The theory of variational hybrid quantum-classical algorithms
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Open Access
- 1 February 2016
- journal article
- research article
- Published by IOP Publishing in New Journal of Physics
- Vol. 18 (2), 023023
- https://doi.org/10.1088/1367-2630/18/2/023023
Abstract
Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as 'the quantum variational eigensolver' was developed (Peruzzo et al 2014 Nat. Commun. 5 4213) with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through a relaxation of exponential operator splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.Keywords
Funding Information
- Army Research Office (W911NF-15-1-0256)
- Air Force Office of Scientific Research (FA9550-12-1-0046)
- Office of Naval Research Global (N00014-16-1-2008)
- Defense Security Science Engineering Fellowship (N00014-16-1-2008)
- Lawrence Berkeley National Laboratory (Luis W. Alvarez Fellowship in Compu)
This publication has 75 references indexed in Scilit:
- Photonic quantum simulatorsNature Physics, 2012
- Polynomial-time quantum algorithm for the simulation of chemical dynamicsProceedings of the National Academy of Sciences of the United States of America, 2008
- Anti-Hermitian Contracted Schrödinger Equation: Direct Determination of the Two-Electron Reduced Density Matrices of Many-Electron MoleculesPhysical Review Letters, 2006
- Algorithmic Complexity and Entanglement of Quantum StatesPhysical Review Letters, 2005
- Robustness of the adiabatic quantum searchPhysical Review A, 2005
- Quantum search by local adiabatic evolutionPhysical Review A, 2002
- Eigenvalue computation in the 20th centuryJournal of Computational and Applied Mathematics, 2000
- Contracted Schrödinger equation: Determining quantum energies and two-particle density matrices without wave functionsPhysical Review A, 1998
- ber das Paulische quivalenzverbotThe European Physical Journal A, 1928
- Beweis des AdiabatensatzesThe European Physical Journal A, 1928