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arXiv:2401.15442 · International Symposium on Quality Electronic Design (ISQED)

Non-parametric Greedy Optimization of Parametric Quantum Circuits

Koustubh Phalak, Swaroop Ghosh

Published Apr 3, 2024• 2 citations
arXivHTMLPDF

Abstract

The use of Quantum Neural Networks (QNN) that are analogous to classical neural networks, has greatly increased in the past decade owing to the growing interest in the field of Quantum Machine Learning (QML). A QNN consists of three major components: (i) data loading/encoding circuit, (ii) Parametric Quantum Circuit (PQC), and (iii) measurement operations. Under ideal circumstances the PQC of the QNN trains well, however that may not be the case for training under quantum hardware due to presence of different kinds of noise. Deeper QNNs with high depths tend to degrade more in terms of performance compared to shallower networks. This work aims to reduce depth and gate count of PQCs by replacing parametric gates with their approximate fixed non-parametric representations. We propose a greedy algorithm to achieve this such that the algorithm minimizes a distance metric based on unitary transformation matrix of original parametric gate and new set of non-parametric gates. From this greedy optimization followed by a few epochs of re-training, we observe roughly 14% reduction in depth and 48% reduction in gate count at the cost of 3.33# reduction in inferencing accuracy. Similar results are observed for a different dataset as well with different PQC structure.

DOI
10.1109/isqed60706.2024.10528696

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The use of Quantum Neural Networks (QNN) that are analogous to classical neural networks, has greatly increased in the past decade owing to the growing interest in the field of Quantum Machine Learning (QML). A QNN consists of three major components: (i) data loading/encoding circuit, (ii) Parametric Quantum Circuit (PQC), and (iii) measurement operations. Under ideal circumstances the PQC of the QNN trains well, however that may not be the case for training under quantum hardware due to presence of different kinds of noise. Deeper QNNs with high depths tend to degrade more in terms of performance compared to shallower networks. This work aims to reduce depth and gate count of PQCs by replacing parametric gates with their approximate fixed non-parametric representations. We propose a greedy algorithm to achieve this such that the algorithm minimizes a distance metric based on unitary transformation matrix of original parametric gate and new set of non-parametric gates. From this greedy optimization followed by a few epochs of re-training, we observe roughly 14% reduction in depth and 48% reduction in gate count at the cost of 3.33# reduction in inferencing accuracy. Similar results are observed for a different dataset as well with different PQC structure.
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Quantum Machine Learning is an emerging sub-field in machine learning where one of the goals is to perform pattern recognition tasks by encoding data into quantum states. This extension from classical to quantum domain has been made possible due to the development of hybrid quantum-classical algorithms that allow a parameterized quantum circuit to be optimized using gradient based algorithms that run on a classical computer. The similarities in training of these hybrid algorithms and classical neural networks has further led to the development of Quantum Neural Networks (QNNs). However, in the current training regime for QNNs, the gradients w.r. t objective function have to be computed on the quantum device. This computation is highly non-scalable and is affected by hardware and sampling noise present in the current generation of quantum hardware. In this paper, we propose a training algorithm that does not rely on gradient information. Specifically, we introduce a novel meta-optimization algorithm that trains a meta-optimizer network to output parameters for the quantum circuit such that the objective function is minimized. We empirically and theoretically show that we achieve a better quality minima in fewer circuit evaluations than existing gradient based algorithms on different datasets.
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Quantum Computing (QC) is fastly growing to replace current computing systems for many high-performance applications. Due to the rapid increase of computational power, machine learning models based on artificial neural networks (ANN) have become highly effective. Even though classical machine learning models have been performing well, quantum computing with machine learning, i.e., Quantum Machine Learning (QML), will enhance the performance in multiple ways. Subsequently, DeepQQQlearning is a prominent approach to reinforcement learning used in solving complex applications for a desired performance. But this performance can be improved using a quantum computer. This paper proposes a quantum-enhanced Deep Q Learning algorithm to see its advantages over its classical counterparts. We implement our approach using parametrized quantum circuit (PQC). The evaluation of the proposed method achieves the metrics rewards and episodes up to 500 points and 1200, respectively. The performance shows that it collects roughly four times more rewards in a given time and takes significantly fewer episodes to converge compared to the classical approach.