Investigating parameter trainability in the SNAP-displacement protocol of a qudit system

Journal Article · Wed Jun 18 00:00:00 EDT 2025 · Physica Scripta

DOI:https://doi.org/10.1088/1402-4896/ade206· OSTI ID:2007031

Ogunkoya, Oluwadara ^[1]; Morris, Kirsten ^[2]; Kürkçüog̃lu, Dog̃a Murat ^[1]

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1. Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
2. Univ. of Nebraska, Lincoln, NE (United States)

Here, in this study, we explore the universality of Selective Number-dependent Arbitrary Phase (SNAP) and Displacement gates for quantum control in qudit-based systems. However, optimizing the parameters of these gates poses a challenging task. Our main focus is to investigate the sensitivity of training any of the SNAP parameters in the SNAP-Displacement protocol. We analyze conditions that could potentially lead to the Barren Plateau problem in a qudit system and draw comparisons with multi-qubit systems. The parameterized ansatz we consider consists of blocks, where each block is composed of hardware operations, namely SNAP and Displacement gates [Fösel et al 2020 Efficient cavity control with snap gates arXiv:2004.14256]. Applying Variational Quantum algorithm (VQA) with observable and gate cost functions, we utilize techniques similar to those in [McClean et al 2018 Barren plateaus in quantum neural network training landscapes Nat. Commun.9 1–6] and [Cerezo et al 2021 Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nat. Commun.12 1–12] along with the concept of t − design. Through this analysis, we make the following key observations: (a) The trainability of a SNAP-parameter does not exhibit a preference for any particular direction within our cost function landscape, (b) By leveraging the first and second moments properties of Haar measures, we establish new lemmas concerning the expectation of certain polynomial functions, and (c) utilizing these new lemmas, we identify a general condition that indicates an expected trainability advantage in a qudit system when compared to multi-qubit systems.

• Research Organization: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE Office of Science (SC)
• Grant/Contract Number: 89243024CSC000002; AC02-07CH11359
• OSTI ID: 2007031
• Report Number(s): FERMILAB-PUB--23-387-SQMS; oai:inspirehep.net:2703096; arXiv:2309.14942
• Journal Information: Physica Scripta, Journal Name: Physica Scripta Journal Issue: 7 Vol. 100; ISSN 1402-4896; ISSN 0031-8949
• Publisher: IOP Publishing
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS