Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session G36: Quantum Algorithms for Optimization
11:30 AM–2:30 PM,
Tuesday, March 15, 2022
Room: McCormick Place W-194A
Sponsoring
Unit:
DQI
Chair: Rebekah Herrman, University of Tennessee
Abstract: G36.00013 : Diagrammatic Analysis for Parameterized Quantum Circuits*
2:18 PM–2:30 PM
Presenter:
Tobias Stollenwerk
(German Aerospace Center (DLR))
Authors:
Tobias Stollenwerk
(German Aerospace Center (DLR))
Stuart Hadfield
(NASA Quantum Artificial Intelligence Lab (QuAIL), USRA Research Institute for Advanced Computer Science (RIACS))
In this work, we describe extensions of the ZX calculus for computing expectation values of parameterized quantum circuits,
which are important quantities in applications ranging from combinatorial optimization to quantum chemistry.
We provide several new ZX rules and generalizations for this setting.
In particular, we give formal rules for linear combinations of ZX diagrams,
where the relative scale factors of each diagram must be kept track of,
in contrast to most previously studied single-diagram cases where these coefficients can be ignored.
We demonstrate that the diagrammatic approach offers novel insights into algorithm structure and performance by considering
several ansätze from the literature including realizations of hardware-efficient ansätze and QAOA.
Moreover, we find that by using a diagrammatic representation the calculation of more sophisticated ansätze, like
deeper QAOA circuits, can become more intuitive and easier to calculate than by alternative means.
Finally, we outline how diagrammatic approaches may aid in the design of new and more effective quantum circuit ansätze.
*SH is grateful for supportĀ from NASA Ames Research Center and from the DARPA ONISQ program under interagency agreement IAA 8839, Annex 114.
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