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.
Highlights
Eigenvalue and more general optimization problems lie at the heart of applications and technologies ranging from Google’s Page Rank and aircraft design to quantum simulation and quantum chemistry [2,3,4]
While the construction of full scale, error corrected quantum devices still poses many technical challenges, great progress is being made in their development
In the era of pre-threshold devices, and beyond it, quantum devices may find an advantage in leveraging classical resources alongside quantum resources to exploit the powerful technologies already in existence today
Summary
Original content from this Abstract work may be used under Many quantum algorithms have daunting resource requirements when compared to what is available the terms of the Creative Commons Attribution 3.0 today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as ‘the licence.
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