Quantum Machine Learning Gains Accuracy Despite Increasing Circuit Complexity

Researchers at the University of Sharjah in collaboration with New York University Abu Dhabi and NYUAD Research Institute have undertaken a detailed investigation into the scaling behaviour of hybrid quantum neural networks, offering valuable insights into optimising their performance with increasing computational complexity. Danil Vyskubov and colleagues systematically explored the effects of both quantum layer count and qubit number on the accuracy and underlying quantum behaviour. Their controlled scaling study, conducted across multiple datasets, reveals key scaling trends and saturation points. This offers practical advice for optimising hybrid quantum-classical classifiers. The study also provides a standardised evaluation protocol, representing a vital step towards understanding and improving the capabilities of quantum machine learning.

Sustained entanglement growth favours wider quantum circuits over increased depth

Hybrid quantum-classical neural networks represent a promising avenue for machine learning, leveraging the potential of quantum computation to enhance classical algorithms. However, understanding how these networks scale with increasing resources, specifically the number of qubits and the depth of the quantum circuit, is crucial for practical implementation. Previous research has often been hampered by a lack of systematic studies controlling for these variables, leading to inconsistent results and difficulty in drawing generalisable conclusions. This work addresses this gap by presenting a controlled scaling study along two primary axes: increasing the number of quantum layers, L, at a fixed number of qubits, Q, and increasing the number of qubits, Q, at a fixed depth, L. The team employed multiple datasets to ensure the robustness of their findings and to identify dataset-dependent behaviours.

Entanglement, a key quantum resource, was found to consistently increase by up to 35% with increasing qubit count. This level of sustained growth is significant, as previous optimisation challenges at fixed circuit depth had previously limited the ability to reliably enhance entanglement. Increasing the number of qubits in a quantum circuit demonstrably boosts quantum expressibility, the ability of the circuit to represent a wide range of functions, and entanglement. In contrast, deepening the circuit, i.e., increasing the number of sequential quantum operations, exhibits dataset-dependent performance saturation and optimisation instability. Across three benchmark image datasets, the team systematically varied circuit depth and width while maintaining consistent training budgets, revealing that performance plateaus are common with increased layers but not with increased qubits. This suggests that, for many applications, prioritising qubit count over circuit depth may be a more effective strategy for improving performance.

F1 score evaluation of predictive performance showed varying trends as qubit count increased, dependent on the number of quantum layers. This highlights the interplay between circuit architecture and dataset characteristics. Quantum Circuit Expressibility (QCE), a metric quantifying the diversity of functions a quantum circuit can represent, and Entanglement Entropy Estimate (EEE), a measure of the entanglement within the quantum state, both changed alongside these performance trends, revealing dataset-dependent scaling regimes and saturation points. The correlation between these quantum properties and predictive performance provides valuable insights into the underlying mechanisms driving the observed behaviour. A consistent evaluation protocol is now available, providing guidance for selecting circuit width and depth in hybrid quantum-classical classifiers for improved performance. This protocol details the specific datasets used, the range of qubit counts and layer depths explored, and the metrics employed for evaluation, allowing other researchers to reproduce and extend these findings.

Pinpointing the reasons for these variations requires further investigation, as the reasons why certain datasets respond differently to changes in circuit depth remain unclear. It is hypothesised that the inherent structure and complexity of each dataset influence its susceptibility to the limitations imposed by increased circuit depth. Datasets with more complex features may benefit more from the increased expressibility afforded by a wider circuit, while simpler datasets may be more prone to overfitting with deeper circuits. A clear method for evaluating and comparing hybrid quantum-classical neural networks, or QNNs, is key for accelerating progress in quantum machine learning. This systematic investigation clarifies how expanding either the computational power or the complexity of hybrid quantum-classical networks impacts performance, allowing assessment of the impact of varying qubit counts and circuit depth. The implications extend beyond improving performance; a better understanding of scaling behaviour is crucial for determining the feasibility of deploying QNNs on near-term quantum hardware, where qubit counts and circuit depths are still limited.

Independently varying qubit count and the number of sequential quantum operations established a standardised method for evaluating these models. This approach allows for a more nuanced understanding of the trade-offs between circuit complexity and performance. A measure of interconnectedness between quantum bits, entanglement, and quantum properties like expressibility consistently enhance with increasing qubits. This suggests that increasing the ‘width’ of the quantum circuit is a more reliable path to improved performance than simply increasing its ‘depth’. However, simply adding more layers does not guarantee improvement, and can introduce dataset-dependent limitations and optimisation challenges. The study’s findings have implications for the development of quantum algorithms for a range of applications, including image recognition, natural language processing, and materials discovery. Further research is needed to explore the optimal balance between circuit depth and width for specific tasks and datasets, and to investigate the potential benefits of incorporating other quantum resources, such as coherence and superposition, into hybrid quantum-classical architectures.

The research demonstrated that increasing the number of qubits in hybrid quantum-classical neural networks generally improves performance, whereas simply adding more quantum layers does not consistently yield better results. This matters because it provides guidance on how to best utilise limited quantum resources, such as qubit counts and circuit depth, in near-term quantum hardware. By establishing a standardised evaluation protocol, the study clarifies the relationship between quantum properties and predictive performance across multiple datasets. The authors suggest future work will focus on optimising the balance between circuit depth and width for specific applications.