6 research outputs found
Quantum gates and quantum algorithms with Clifford algebra technique
We use our Clifford algebra technique, that is nilpotents and projectors
which are binomials of the Clifford algebra objects with the
property , for representing quantum
gates and quantum algorithms needed in quantum computers in an elegant way. We
identify -qubits with spinor representations of the group SO(1,3) for a
system of spinors. Representations are expressed in terms of products of
projectors and nilpotents. An algorithm for extracting a particular information
out of a general superposition of qubit states is presented. It
reproduces for a particular choice of the initial state the Grover's algorithm.Comment: 9 pages, revte
Clifford algebras and universal sets of quantum gates
In this paper is shown an application of Clifford algebras to the
construction of computationally universal sets of quantum gates for -qubit
systems. It is based on the well-known application of Lie algebras together
with the especially simple commutation law for Clifford algebras, which states
that all basic elements either commute or anticommute.Comment: 4 pages, REVTeX (2 col.), low-level language corrections, PR
Simulating Physical Phenomena by Quantum Networks
Physical systems, characterized by an ensemble of interacting elementary
constituents, can be represented and studied by different algebras of
observables or operators. For example, a fully polarized electronic system can
be investigated by means of the algebra generated by the usual fermionic
creation and annihilation operators, or by using the algebra of Pauli
(spin-1/2) operators. The correspondence between the two algebras is given by
the Jordan-Wigner isomorphism. As we previously noted similar one-to-one
mappings enable one to represent any physical system in a quantum computer. In
this paper we evolve and exploit this fundamental concept in quantum
information processing to simulate generic physical phenomena by quantum
networks. We give quantum circuits useful for the efficient evaluation of the
physical properties (e.g, spectrum of observables or relevant correlation
functions) of an arbitrary system with Hamiltonian .Comment: 44 pages, 15 psfigur