Book Chapter10.1201/9781420035377-5
Universal quantum gates
TL;DR: In this paper, the universality of 2-qudit gates acting on qudits was studied, and it was shown that a primitive gate is primitive if it transforms any decomposable tensor into a decomposition of a tensor tensor.
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Abstract: In this paper we study universality for quantum gates acting on qudits. Qudits are states in a Hilbert space of dimension d where
d can be any integer ≥ 2. We determine which 2-qudit gates V have the
properties: (i) the collection of all 1-qudit gates together with V produces all n-qudit gates up to arbitrary precision, or (ii) the collection
of all 1-qudit gates together with V produces all n-qudit gates exactly.
We show that (i) and (ii) are equivalent conditions on V , and they hold
if and only if V is not a primitive gate. Here we say V is primitive if
it transforms any decomposable tensor into a decomposable tensor. We
discuss some applications and also relations with work of other authors.
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References
Elementary gates for quantum computation.
Adriano Barenco,Charles H. Bennett,Richard Cleve,David P. DiVincenzo,Norman Margolus,Peter W. Shor,Tycho Sleator,John A. Smolin,Harald Weinfurter +8 more
TL;DR: U(2) gates are derived, which derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number of unitary operations on arbitrarily many bits.
4.7K
Quantum computational networks
TL;DR: The theory of quantum computational networks is the quantum generalization of the theory of logic circuits used in classical computing machines, and a single type of gate, the universal quantum gate, together with quantum ‘unit wires' is adequate for constructing networks with any possible quantum computational property.
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Two-bit gates are universal for quantum computation
TL;DR: A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit.
Almost any quantum logic gate is universal.
TL;DR: Almost any quantum logic gate with two or more inputs is computationally universal in that copies of the gate can be "wired together" to effect any desired logic circuit, and to perform any desired unitary transformation on a set of quantum variables.
794
Universality in Quantum Computation
TL;DR: In this article, it was shown that in quantum computation, almost every gate that operates on two or more bits is a universal gate and discussed various physical considerations bearing on the proper definition of universality for computational components such as logic gates.
449