InterJournal Complex Systems, 85
Status: Accepted
Manuscript Number: [85]
Submission Date: 963011
Quantum logic on qubytes
Author(s): Wojciech Zurek , Raymond Laflamme

Subject(s): CX.09

Category: Brief Article

Abstract:

Quantum computation can be thought of as a massive parallel Monte-Carlo simulation, in which all of the conceivable paths are explored starting from a superposition of all the possible candidate answers. However, owing to the phase relation between the different paths, the wrong alternatives interfere destructively, and the probability at the output is peaked about the correct answers. Most importantly, this is a quantum Monte-Carlo: the superposition principle allows for all the paths to be explored simultaneously. To carry out such a quantum computation, phase relations between the alternatives must be preserved, and small software and hardware errors must be corrected. We show how to carry out quantum logical operations (controlled-not and Toffoli gates) on encoded qubits (qubytes) for several encodings which protect against various 1-bit errors. This improves the reliability of these operations by allowing one to correct for one bit errors which either preexisted or occurred in course of the operation. The logical operations we consider are classically universal, and allow one to carry out the vast majority of the steps in the quantum factoring algorithm. Thus, our results help bring quantum factoring and other quantum computations closer to reality.

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