Exponential Hardness of Optimization from the Locality in Quantum Neural Networks

Authors: Hao-Kai Zhang, Chengkai Zhu, Geng Liu, Xin Wang

AAAI 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental We showcase the validity of our results with numerical simulations of representative models and examples. Our findings, as a fundamental property of random quantum circuits, deepen the understanding of the role of locality in QNNs and serve as a guideline for assessing the effectiveness of diverse training strategies for quantum neural networks.
Researcher Affiliation Collaboration 1Institute for Advanced Study, Tsinghua University, Beijing 100084, China 2Thrust of Artificial Intelligence, Information Hub, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou 511453, China 3Institute for Quantum Computing, Baidu Research, Beijing 100193, China
Pseudocode No The paper describes mathematical derivations and experimental procedures but does not include any explicitly labeled pseudocode or algorithm blocks.
Open Source Code No The paper does not contain any explicit statements about releasing code for the described methodology, nor does it provide a link to a code repository.
Open Datasets No The paper conducts numerical simulations using a theoretical construct, the '1-dimensional spin-1/2 antiferromagnetic Heisenberg model,' and other QNN models, but it does not specify or provide access information for a traditional, publicly available dataset.
Dataset Splits No The paper describes numerical simulations of quantum neural networks and their properties but does not mention specific training, validation, or test dataset splits (e.g., percentages, sample counts) as would be typical for a machine learning experiment involving empirical data.
Hardware Specification No The paper does not specify the hardware (e.g., CPU, GPU, memory, specific compute clusters) used for running the numerical simulations.
Software Dependencies No The paper mentions using the 'Adam optimizer' and describes the quantum circuit components, but it does not specify any software dependencies with version numbers (e.g., Python version, library versions like TensorFlow or PyTorch).
Experiment Setup Yes Consider subsystem A only containing a single qubit, namely m = 1, and parameterize the local unitary UA U(2) with 3 Euler angles... To construct random circuits forming 2-designs as V1 or V2 used in the VQE and QAE examples, we employ the following hardware-efficient ansatz as in (Mc Clean et al. 2018) for comparison. ... Each layer consists of n single-qubit rotation gates RP (θ) on each qubit together with n 1 controlled phase gates... To compute max UA C and min UA C ... we employ the Adam optimizer to update UA iteratively until convergence for each of the 100 samples of V1, V2.