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Bits and Qubits

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Book cover A Primer on Quantum Computing

Part of the book series: SpringerBriefs in Computer Science ((BRIEFSCOMPUTER))

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Abstract

Quantum computing is an interdisciplinary field of research, and it is natural that many people starting in this area should feel uncomfortable with the fundamentals of either computer science or physics. In this chapter, we briefly review the basic concepts necessary to follow the rest of the book.

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Notes

  1. 1.

    Sometimes it may be convenient to have a CNOT with negative control, so that the target bit is flipped if and only if the control bit is zero. A negative control is usually represented in the circuit model by replacing the full bullet • by an empty bullet ∘ on the control line.

  2. 2.

    Currently, there is an excellent website known as the Quantum Algorithm Zoo, available at http://math.nist.gov/quantum/zoo/.

  3. 3.

    Other influential models are adiabatic quantum computing [16, 44] , topological quantum computing [22, 24, 34] , cluster-state quantum computing (a.k.a. measurement-based quantum computing or one-way quantum computing) [35, 40] , quantum Turing machines [14, 45], quantum random access machines (qRAM) [17, 31] , deterministic quantum computing with one qubit (DQC1) [13, 23] , IQP computing (a.k.a. temporally unstructured quantum computations) [8, 42], quantum walks [10, 11, 27], and the quantum query model [2, 6], for instance.

  4. 4.

    T gate is also known in the literature as the π∕8 gate, which may seem a little counterintuitive. The reader should consider that as a special case P(2π∕8).

  5. 5.

    Sometimes it may be convenient to have a CNOT with negative control, so that the target qubit is flipped if and only if the control qubit is \({\left \vert {0}\right \rangle }\). A negative control is usually represented in the circuit model by replacing the full bullet • by an empty bullet ∘ on the control line.

  6. 6.

    Negative controls can also be applied in this case. The notation is the same as the one adopted in classical and quantum CNOTs, that is, replacing the full bullet • by the empty bullet ∘ on the negative control lines.

  7. 7.

    Microsoft LIQUiD can be downloaded from http://stationq.github.io/Liquid. The Microsoft Quantum Development Kit, which includes Q#, can be downloaded from https://www.microsoft.com/en-us/quantum/development-kit.

  8. 8.

    IBM Quantum Experience can be accessed at https://www.research.ibm.com/ibm-q/.

  9. 9.

    ProjectQ can be downloaded from http://projectq.ch.

  10. 10.

    More details at https://www.rigetti.com/qcs.

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Authors and Affiliations

  1. Federal University of Rio de Janeiro, Rio de Janeiro, Rio de Janeiro, Brazil

    Franklin de Lima Marquezino

  2. National Lab of Scientific Computing, PetrĂ³polis, Rio de Janeiro, Brazil

    Renato Portugal

  3. Department of Applied Mathematics (IMECC-UNICAMP), University of Campinas, Campinas, SĂ£o Paulo, Brazil

    Carlile Lavor

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de Lima Marquezino, F., Portugal, R., Lavor, C. (2019). Bits and Qubits. In: A Primer on Quantum Computing. SpringerBriefs in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-030-19066-8_2

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