Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session T70: Quantum Machine Learning II
11:30 AM–2:30 PM,
Thursday, March 9, 2023
Room: Room 409
Sponsoring
Unit:
DQI
Chair: Ruslan Shayludin, JPMorgan Chase
Abstract: T70.00002 : Investigating trainability of parameters in the Snap-Displacement protocol of a Qudit system.*
11:42 AM–11:54 AM
Presenter:
Oluwadara Ogunkoya
(Fermi National Accelerator Laboratory)
Authors:
Oluwadara Ogunkoya
(Fermi National Accelerator Laboratory)
Doga M Kurkcuoglu
(Fermi National Accelerator Laboratory)
Kirsten Morris
(University of Nebraska-Lincoln)
Jasmine Panthee
(Illinois Institute of Technology, Chicago IL, USA)
optimal parameters for these gates is a non-trivial problem. We analyze optimization problems
caused by the multi-modal nature of the cost function which leads to trapping in points of the local
minima and we investigate whether the SNAP and displacement protocol has the barren plateau
problem. We consider a parameterized ansatz comprising of sequence of blocks where each block
is made up of hardware operations –Snap and Displacement gates [2]. For a Variational Quantum
Algorithm (VQA) with Observable and Gate cost functions, we apply similar techniques in [1]
and [3] and t−design concept to show that (a) the trainability of a parameter does not favor any
particular direction in our cost function landscape, (b) by applying the first and second moments
properties of Haar measures we give new lemmas for the expectation of functions of particular
forms, and (c) by applying these new lemmas, we show that the chances of training a parameter
decreases polynomially in the Hilbert space dimension. Specifically, we show that we do not have
dependency on the length of the ansatz in contrast to the qubit result in [3] and also, we give a
particular case of trainability of parameters in the observable cost function.
References
[1] Jarrod R McClean et al. “Barren plateaus in quantum neural network training landscapes”.
In: Nature communications 9.1 (2018), pp. 1–6.
[2] Thomas F ¨osel et al. “Efficient cavity control with SNAP gates”. In: arXiv preprint arXiv:2004.14256
(2020).
[3] Marco Cerezo et al. “Cost function dependent barren plateaus in shallow parametrized quan-
tum circuits”. In: Nature communications 12.1 (2021), pp. 1–12.
This material is based upon work supported by the U.S. Department of Energy, Office of Science,
National Quantum Information Science Research Centers, Superconducting Quantum Materials
and Systems Center (SQMS) under contract number DE-AC02-07CH11359.”
*This material is based upon work supported by the U.S. Department of Energy, Office of Science,National Quantum Information Science Research Centers, Superconducting Quantum Materialsand Systems Center (SQMS) under contract number DE-AC02-07CH11359.”
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