Quantum Computing With Quasiparticles of the Fractional Quantum Hall Effect

摘要

The focus of this project was the theoretical study of quantum computation based on controlled transfer of individual quasiparticles in systems of quantum antidots in the regime of the Fractional Quantum Hall Effect (FQHE). The work addressed the basic issues of operation of such FQHE qubits as well as related questions of physics of FQHE transport and topological quantum computation. The main parts of our effort were the studies of mechanisms of decoherence, design of single- and two-qubit operations for FQHE qubits, quantitative description of quasiparticle tunnelling between the edges of FQHE liquids, and decoherence properties of some of the generic models of topological quantum computation. The basic conclusion of this project is that the FQHE qubits provide a realistic way of implementation of semiconductor solid-state quantum logic devices competitive with other types of semiconductor qubits. Non- trivial exchange statistics of FQHE quasiparticles should enable convenient realization of the two-qubit operations that does not require the control of the two-particle interaction. For quasiparticles with the non-abelian statistics, the topological nature of this statistics can provide additional stability against decoherence.