The Stabilizer Bootstrap of Quantum Machine Learning with up to 10000 qubits

Aug 4, 2026

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Quantum machine learning is a leading use case for quantum computers, yet the conditions for realizing quantum advantages and the design principles for effective variational ansätze remain unclear. This work introduces a stabilizer bootstrap method that uses stabilizer-based optimization before quantum execution, supported by theoretical analysis and high-performance simulations up to 10000 qubits and datasets up to 1000. Results show improvement likelihood depends on observable structure and dataset size, forming strong vs weak stabilizer enhancement regimes with behavior spanning constant and exponentially decaying improvement probabilities.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages15

Reading Time38 min

AccessFree to download

Introduction

Quantum machine learning and initialization

Stabilizer bootstrap method and circuit setup

Observables and improvement regimes

arXiv :2412 . 11356v1 [ quant-ph] 16 Dec 2024 The Stabilizer Bootstrap of Quantum Machine Learning with up to 10000 qubits Yuqing Li, 1, ∗ Jinglei Cheng, 1,† Xulong Tang, 1,‡ Youtao Zhang, 1, § Frederic T. Chong,2, ¶ and Junyu Liu 1, ∗∗ 1 Department of Computer Science, University of Pittsburgh, Pittsburgh, PA 15260, USA 2 Department of Computer Science, University of Chicago, Chicago, IL 60637 (Dated: December 17, 2024) Quantum machine learning is considered one of the flagship applications of quantum computers, where variational quantum circuits could be the leading paradigm both in the near-term quantum devices and the early fault-tolerant quantum computers. However, it is not clear how to identify the regime of quantum advantages from these circuits, and there is no explicit theory to guide the practical design of variational ans¨atze to achieve better performance. We address these challenges with the stabilizer bootstrap, a method that uses stabilizer-based techniques to optimize quantum neural networks before their quantum execution, together with theoretical proofs and highperformance computing with 10000 qubits or random datasets up to 1000 data. We find that, in a general setup of variational ans¨atze, the possibility of improvements from the stabilizer bootstrap depends on the structure of the observables and the size of the datasets. The results reveal that configurations exhibit two distinct behaviors: some maintain a constant probability of circuit improvement, while others show an exponential decay in improvement probability as qubit numbers increase. These patterns are termed strong stabilizer enhancement and weak stabilizer enhancement, respectively, with most situations falling in between. Our work seamlessly bridges techniques from fault-tolerant quantum computing with applications of variational quantum algorithms. Not only does it offer practical insights for designing variational circuits tailored to large-scale machine learning challenges, but it also maps out a clear trajectory for defining the boundaries of feasible and practical quantum advantages. I. INTRODUCTION Quantum machine learning (QML) represents a powerful approach with demonstrated applications across multiple scientific domains, from protein folding and drug discovery in biology [1–3] to molecular structure optimization in chemistry [4] . The performance of QML algorithms depends heavily on initial conditions, which is a characteristic shared with classical machine learning. Research shows that optimal initialization of training circuits can reduce convergence time and improve final results [5, 6] . The classical bootstrap [7], a process for searching and optimizing certain parameters under constraints, serves as a crucial step in developing effective variational quantum algorithm initial parameters [8] . In general, recent research has established several parameter initialization approaches for QML, including tensor network methods [9], Gaussian initialization techniques [10], matrix product state optimization [11], and deep neural network integration [12] . These initialization methods have advanced QML performance through reduced training epochs, faster loss function convergence, and improved final accuracy. The prior work [8] introduced CAFQA, a novel approach that searches Clifford space with Bayesian optimization to identify op- ∗ † ‡ § ¶ ∗∗ [yli@pitt.edu](yli@pitt.edu)[ ](yli@pitt.edu)[jic373@pitt.edu](jic373@pitt.edu)[ ](jic373@pitt.edu)[xulongtang@pitt.edu](xulongtang@pitt.edu)[ ](xulongtang@pitt.edu)[youtao@pitt.edu](youtao@pitt.edu)[ ](youtao@pitt.edu)[chong@cs.uchicago.edu](chong@cs.uchicago.edu)[ ](chong@cs.uchicago.edu)[junyuliu@pitt.edu](junyuliu@pitt.edu) timal quantum states for Variational Quantum Eigensolver (VQE) tasks, naturally leveraging concepts from fault-tolerant quantum computing towards practical applications. In various experiments, CAFQA surpasses the traditional chemical approac

FAQs

What is the stabilizer bootstrap method proposed in the document?

It is a stabilizer-based procedure that optimizes quantum neural networks before their quantum execution, using theoretical proofs and large-scale high-performance simulations.

How does the document characterize when stabilizer bootstrap improves variational ansätze?

Improvement depends on the structure of the observables and the size of the datasets, producing two distinct behaviors: strong stabilizer enhancement and weak stabilizer enhancement.

Which factors and circuit designs are studied to evaluate performance?

The study considers variational circuits with different measurement observables and entanglement structures, including linear and reverse-linear CNOT layer configurations, and analyzes observables built from Pauli-X and Pauli-Z operators with varying X proportions.

Aug 4, 2026

Upload by Ophelia