7,382 research outputs found
Classically time-controlled quantum automata
In this paper we introduce classically time-controlled quantum automata or CTQA, which is a slight but reasonable modification of Moore-Crutchfield quantum finite automata that uses time-dependent evolution operators and a scheduler defining how long each operator will run. Surprisingly enough, time-dependent evolutions provide a significant change in the computational power of quantum automata with respect to a discrete quantum model. Furthermore, CTQA presents itself as a new model of computation that provides a different approach to a formal study of “classical control, quantum data” schemes in quantum computing.CONACYT – Consejo Nacional de Ciencia y TecnologĂaPROCIENCI
Methodology for quantum logic gate constructions
We present a general method to construct fault-tolerant quantum logic gates
with a simple primitive, which is an analog of quantum teleportation. The
technique extends previous results based on traditional quantum teleportation
(Gottesman and Chuang, Nature {\bf 402}, 390, 1999) and leads to
straightforward and systematic construction of many fault-tolerant encoded
operations, including the and Toffoli gates. The technique can also be
applied to the construction of remote quantum operations that cannot be
directly performed.Comment: 17 pages, mypsfig2, revtex. Revised with a different title, a new
appendix for clarifying fault-tolerant preparation of quantum states, and
various minor change
Matchgates and classical simulation of quantum circuits
Let G(A,B) denote the 2-qubit gate which acts as the 1-qubit SU(2) gates A
and B in the even and odd parity subspaces respectively, of two qubits. Using a
Clifford algebra formalism we show that arbitrary uniform families of circuits
of these gates, restricted to act only on nearest neighbour (n.n.) qubit lines,
can be classically efficiently simulated. This reproduces a result originally
proved by Valiant using his matchgate formalism, and subsequently related by
others to free fermionic physics. We further show that if the n.n. condition is
slightly relaxed, to allowing the same gates to act only on n.n. and next-n.n.
qubit lines, then the resulting circuits can efficiently perform universal
quantum computation. From this point of view, the gap between efficient
classical and quantum computational power is bridged by a very modest use of a
seemingly innocuous resource (qubit swapping). We also extend the simulation
result above in various ways. In particular, by exploiting properties of
Clifford operations in conjunction with the Jordan-Wigner representation of a
Clifford algebra, we show how one may generalise the simulation result above to
provide further classes of classically efficiently simulatable quantum
circuits, which we call Gaussian quantum circuits.Comment: 18 pages, 2 figure
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