Hamiltonian gadgets with reduced resource requirements

Yudong Cao, Ryan Babbush, Jacob Biamonte, Sabre Kais

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Application of the adiabatic model of quantum computation requires efficient encoding of the solution to computational problems into the lowest eigenstate of a Hamiltonian that supports universal adiabatic quantum computation. Experimental systems are typically limited to restricted forms of two-body interactions. Therefore, universal adiabatic quantum computation requires a method for approximating quantum many-body Hamiltonians up to arbitrary spectral error using at most two-body interactions. Hamiltonian gadgets, introduced around a decade ago, offer the only current means to address this requirement. Although the applications of Hamiltonian gadgets have steadily grown since their introduction, little progress has been made in overcoming the limitations of the gadgets themselves. In this experimentally motivated theoretical study, we introduce several gadgets which require significantly more realistic control parameters than similar gadgets in the literature. We employ analytical techniques which result in a reduction of the resource scaling as a function of spectral error for the commonly used subdivision, three- to two-body and k-body gadgets. Accordingly, our improvements reduce the resource requirements of all proofs and experimental proposals making use of these common gadgets. Next, we numerically optimize these gadgets to illustrate the tightness of our analytical bounds. Finally, we introduce a gadget that simulates a YY interaction term using Hamiltonians containing only {X,Z,XX,ZZ} terms. Apart from possible implications in a theoretical context, this work could also be useful for a first experimental implementation of these key building blocks by requiring less control precision without introducing extra ancillary qubits.

Original languageEnglish
Article number012315
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume91
Issue number1
DOIs
Publication statusPublished - 12 Jan 2015

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resources
quantum computation
requirements
tightness
subdivisions
interactions
proposals
eigenvectors
coding
scaling

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Hamiltonian gadgets with reduced resource requirements. / Cao, Yudong; Babbush, Ryan; Biamonte, Jacob; Kais, Sabre.

In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 91, No. 1, 012315, 12.01.2015.

Research output: Contribution to journalArticle

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