\rho U^\dagger$$$$ $U\rho U^{†}$ is from being diagonal. We introduce short-depth quantum circuits to quantify our cost. Minimizing this cost returns a gate sequence that approximately diagonalizes ρ . One can then read out approximations of the largest eigenvalues, and the associated eigenvectors, of ρ . As a proof-of-principle, we implement our algorithm on Rigetti’s quantum computer to diagonalize one-qubit states and on a simulator to find the entanglement spectrum of the Heisenberg model ground state.

Authors:

LaRose, Ryan; Tikku, Arkin; O’Neel-Judy, Étude; Cincio, Lukasz; Coles, Patrick J.

Publication Date:

Wed Jun 26 00:00:00 EDT 2019

Research Org.:

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Quantum Information Science (QIS)

Sponsoring Org.:

USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:

1619716

Alternate Identifier(s):

OSTI ID: 1544727

Report Number(s):

LA-UR-18-29266
Journal ID: ISSN 2056-6387; 57; PII: 167

Grant/Contract Number:  

89233218CNA000001

Resource Type:

Published Article

Journal Name:

npj Quantum Information

Additional Journal Information:

Journal Name: npj Quantum Information Journal Volume: 5 Journal Issue: 1; Journal ID: ISSN 2056-6387

Publisher:

Nature Publishing Group

Country of Publication:

United Kingdom

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; Quantum Information Science (QIS)