Quantum Machine Learning Sidesteps Costly Steps with Direct Matrix Training

A new approach, termed “soft-quantum algorithms”, tackles lengthy training times and limitations in quantum machine learning by directly training matrices while preserving unitarity through a unique regularization technique. Basil Kyriacou and colleagues have bypassed the need to decompose data into complex gate operations, offering a speedup demonstrated on a five-qubit classification task where training completed in under four minutes, compared to over two hours using conventional methods. The team successfully integrated these soft-unitaries into a hybrid quantum-classical reinforcement learning agent, achieving performance gains over a classical counterpart and suggesting a pathway towards more efficient and scalable quantum machine learning applications.

Soft-unitary optimisation accelerates five-qubit classification and enhances reinforcement learning

A five-qubit supervised classification task now takes under four minutes to train using a variational quantum circuit, a reduction from over two hours previously required for direct circuit training. Conventional methods struggle with the computational demands of decomposing data into complex gate operations, effectively making such tasks impractical with limited quantum resources. Variational quantum circuits (VQCs) are a promising avenue for quantum machine learning, employing parameterised quantum circuits whose parameters are optimised to perform a specific task. However, the training of VQCs is often hampered by the ‘barren plateau’ phenomenon, where gradients vanish exponentially with the number of qubits, and the computational cost of simulating quantum circuits scales exponentially with the number of qubits. This new technique circumvents this bottleneck by directly optimising the matrices representing quantum operations, offering a pathway to scalable quantum machine learning. The conventional approach involves expressing the desired quantum operation as a sequence of elementary quantum gates, a process that becomes increasingly complex and computationally expensive as the circuit depth increases. By directly optimising the matrix elements, the researchers avoid this decomposition step, significantly reducing the computational burden.

Better performance than a purely classical network of comparable size on the cartpole task resulted from embedding soft-unitaries into a hybrid quantum-classical reinforcement learning agent. Experiments with this approach on the cartpole task achieved a mean duration of 417.0 over 340 episodes. The cartpole task is a classic control problem in reinforcement learning, where an agent must learn to balance a pole on a moving cart. The use of a hybrid quantum-classical agent allows the quantum component to potentially accelerate the learning process by efficiently representing and processing complex state spaces. The final soft-unitaries deviated from perfect unitarity by only 3 × 10−4, suggesting a well-trained model despite the approximation used. Unitarity is a fundamental requirement for quantum operations, ensuring that probability is conserved during the evolution of the quantum state. The small deviation from perfect unitarity indicates that the regularization technique effectively constrains the optimisation process, preventing the model from diverging into physically unrealistic solutions. These results, however, are limited to problems involving 1000 datapoints and five qubits. The limited scale of the initial experiments highlights the need for further research to assess the scalability and generalizability of the soft-quantum algorithm to larger and more complex problems.

Further investigation is needed to evaluate performance on larger, more complex datasets relevant to practical applications. Direct training of matrix elements can be faster than decomposing data and parameters into gates for few-qubit problems with large datasets. A regularization term added to the loss function maintains unitarity during training, yielding these soft-unitaries, and a second training step, circuit alignment, recovers a gate-based architecture from the resulting soft-unitary. The regularization term penalizes deviations from unitarity, encouraging the optimisation algorithm to find solutions that are close to being unitary. Circuit alignment is a crucial step that maps the optimised soft-unitary back to a physically realizable quantum circuit, allowing the algorithm to be implemented on actual quantum hardware. This process involves decomposing the soft-unitary into a sequence of standard quantum gates, which can be executed on a quantum computer. The choice of decomposition algorithm and the resulting circuit depth can significantly impact the performance and fidelity of the quantum computation.

Direct matrix training streamlines optimisation for small-scale quantum circuits

This new approach to training quantum circuits offers a clear speed advantage, but it is not a universally applicable fix for the challenges facing quantum machine learning. The limitations of the five-qubit system and 1000-datapoint dataset are acknowledged, raising concerns about scalability as problems grow more complex, potentially diminishing the benefits of direct matrix training. The computational complexity of training the matrix elements also increases with the number of qubits, potentially offsetting the gains achieved by avoiding circuit decomposition. Despite the limited scale of this initial demonstration, the findings represent a valuable step forward. The current generation of quantum computers, known as noisy intermediate-scale quantum (NISQ) devices, are characterised by a limited number of qubits and high error rates. These limitations pose significant challenges for quantum machine learning algorithms, requiring sophisticated error mitigation techniques and efficient training strategies.

Quantum circuits, which use quantum bits or qubits, are notoriously difficult to train due to the complex calculations involved. This method offers a potential route to sidestep some of those hurdles by optimising the underlying mathematical representations with a process of regularization. The inherent complexity arises from the high-dimensional parameter space and the non-convex nature of the optimisation landscape. By sidestepping the computational cost of building circuits gate by gate, this direct training method offers a faster route to developing variational quantum circuits, a type of quantum computer program designed to learn from data. VQCs are particularly well-suited for tasks such as classification, regression, and generative modelling. The five-qubit system demonstrated a substantial improvement in training time during experiments, and future work will focus on exploring the limits of this technique and investigating methods to improve its scalability. Future research directions include exploring different regularization techniques, developing more efficient circuit alignment algorithms, and investigating the potential of combining soft-quantum algorithms with other quantum machine learning techniques, such as quantum kernel methods and quantum generative adversarial networks. The ultimate goal is to develop quantum machine learning algorithms that can outperform classical algorithms on real-world problems, unlocking the full potential of quantum computation.

The researchers successfully trained a variational quantum circuit using a two-step process involving direct matrix training and circuit alignment. This method reduces training time, achieving results in under four minutes for a five-qubit classification task with 1000 datapoints, compared to over two hours with conventional circuit training. Furthermore, the resulting soft-unitary matrices improved performance in a reinforcement learning task, outperforming a classical baseline. The authors intend to explore scalability and alternative regularization techniques in future work.