Chapman & Hall/CRC eBooks

Invertible digital circuits and their quantum emulations

Helmut Bez, Tony Croft

Published Jan 6, 2023• 0 citations

Abstract

Black box representations of functions, by definition, do not provide information on how a function, so represented, is computed. By a ‘circuit’ for the computation of a function we mean a sequence of ‘basic’ gates that implement the function. It can be shown that, given a classical circuit for the Boolean function https://www.w3.org/1998/Math/MathML" display="inline"> f ^ https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003264569/7139ce19-0d58-4a0c-820f-b76fb033e438/content/math18_1.tif "/> , there is a quantum circuit of equal ‘efficiency’ for the implementation of the unitary operator https://www.w3.org/1998/Math/MathML" display="inline"> U f ^ https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003264569/7139ce19-0d58-4a0c-820f-b76fb033e438/content/math18_2.tif "/> and hence the quantum computation of f . In this chapter we consider examples of invertible digital functions and their evaluation using basic invertible Boolean gates; specifically the Toffoli and Feynman gates T D and F D . We recall that the Toffoli gate is complete for invertible digital computation, however, the inclusion of the Feynman gate, F D , simplifies the circuits. We proceed by example to demonstrate the process and consequential side-effects of such implementations and their quantum emulations. It is seen that the cost of using only Toffoli gates is that additional input bits/qubits may be required, and the computation of intermediate results (usually referred to as garbage or junk) may be necessary. We also consider a general circuit for re-setting registers containing ‘junk’, this is helpful to avoid problems with downstream computation.

DOI: 10.1201/9781003264569-18

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Chapman & Hall/CRC eBooksJan 6, 20230 citations

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Chapman & Hall/CRC eBooksJan 6, 20230 citations

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