Quasi-particle interferometry for logical gates

Abstract

A quantum computer can only function stably if it can execute gates with extreme accuracy. “Topological protection” is a road to such accuracies. Quasi-particle interferometry is a tool for constructing topologically protected gates. Assuming the corrections of the Moore-Read Model for v=5/2's FQHE (Nucl. Phys. B 360, 362 (1991)) we show how to manipulate the collective state of two e/4-charge anti-dots in order to switch said collective state from one carrying trivial SU(2) charge, |1>, to one carrying a fermionic SU(2) charge |ε>. This is a NOT gate on the {|1>, |ε>} qubit and is effected by braiding of an electrically charged quasi particle σ which carries an additional SU(2)-charge. Read-out is accomplished by σ-particle interferometry.

Description

GOVERNMENT RIGHTS [0001] This invention was supported in part by funds from the U.S. Government (National Science Foundation Grant No. DMR-0411800 and Army Research Office Grant No. W911NF-04-1-236). The U.S. Government, therefore, may have certain rights in this invention.BACKGROUND OF THE INVENTION [0002] Since the discovery of the fractional quantum Hall effect (FQHE) in 1982, topological phases of electrons have been a subject of great interest. Many abelian topological phases have been discovered in the context of the quantum Hall regime. More recently, high-temperature superconductivity and other complex materials have provided the impetus for further theoretical studies of and experimental searches for abelian topological phases. The types of microscopic models admitting such phases are now better understood. Much less is known about non-abelian topological phases. They are reputed to be obscure and complicated, and there has been little experimental motivation to consider no...

AI Technical Summary

Benefits of technology

[0013] In order to establish which topological phase the v=5 / 2 plateau is in, one must directly measure quasiparticle braiding statistics. Remarkably, this has never been done even in the case of the usual v=1 / 3 quantum Hall plateau (although in this case, unlike in the v=5 / 2 case, computational solutions of small systems leave little doubt about which topological phase the plateau is in). Part of the problem is that it is difficult to disentangle the phase associated with braiding from the phase which charged particles accumulate in a magnetic field. Ironically, it may actually be easier to measure the effect of non-Abelian braiding statistics because it is not just a phase and is therefore qualitatively different from the effect of the magnetic field.

[0014] A logical gate according to the invention enables the manipulation of a collective quantum state of one or more anti-dots disposed in a fractional quantum Hall effect (FQHE) fluid. A FQHE fluid is an exotic form of matter that arises when electrons at the flat interface of two semiconductors are subjected to a powerful magnetic field and cooled to temperatures close to absolute zero. The electrons on the flat surface form a disorganized liquid sea of electrons, and if some extra electrons are added, quasi-particles called anyons emerge. Quasi-particles are excitations of electrons, and, unlike electrons or protons, anyons can have a charge that is a fraction of a whole number.

Problems solved by technology

Part of the problem is that it is difficult to disentangle the phase associated with braiding from the phase which charged particles accumulate in a magnetic field.

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