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Supervised Learning with Quantum Computers

Part of the book series: Quantum Science and Technology ((QST))

Abstract

If we want to use a quantum computer to learn from classical data—which was in the introduction referred to as the CQ case—we have to think about how to represent features by a quantum system. We furthermore have to design a recipe for “loading” data from a classical memory into the quantum computer. In quantum computing, this process is called state preparation and constructs the initial state that is the input of the quantum machine learning algorithm.

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Notes

  1. 1.

    This is not only true for quantum machine learning algorithms. For example, the classically hard graph isomorphism problem is efficiently solvable on a quantum computer if a superposition of isomorph graphs can be created efficiently [1].

  2. 2.

    Bernoulli sampling is equivalent to a (biased) coin toss experiment: We flip a coin S times and want to estimate the bias p, i.e. with what probability the coin produces ‘heads’.

  3. 3.

    Note that there are effective nonlinear dynamics, see for example [31].

  4. 4.

    Hamiltonian simulation research can be distinguished into analog and digital approaches to simulation. Roughly speaking, analog simulation finds quantum systems that “naturally” simulate Hamiltonians, while digital simulation decomposes the time evolution into quantum gates, which is more relevant in the context of this book.

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Author information

Authors and Affiliations

  1. School of Chemistry and Physics, Quantum Research Group, University of KwaZulu-Natal, Durban, South Africa

    Maria Schuld

  2. National Institute for Theoretical Physics (NITheP), KwaZulu-Natal, South Africa

    Maria Schuld & Francesco Petruccione

  3. Xanadu Quantum Computing Inc, Toronto, Canada

    Maria Schuld

  4. School of Chemistry and Physics, University of KwaZulu-Natal, Durban, South Africa

    Francesco Petruccione

  5. School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea

    Francesco Petruccione

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  1. Maria Schuld
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  2. Francesco Petruccione
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Correspondence to Maria Schuld .

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Schuld, M., Petruccione, F. (2018). Information Encoding. In: Supervised Learning with Quantum Computers. Quantum Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-96424-9_5

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