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Quasi-particle interferometry for logical gatesQuasi-particle interferometry for logical gates description/claimsThe Patent Description & Claims data below is from USPTO Patent Application 20070170952, Quasi-particle interferometry for logical gates. Brief Patent Description - Full Patent Description - Patent Application Claims
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 non-abelian topological phases. However, non-abelian topological states would be an attractive milieu for quantum computation. [0003] It has become increasingly clear that if a new generation of computers could be built to exploit quantum mechanical superpositions, enormous technological implications would follow. In particular, solid state physics, chemistry, and medicine would have a powerful new tool, and cryptography also would be revolutionized. [0004] The standard approach to quantum computation is predicated on the quantum bit ("qubit") model in which one anticipates computing on a local degree of freedom such as a nuclear spin. In a qubit computer, each bit of information is typically encoded in the state of a single particle, such as an electron or photon. This makes the information vulnerable. If a disturbance in the environment changes the state of the particle, the information is lost forever. This is known as decoherence--the loss of the quantum character of the state (i.e., the tendency of the system to become classical). All schemes for controlling decoherence must reach a very demanding and possibly unrealizable accuracy threshold to function. [0005] Topology has been suggested to stabilize quantum information. A topological quantum computer would encode information not in the conventional zeros and ones, but in the configurations of different braids, which are similar to knots but consist of several different threads intertwined around each other. The computer would physically weave braids in space-time, and then nature would take over, carrying out complex calculations very quickly. By encoding information in braids instead of single particles, a topological quantum computer does not require the strenuous isolation of the qubit model and represents a new approach to the problem of decoherence. [0006] In 1997, there were independent proposals by Kitaev and Freedman that quantum computing might be accomplished if the "physical Hilbert space" V of a sufficiently rich TQFT (topological quantum field theory) could be manufactured and manipulated. Hilbert space describes the degrees of freedom in a system. The mathematical construct V would need to be realized as a new and remarkable state for matter and then manipulated at will. [0007] The computational power of a quantum mechanical Hilbert space is potentially far greater than that of any classical device. However, it is difficult to harness it because much of the quantum information contained in a system is encoded in phase relations which one might expect to be easily destroyed by its interactions with the outside world ("decoherence" or "error"). Therefore, error-correction is particularly important for quantum computation. Fortunately, it is possible to represent information redundantly so that errors can be diagnosed and corrected. [0008] An interesting analogy with topology suggests itself: local geometry is a redundant way of encoding topology. Slightly denting or stretching a surface such as a torus does not change its genus, and small punctures can be easily repaired to keep the topology unchanged. Only large changes in the local geometry change the topology of the surface. Remarkably, there are states of matter for which this is more than just an analogy. A system with many microscopic degrees of freedom can have ground states whose degeneracy is determined by the topology of the system. The excitations of such a system have exotic braiding statistics, which is a topological effective interaction between them. Such a system is said to be in a topological phase. The unusual characteristics of quasiparticles in such states can lead to remarkable physical properties, such as a fractional quantized Hall conductance. Such states also have intrinsic fault-tolerance. Since the ground states are sensitive only to the topology of the system, interactions with the environment, which are presumably local, cannot cause transitions between ground states unless the environment supplies enough energy to create excitations which can migrate across the system and affect its topology. When the temperature is low compared to the energy gap of the system, such events will be exponentially rare. [0009] A different problem now arises: if the quantum information is so well-protected from the outside world, then how can we--presumably part of the outside world--manipulate it to perform a computation? The answer is that we must manipulate the topology of the system. In this regard, an important distinction