Unsupervised Machine Learning on a Hybrid Quantum Computer (1712.05771v1)

Abstract: Machine learning techniques have led to broad adoption of a statistical model of computing. The statistical distributions natively available on quantum processors are a superset of those available classically. Harnessing this attribute has the potential to accelerate or otherwise improve machine learning relative to purely classical performance. A key challenge toward that goal is learning to hybridize classical computing resources and traditional learning techniques with the emerging capabilities of general purpose quantum processors. Here, we demonstrate such hybridization by training a 19-qubit gate model processor to solve a clustering problem, a foundational challenge in unsupervised learning. We use the quantum approximate optimization algorithm in conjunction with a gradient-free Bayesian optimization to train the quantum machine. This quantum/classical hybrid algorithm shows robustness to realistic noise, and we find evidence that classical optimization can be used to train around both coherent and incoherent imperfections.

• The paper introduces a hybrid quantum-classical algorithm that integrates QAOA with Bayesian optimization to solve NP-complete Maxcut clustering problems.
• The methodology employs a 19-qubit superconducting processor to achieve noise-resilient clustering with statistically significant improvements over random sampling.
• The study provides a practical blueprint for quantum-enhanced machine learning and outlines future directions for scaling qubit fidelity and algorithm integration.

Unsupervised Machine Learning on a Hybrid Quantum Computer: A Summary

The paper addresses a significant advancement in quantum computing by demonstrating a hybrid quantum-classical algorithm aimed at solving clustering, a key problem in unsupervised machine learning. Utilizing a 19-qubit superconducting quantum processor, the research integrates the quantum approximate optimization algorithm (QAOA) with a classical Bayesian optimization framework to handle clustering tasks formulated as Maxcut problems, a well-known NP-complete problem class.

This paper is framed within the emergent capability of quantum processors to harness quantum distributions — a superset of classical distributions — for computational tasks, particularly to amplify the efficiency and robustness of machine learning algorithms. The hybrid approach proposed marries classical resource accessibility with the unique features of quantum computation, paving the way for improvements over purely classical performance, especially in scenarios involving complex probability distributions and noise resilience.

Key Aspects of the Research

The research leverages advanced quantum algorithmic techniques, particularly:

• Quantum Approximate Optimization Algorithm (QAOA): QAOA serves as the quantum subroutine that encodes clustering into a combinatorial optimization task, specifically Maxcut, and iteratively refines solutions using parameterized quantum circuits.
• Bayesian Optimization: Employed in the classical optimization loop, Bayesian optimization is responsible for navigating the parameter space of QAOA efficiently, exploring angles in such a way as to maximize the probability of deriving the optimal bit-strings.

Results and Observations

The hybrid algorithm was implemented on a custom-crafted 19-qubit quantum processor, showcasing the following results:

• Robustness and Accuracy: Despite gate noise, the system successfully found optimal clusters with high probability, demonstrating the potential effectiveness of quantum-classical hybrid architectures in realistic noisy environments.
• Efficiency Over Random Sampling: The quantum algorithm significantly outperformed random sampling strategies with regards to finding the correct clusters, a statistical advantage quantified through empirical data comparisons.

Practical and Theoretical Implications

Theoretically, this work substantiates the practical utility of quantum computation by demonstrating application-relevant tasks on architecture of increasing complexity. Practically, the paper provides:

• Blueprint for Quantum-Enhanced Learning Tasks: Evidence that hybrid algorithms could, in principle, be deployed in commercial settings for tasks that are classically computationally intensive.
• Insight into Quantum-Classical Synchronization: A methodology for how classical algorithms can complement quantum operations in real-world applications, improving the feasibility of complex problem-solving.

Future Challenges and Developments

While promising, the paper acknowledges the challenges in scaling quantum algorithms in terms of qubit fidelity and quantum gate count. Future research avenues could involve:

• Enhancing Qubit Counts and Gate Fidelity: As optical proposes scaling the quantum computing resources, the goal would be to tackle larger and more complex problem sizes.
• Exploring Other NP-Complete Problems: Utilizing the hybrid framework for a broader class of NP-Complete problems, extending beyond Maxcut.
• Integration into Larger Systems: Designing hybrid algorithms that can seamlessly integrate into existing machine learning platforms, providing standardized interfaces.

In conclusion, this paper exemplifies a pivotal step towards utilizing quantum computing in practical, non-trivial tasks. It lays the groundwork for future explorations into hybridized quantum-classical algorithms, positioning quantum computing as an elevating component in advancing computational efficiencies across varied domains.