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

TL;DR

This paper introduces the stabilizer bootstrap method to optimize quantum neural networks, demonstrating its effectiveness on up to 10,000 qubits and providing insights into the potential for quantum advantages in machine learning.

Contribution

It presents a novel stabilizer bootstrap technique for pre-optimization of variational quantum circuits, supported by theoretical proofs and large-scale simulations.

Findings

Stabilizer bootstrap effectiveness varies with observable structure and dataset size.

Two behaviors identified: constant improvement probability and exponential decay with qubit number.

Provides practical guidelines for designing scalable variational quantum circuits.

Abstract

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 ansatze 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 high-performance computing with 10000 qubits or random datasets up to 1000 data. We find that, in a general setup of variational ansatze, 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.