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Avoiding barren plateaus using classical shadows

Stefan H. Sack, Raimel A. Medina, Alexios A. Michailidis, Richard Kueng, Maksym SerbynJan 21 2022 quant-ph arXiv:2201.08194v1

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Variational quantum algorithms are promising algorithms for achieving quantum advantage on near-term devices. The quantum hardware is used to implement a variational wave function and measure observables, whereas the classical computer is used to store and update the variational parameters. The optimization landscape of expressive variational ansätze is however dominated by large regions in parameter space, known as barren plateaus, with vanishing gradients which prevents efficient optimization. In this work we propose a general algorithm to avoid barren plateaus in the initialization and throughout the optimization. To this end we define a notion of weak barren plateaus (WBP) based on the entropies of local reduced density matrices. The presence of WBPs can be efficiently quantified using recently introduced shadow tomography of the quantum state with a classical computer. We demonstrate that avoidance of WBPs suffices to ensure sizable gradients in the initialization. In addition, we demonstrate that decreasing the gradient step size, guided by the entropies allows to avoid WBPs during the optimization process. This paves the way for efficient barren plateau free optimization on near-term devices.

Decompositional Quantum Graph Neural Network

Xing Ai, Zhihong Zhang, Luzhe Sun, Junchi Yan, Edwin HancockJan 17 2022 quant-ph cs.LG arXiv:2201.05158v1

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Quantum machine learning is a fast emerging field that aims to tackle machine learning using quantum algorithms and quantum computing. Due to the lack of physical qubits and an effective means to map real-world data from Euclidean space to Hilbert space, most of these methods focus on quantum analogies or process simulations rather than devising concrete architectures based on qubits. In this paper, we propose a novel hybrid quantum-classical algorithm for graph-structured data, which we refer to as the Decompositional Quantum Graph Neural Network (DQGNN). DQGNN implements the GNN theoretical framework using the tensor product and unity matrices representation, which greatly reduces the number of model parameters required. When controlled by a classical computer, DQGNN can accommodate arbitrarily sized graphs by processing substructures from the input graph using a modestly-sized quantum device. The architecture is based on a novel mapping from real-world data to Hilbert space. This mapping maintains the distance relations present in the data and reduces information loss. Experimental results show that the proposed method outperforms competitive state-of-the-art models with only 1.68\% parameters compared to those models.

Quantum Neuronal Sensing of Quantum Many-Body States on a 61-Qubit Programmable Superconducting Processor

Ming Gong, He-Liang Huang, Shiyu Wang, Chu Guo, Shaowei Li, Yulin Wu, Qingling Zhu, Youwei Zhao, Shaojun Guo, Haoran Qian, Yangsen Ye, Chen Zha, Fusheng Chen, Chong Ying, Jiale Yu, Daojin Fan, Dachao Wu, Hong Su, Hui Deng, Hao Rong, et al (16)Jan 19 2022 quant-ph arXiv:2201.05957v1

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Classifying the many-body quantum states with distinct properties and phases of matter is one of the most fundamental tasks in quantum many-body physics. However, due to the exponential complexity that emerges from enormous numbers of interacting particles, classifying large-scale quantum states is often very challenging for classical approaches. Here, we propose a new approach using quantum neuronal sensing. Utilizing a 61 qubit superconducting quantum processor, we show that our scheme can efficiently classify two different types of many-body phenomena: the ergodic and localized phases of matter. The quantum neuronal process in the sensing allows us to extract the necessary information coming from the statistical characteristics of the eigenspectrum by measuring only one qubit. Our work demonstrates the feasibility and scalability of quantum neuronal sensing for near-term quantum processors and opens new avenues for exploring quantum many-body phenomena in larger-scale systems.

Transfer Learning in Quantum Parametric Classifiers: An Information-Theoretic Generalization Analysis

Sharu Theresa Jose,Osvaldo SimeoneJan 19 2022 quant-phcs.ITcs.LGmath.IT arXiv:2201.06297v1

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A key step in quantum machine learning with classical inputs is the design of an embedding circuit mapping inputs to a quantum state. This paper studies a transfer learning setting in which classical-to-quantum embedding is carried out by an arbitrary parametric quantum circuit that is pre-trained based on data from a source task. At run time, the binary classifier is then optimized based on data from the target task of interest. Using an information-theoretic approach, we demonstrate that the average excess risk, or optimality gap, can be bounded in terms of two Rényi mutual information terms between classical input and quantum embedding under source and target tasks, as well as in terms of a measure of similarity between the source and target tasks related to the trace distance. The main theoretical results are validated on a simple binary classification example

Feedforward Quantum Control and Coherence Protection of Single Electron Spin in Diamond using Deep Learning

Nanyang Xu, Feifei Zhou, Xiangyu Ye, Xue Lin, Bao Chen, Ting Zhang, Feng Yue, Bing Chen, Ya Wang, Jiangfeng DuJan 19 2022 quant-ph arXiv:2201.06002v1

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Measurement-based realtime control is an important strategy in quantum information processing, which is applied in fields from qubit readout to error corrections. However, the time cost of quantum measurement inevitably induces a latency in the control process and limits its performance. Here we introduce the deep learning approach to relax this restriction by predicting and compensating the latency-induced control error. We experimentally implement feedforward quantum control of a single-spin system of nitrogen-vacancy (NV) center in diamond to protect the coherence of the electron spin. The new approach enhances the decoherence time as well as the the spectrum resolution of Ramsey interferometry about three times comparing with conventional scheme. This enables resolving optically indistinguishable NV centers from their magnetic spectrum with a frequency difference less than 20 kHz. A theoretical model is proposed to explain the improvement, where we show that the low-frequency magnetic noise is perfectly reduced. This scheme could be applied in general measurement schemes and extended to other quantum control systems.

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