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Quantum computing methods for supervised learning


The last two decades have seen an explosive growth in the theory and practice of both quantum computing and machine learning. Modern machine learning systems process huge volumes of data and demand massive computational power. As silicon semiconductor miniaturization approaches its physics limits, quantum computing is increasingly being considered to cater to these computational needs in the future. Small-scale quantum computers and quantum annealers have been built and are already being sold commercially. Quantum computers can benefit machine learning research and application across all science and engineering domains. However, owing to its roots in quantum mechanics, research in this field has so far been confined within the purview of the physics community, and most work is not easily accessible to researchers from other disciplines. In this paper, we provide a background and summarize key results of quantum computing before exploring its application to supervised machine learning problems. By eschewing results from physics that have little bearing on quantum computation, we hope to make this introduction accessible to data scientists, machine learning practitioners, and researchers from across disciplines.

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Fig. 1


  1. 1.

    Different interpretations exist regarding the collapse of the quantum state (Schlosshauer et al. 2013). The popular Copenhagen Interpretation suggests that the wave function of a quantum system collapses on observation. The alternative Many Worlds Interpretation suggests that there is no collapse of the wave function; instead, the act of observation results in the observer getting entangled with the observed system.

  2. 2.

    Although perfect cloning is impossible, Bužek and Hillery (1996) proposed a universal cloning machine that can make imperfect copies of unknown quantum states with high fidelity.

  3. 3.

    In the context of quantum computing, an adiabatic process is a process which changes the state of a system so gradually that the state can adapt its configuration at each point.

  4. 4.

    The Hamiltonian operator represents the total energy of the system.

  5. 5.

    The recent quantum supremacy experiment conducted by Google used only 54 qubits (Arute et al. 2019).

  6. 6.

    Input qubits that do not hold any input data but are added to satisfy other conditions (most often reversibility of the transformation) are called auxiliary or ancillary qubits.

  7. 7.

    The quantum phase estimation algorithm can estimate the phase (or eigenvalue) of an eigenvector of a unitary operator.

  8. 8.

    This is the general form used in modern feedforward neural networks. The original perceptron used a step activation function and produced only binary outputs 0 and 1.

  9. 9.

    Many informal texts now relegate all other learning algorithms to the category conventional machine learning.

  10. 10.

    Developing a quantum alternative to a classical computation technique is often referred to as quantizing it although we prefer this term is used sparingly.

  11. 11.

    Quantum dots are nanometre-scale semiconductor particles.

  12. 12.

    Quantum tomography is the process by which a quantum state is reconstructed using measurements on an ensemble of identical quantum states.


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Kulkarni, V., Kulkarni, M. & Pant, A. Quantum computing methods for supervised learning. Quantum Mach. Intell. 3, 23 (2021).

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  • Quantum machine learning
  • Quantum computing
  • Machine learning
  • Artificial intelligence