Progress towards practical quantum variational algorithms

Dave Wecker, Matthew B. Hastings, and Matthias Troyer
Phys. Rev. A 92, 042303 – Published 2 October 2015

Abstract

The preparation of quantum states using short quantum circuits is one of the most promising near-term applications of small quantum computers, especially if the circuit is short enough and the fidelity of gates high enough that it can be executed without quantum error correction. Such quantum state preparation can be used in variational approaches, optimizing parameters in the circuit to minimize the energy of the constructed quantum state for a given problem Hamiltonian. For this purpose we propose a simple-to-implement class of quantum states motivated by adiabatic state preparation. We test its accuracy and determine the required circuit depth for a Hubbard model on ladders with up to 12 sites (24 spin orbitals), and for small molecules. We find that this ansatz converges faster than previously proposed schemes based on unitary coupled clusters. While the required number of measurements is astronomically large for quantum chemistry applications to molecules, applying the variational approach to the Hubbard model (and related models) is found to be far less demanding and potentially practical on small quantum computers. We also discuss another application of quantum state preparation using short quantum circuits, to prepare trial ground states of models faster than using adiabatic state preparation.

  • Received 3 August 2015

DOI:https://doi.org/10.1103/PhysRevA.92.042303

©2015 American Physical Society

Authors & Affiliations

Dave Wecker1, Matthew B. Hastings1,2, and Matthias Troyer3

  • 1Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
  • 2Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
  • 3Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 92, Iss. 4 — October 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
×