Why QML?
Quantum machine learning (QML) combines quantum computing and machine learning by integrating quantum algorithms into the machine learning pipeline.
Competitive Advantage Today
Many QML algorithms do not require advanced quantum hardware. Instead of aiming for exponential speed-ups, they focus on other benefits such as:
Encode Exponentially Large Data Samples: Quantum algorithms can encode and manipulate exponentially larger data samples than classical algorithms by leveraging superposition and entanglement. This can lead to a significant reduction in the number of qubits needed.
Reduced Complexity and Computing Costs: Some quantum machine learning models require significantly fewer training parameters to achieve the same expressive power as classical models.
Smoother Training and Fewer Chances of Overfitting: Variational quantum algorithms and quantum neural networks can offer smoother convergence of the loss function compared to classical models due to the reduced complexity of the resulting model. This often leads to better generalization capacity on the test set.
Explainability: Some quantum machine learning algorithms enhance the explainability of solutions. For instance, quantum Bayesian networks can perform inference more efficiently by exploiting quantum parallelism, providing direct access to joint and marginal probability distributions and a deeper understanding of causal relationships between nodes.
Efficiency: Quantum computing excels in solving optimization problems like graph partitions (Maxcut) or combinatorial problems (QUBO). Many machine learning problems can be formulated as combinatorial optimization problems.
Novel Representations of Data: Selecting suitable representations for input data is essential for achieving optimal performance in many classification or regression algorithms. Quantum algorithms, such as quantum kernel methods, can generate novel data representations that are challenging or impossible to create with classical kernels.
Efficient Sampling: The probabilistic nature of quantum computing allows for the generation of realistic distributions, useful in quantum generative models that leverage quantum mechanics to generate complex data distributions. Quantum generative models often demonstrate better generalization, especially when data is scarce.
Even Greater Advantage Tomorrow
Other QML algorithms promise significant benefits over classical methods, but they require advanced quantum hardware. Here’s what will be possible when the hardware is ready.
Fourier Transform: The Fourier Transform is used in tasks like speech recognition, audio analysis, and vibration analysis. It helps extract frequency-based features from raw signals and is also used for denoising, image filtering, and audio compression. Classically, it operates with a complexity of O(NlogN) for N data points. The quantum version (Quantum Fourier Transform) achieves this with a complexity of only O(log2(N)), offering an exponential advantage.
Solving Linear Systems of Equations: The Harrow-Hassidim-Lloyd (HHL) Algorithm solves systems of linear equations, which is a common requirement in many machine learning models such as support vector machines and recommender systems. Classical algorithms, like the Conjugate Gradient method, have polynomial complexity O(N⋅k) where k is the condition number of the matrix. The HHL algorithm, however, operates with a complexity of O(log(N)⋅poly(k,1ϵ)), where ϵ is the desired precision of the solution. This represents an exponential speedup in terms of dimensionality, assuming k and 1ϵ are manageable.
Diagonalizing Matrices: The Quantum Phase Estimation (QPE) algorithm is used to estimate the eigenvalues of a unitary operator. In spectral graph theory applications, such as spectral clustering, QPE can be used to find the eigenvalues of the graph Laplacian, significantly speeding up the clustering process. Principal component analysis, a method for dimensionality reduction, also involves solving eigenvalue problems, which can be accelerated using QPE. The classical complexity of these problems is around O(N2), while the quantum complexity can be reduced to O(log2(N)), providing an exponential advantage.