quantum algorithms:
With braiding
With duals for objects
category with duals (list of them)
dualizable object (what they have)
ribbon category, a.k.a. tortile category
With duals for morphisms
monoidal dagger-category?
With traces
Closed structure
Special sorts of products
Semisimplicity
Morphisms
Internal monoids
Examples
Theorems
In higher category theory
Analogously to how a classical logic gate is a function between (finite) sets of tuples of bits (truth values), so a quantum logic gate is a (unitary) linear operator on (finite-dimensional) Hilbert spaces of tensor products of qbits:
Specifically, one calls such a linear map a quantum gate if it is thought of as potentially implemented as a basic operation performed by a quantum computing machine.
As such, typical quantum logic gates operate on a small number of qbits, with more complicated such linear maps obtained by composing a given set of quantum logic gates into quantum logic circuits. Such compilation is hence one model of quantum computation.
The first examples are linearizations of classical logic gates, or rather of their reversible versions:
AND:
The following examples have no classical analog:
(…)
(…)
The notion of quantum logic gates and quantum circuits originates with
Richard Feynman, Quantum mechanical computers, Foundations of Physics 16 (1986) 507–531 [doi:10.1007/BF01886518]
David E. Deutsch, Quantum computational networks, Proceedings of the Royal Society A, 425 1868 (1989) 73-90 [doi:10.1098/rspa.1989.0099, jstor:2398494]
Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, Harald Weinfurter, Elementary gates for quantum computation, Phys. Rev. A52 (1995) 3457 [arXiv:quant-ph/9503016, doi:10.1103/PhysRevA.52.3457]
See also:
Implementation of quantum logic gates on qbits realized via nucleon-spin, via pulse protocols in nuclear magnetic resonance-technology:
and analogously on electron-spin:
Last revised on September 18, 2023 at 09:05:43. See the history of this page for a list of all contributions to it.