Hamiltonian gadgets with reduced resource requirements

Yudong Cao, Ryan Babbush, Jacob Biamonte, and Sabre Kais
Phys. Rev. A 91, 012315 – Published 12 January 2015

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
2 More
  • Received 24 January 2014
  • Revised 18 August 2014

DOI:https://doi.org/10.1103/PhysRevA.91.012315

©2015 American Physical Society

Authors & Affiliations

Yudong Cao1,2,*, Ryan Babbush3,†, Jacob Biamonte4,‡, and Sabre Kais1,2,5,6,§

  • 1Department of Computer Science, Purdue University, 601 Purdue Mall, West Lafayette, Indiana 47907, USA
  • 2Qatar Energy and Environment Research Institute (QEERI), Ar-Rayyān, P.O Box 5825, Doha, Qatar
  • 3Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
  • 4ISI Foundation, Via Alassio 11/c, 10126, Torino, Italy
  • 5Department of Chemistry, Physics and Birck Nanotechnology Center, Purdue University, 601 Purdue Mall, West Lafayette, Indiana 47907, USA
  • 6Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, New Mexico 87501, USA

  • *cao23@purdue.edu
  • babbush@fas.harvard.edu
  • jacob.biamonte@qubit.org
  • §kais@purdue.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 91, Iss. 1 — January 2015

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×