Abstract
In this chapter we introduced the idea of a quantum gate, and contrasted it with logically irreversible and logically reversible classical gates. Quantum gates are, like classical reversible gates, logically reversible, but they differ markedly on their universality properties. Whereas the smallest universal classical reversible gates have to use three bits, the smallest universal quantum gates need only use two bits. As the classical reversible gates are also unitary, it is conceivable that one of the first practical applications of quantum gates is in non-standard (e.g., “spintronic”) implementations of classical reversible computers.
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Notes
- 1.
Source: Opening words of the “Atoms in a SmallWorld” section of Richard Feynman’s classic talk “There’s Plenty of Room at the Bottom,” given on 29th December 1959 at the annual meeting of the American Physical Society at the California Institute of Technology. The full transcript of the talk is available at http://www.zyvex.com/nanotech/feynman.html.
- 2.
What we call an “ancilla bit” is also referred to as a “storage bit” or a “garbage bit” in the literature.
- 3.
A balanced function on {0,1}n returns a value “1” for 2n−1 of its inputs and a value “0” for the other 2n−1 inputs.
- 4.
If A and B are two matrices B is the inverse of A when A.B = 1 where 1 is the identity matrix, i.e., a matrix having only ones down the main diagonal.
- 5.
N.B. the leading “1” in the series expansion of the exponential function is replaced with the identity matrix, 1.
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Williams, C.P. (2011). Quantum Gates. In: Explorations in Quantum Computing. Texts in Computer Science. Springer, London. https://doi.org/10.1007/978-1-84628-887-6_2
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