must be made between different types of topological phases. In the case of those states which are Abelian, we can only alter the phase of the state by braiding quasiparticles. In the non-Abelian case, however, there will be a set of g>1 degenerate states, .PSI..sub.a, a=1, 2, . . . , g of particles at x.sub.1,x.sub.2, . . . , x.sub.n. Exchanging particles 1 and 2 might do more than just change the phase of the wave function. It might rotate it into a different one in the space spanned by the .PSI..sub.aS: .psi. a .fwdarw. M ab 12 .times. .psi. b ( 1 ) [0010] On the other hand, exchanging particles 2 and 3 leads to .psi. a .fwdarw. M ab 23 .times. .psi. b . If M.sub.ab.sup.12 and M.sub.ab.sup.23 do not commute (for at least some pairs of particles), then the particles obey non-Abelian braiding statistics. In the case of a large class of states, the repeated application of raiding transformations M.sub.ab.sup.ij allows one to approximate any desired unitary transformation to arbitrary accuracy and, in this sense, they are universal quantum computers. Unfortunately, no non-Abelian topological states have been unambiguously identified so far. Some proposals have been put forward for how such states might arise in highly frustrated magnets, where such states might be stabilized by very large energy gaps on the order of magnetic exchange couplings, but the best prospects in the short run are in quantum Hall systems, where Abelian topological phases are already known to exist. [0011] The best candidate is the quantized Hall plateau with .sigma. ab = 5 2 .times. e 2 h . The 5/2 fractional quantum Hall state (as well as its particle-hole symmetric analog, the 7/2 state) is now routinely observed in high-quality (i.e., low-disorder) samples. In addition, extensive numerical work using finite-size diagonalization and wavefunction overlap calculations indicates that the 5/2 state belongs to the non-Abelian topological phase characterized by a Pfaffian quantum Hall wavefunction. The set of transformations generated by braiding quasiparticle excitations in the Pfaffian state is not computationally universal (i.e., is not dense in the unitary group), but other non-Abelian states in the same family are. Thus, it is important to (a) determine if the v=5/2 state is, indeed, in the Pfaffian universality class and, if so, to (b) use it to store and manipulate quantum information. SUMMARY OF THE INVENTION [0012] An experimental device as described herein can address both of the aforementioned determinations. Features of such a device are inspired by anti-dot experiments measuring the charge of quasiparticles in Abelian fractional quantum Hall states such as v=1/3 and proposals for measuring their statistics. Our measurement procedure relies upon quantum interference as in the electronic Mach-Zehnder interferometer in which Aharonov-Bohm oscillations were observed in a two dimensional electron gas. [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. [0015] Anti-dots are "holes" in the FQHE fluid created by charge, i.e., islands of higher potential where the FQHE fluid does not exist. Anti-dots are not quasi particles, per se, but can have a quasi-particle charge. The collective quantum state of the one or more anti-dots may be a state carrying trivial SU(2) charge |1>, or a state carrying a fermionic SU(2) charge |.epsilon.>. [0016] The collective state of the quasi-particles may be read out by drawing an output current out of the quantum Hall fluid. The value of the output current will indicate whether the collective state is |1> or |.epsilon.>. The state can be the state of a single anti-dot, or the collective state of two or more anti-dots. [0017] To operate the logical gate, i.e., to flip between states |1> and |.epsilon.>, a .sigma. quasi-particle may be caused to tunnel by adjusting the electrical potential on conductive gates that are provided for adjusting electrical potentials confining a fractional quantum Hall fluid. Tunneling of the quasi-particle may deform the contours of the FQHE fluid. It should be understood that quasi-particles tunnel more easily than electrons because quasi-particles have less charge being in essence electron fractions. [0018] As described in detail below, quasi-particle interferometry by electrically charged particles may be used to build logical gates and read out for quantum computers, as realized in a system for implementing a NOT-gate in v=5/2 FQHE systems. BRIEF DESCRIPTION OF THE DRAWINGS [0019] FIGS. 1A-1D depict links formed by taking a quasiparticle around a qubit pair. [0020] FIG. 2 depicts an example embodiment of a NOT gate for a quantum computer. [0021] FIG. 3 is a block diagram showing an example computing environment in which aspects of the invention may be implemented. DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS Continue reading about Quasi-particle interferometry for logical gates... 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