Quantum Machine Learning: Unleashing the Power of Data

Unsealing the power of Quantum Q bits.

Quantum Computer

Introduction:

Quantum computing has been making significant strides in recent years, paving the way for exciting advancements in various fields. One area of great interest is the intersection of quantum computing and machine learning. Researchers have experimentally demonstrated that quantum computers have a natural ability to solve complex problems with intricate correlations, which can be incredibly challenging for classical computers. This suggests that quantum machine learning models have the potential to offer faster computation and improved generalisation on limited data. However, achieving a "quantum advantage" in machine learning depends not only on the task at hand but also on the available data. In this blog, we explore the concept of quantum advantage in machine learning and delve into the crucial role of data in unlocking its potential.

Computational Power of Data:

To understand quantum advantage, we must first grasp the notion of computational complexity classes. Quantum computers excel at solving problems categorised as bounded quantum polynomial time (BQP), which classical systems struggle with. On the other hand, classical computers handle problems falling under bounded probabilistic polynomial (BPP) efficiently. However, learning algorithms equipped with data from quantum processes introduce a new class of problems called BPP/Samp. These problems can perform certain tasks efficiently, surpassing traditional algorithms that lack access to data. Understanding the quantum advantage requires us to consider the availability of data.

Geometric Test for Quantum Learning Advantage:

To help practitioners assess the potential for quantum advantage in their problems, a workflow for evaluating advantage within a kernel learning framework has been developed. One of the most powerful tests in this workflow is a novel geometric test. In quantum machine learning methods, the data is often quantum-embedded using a quantum computer, and a function is applied to this embedding. The geometric test allows us to compare the quantum embedding, kernel, and data set with classical kernels, helping determine if a quantum advantage is achievable. It quantifies the theoretical amount of data required to bridge the gap between classical and quantum geometries, offering valuable insights for selecting a quantum solution.

Projected Quantum Kernel Approach:

The geometric test revealed that existing quantum kernels often prioritise memorisation over understanding, making them susceptible to being outperformed by classical methods. To address this, a projected quantum kernel was developed. This approach involves projecting the quantum embedding back to a classical representation. While still challenging to compute with classical computers directly, the projected quantum kernel offers practical advantages. It enables the description of non-linear functions, reduces the resources required for processing the kernel, and improves generalization at larger data sizes. The projected quantum kernel expands the potential for quantum advantage while facilitating integration with powerful non-linear classical kernels.

Data Sets Exhibit Learning Advantages:

Quantifying the potential advantage for all possible label functions is essential, but in practice, we are primarily interested in specific label functions. Through learning theoretic approaches, we bounded the generalisation error for specific tasks, including those originating from quantum processes. To ensure scalability to real-world problems, these tasks were verified at reasonably large qubit sizes, up to 30 qubits, using TensorFlow-Quantum. Surprisingly, we discovered that many naturally quantum problems could be efficiently tackled by classical learning methods when provided with sufficient data. This suggests that classical machine learning empowered by data can rival the power of quantum computers. However, our work also demonstrated the existence of label functions where a quantum advantage could be realised, even though this problem was engineered and would require larger and more challenging embedding.

Conclusion:

The role of data is fundamental when considering the potential of quantum computers in aiding machine learning. Our research has provided practical tools for examining the interplay between quantum advantage and data availability. The development of the projected quantum kernel method, with its numerous advantages, represents a significant step forward. We showcased the largest numerical demonstration to date, involving 30 qubits.

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