Threshold Error Penalty for Fault Tolerant Computation with Nearest Neighbour Communication

The error threshold for fault tolerant quantum computation with concatenated encoding of qubits is penalized by internal communication overhead. Many quantum computation proposals rely on nearest-neighbour communication, which requires excess gate operations. For a qubit stripe with a width of L+1 physical qubits implementing L levels of concatenation, we find that the error threshold of 2.1x10^-5 without any communication burden is reduced to 1.2x10^-7 when gate errors are the dominant source of error. This ~175X penalty in error threshold translates to an ~13X penalty in the amplitude and timing of gate operation control pulses.Comment: minor correctio

Computation by measurements: a unifying picture

The ability to perform a universal set of quantum operations based solely on static resources and measurements presents us with a strikingly novel viewpoint for thinking about quantum computation and its powers. We consider the two major models for doing quantum computation by measurements that have hitherto appeared in the literature and show that they are conceptually closely related by demonstrating a systematic local mapping between them. This way we effectively unify the two models, showing that they make use of interchangeable primitives. With the tools developed for this mapping, we then construct more resource-effective methods for performing computation within both models and propose schemes for the construction of arbitrary graph states employing two-qubit measurements alone.Comment: 13 pages, 18 figures, REVTeX

Tight-binding study of interface states in semiconductor heterojunctions

Localized interface states in abrupt semiconductor heterojunctions are studied within a tight-binding model. The intention is to provide a microscopic foundation for the results of similar studies which were based upon the two-band model within the envelope function approximation. In a two-dimensional description, the tight-binding Hamiltonian is constructed such that the Dirac-like bulk spectrum of the two-band model is recovered in the continuum limit. Localized states in heterojunctions are shown to occur under conditions equivalent to those of the two-band model. In particular, shallow interface states are identified in non-inverted junctions with intersecting bulk dispersion curves. As a specific example, the GaSb-AlSb heterojunction is considered. The matching conditions of the envelope function approximation are analyzed within the tight-binding description.Comment: RevTeX, 11 pages, 3 figures, to appear in Phys. Rev.

Notes

Notes by John M. Anderton, B. M. Apker, J. V. Wilcox, Leonard Boykin, Jr., John J. Broderick, Jr., Thomas F. Broden, Robert F. Burns, John E. Cosgrove, James K. Sugnet, and James D. Sullivan

CdZnTe strip detectors as sub-millimeter resolution imaging gamma radiation spectrometers

We report γ-ray detection performance measurements and computer simulations of a sub-millimeter pitch CdZnTe strip detector. The detector is a prototype for γ-ray measurements in the range of 20-600 keV. The prototype is a 1.5 mm thick, 64×64 orthogonal stripe CdZnTe detector of 0.375 mm pitch in both dimensions, with approximately one square inch of sensitive area. Using discrete laboratory electronics to process signals from an 8×8 stripe region of the prototype we measured good spectroscopic uniformity and sub-pitch (~0.2 mm) spatial resolution in both x and y dimensions. We present below measurements of the spatial uniformity, relative timing and pulse height of the anode and cathode signals. We simulated the photon interactions and signal generation in the strip detector and the test electronics and we compare these results with the data. The data indicate that cathode signal-as well as the anode signal-arises more strongly from the conduction electrons rather than the holes

Performance of CdZnTe strip detectors as sub-millimeter resolution imaging gamma radiation spectrometers

We report & gamma;-ray detection performance measurements and computer simulations of a sub-millimeter pitch CdZnTe strip detector. The detector is a prototype for & gamma;-ray astronomy measurements in the range of 20-200 keV. The prototype is a 1.5 mm thick, 64×64 orthogonal stripeCdZnTe detector of 0.375 mm pitch in both dimensions, with approximately one square inch of sensitive area. Using discrete laboratory electronics to process signals from an 8×8 stripe region of the prototype we measured good spectroscopic uniformity and sub-pitch (~0.2 mm) spatial resolution in both x and y dimensions. We present below measurements of the spatial uniformity, relative timing and pulse height of the anode and cathode signals, and the photon detection efficiency. We also present a technique for determining the location of the event in the third dimension (depth). We simulated the photon interactions and signal generation in the strip detector and the test electronics and we compare these results with the data. The data indicate that the cathode signal-as well as the anode signal-arises more strongly from the conduction electrons rather than the holes

Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements

We introduce the problem of constructing weighted complex projective 2-designs from the union of a family of orthonormal bases. If the weight remains constant across elements of the same basis, then such designs can be interpreted as generalizations of complete sets of mutually unbiased bases, being equivalent whenever the design is composed of d+1 bases in dimension d. We show that, for the purpose of quantum state determination, these designs specify an optimal collection of orthogonal measurements. Using highly nonlinear functions on abelian groups, we construct explicit examples from d+2 orthonormal bases whenever d+1 is a prime power, covering dimensions d=6, 10, and 12, for example, where no complete sets of mutually unbiased bases have thus far been found.Comment: 28 pages, to appear in J. Math. Phy

Balloon-borne coded aperture telescope for arc-minute angular resolution at hard x-ray energies

We are working on the development of a new balloon-borne telescope, MARGIE (minute-of-arc resolution gamma ray imaging experiment). It will be a coded aperture telescope designed to image hard x-rays (in various configurations) over the 20 - 600 keV range with an angular resolution approaching one arc minute. MARGIE will use one (or both) of two different detection plane technologies, each of which is capable of providing event locations with sub-mm accuracies. One such technology involves the use of cadmium zinc telluride (CZT) strip detectors. We have successfully completed a series of laboratory measurements using a prototype CZT detector with 375 micron pitch. Spatial location accuracies of better than 375 microns have been demonstrated. A second type of detection plane would be based on CsI microfiber arrays coupled to a large area silicon CCD readout array. This approach would provide spatial resolutions comparable to that of the CZT prototype. In one possible configuration, the coded mask would be 0.5 mm thick tungsten, with 0.5 mm pixels at a distance of 1.5 m from the central detector giving an angular resolution of 1 arc-minute and a fully coded field of view of 12 degrees. We review the capabilities of the MARGIE telescope and report on the status of our development efforts and our plans for a first balloon flight

Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics

This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z^n which are discrete analogs of the Schr\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of so-called pseudodifference operators (i.e., pseudodifferential operators on the group Z^n) with analytic symbols and on the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunctions of the discrete spectra of the main lattice operators of quantum mechanics, namely: matrix Schr\"{o}dinger operators on Z^n, Dirac operators on Z^3, and square root Klein-Gordon operators on Z^n

Hjelmslev Geometry of Mutually Unbiased Bases

The basic combinatorial properties of a complete set of mutually unbiased bases (MUBs) of a q-dimensional Hilbert space H\_q, q = p^r with p being a prime and r a positive integer, are shown to be qualitatively mimicked by the configuration of points lying on a proper conic in a projective Hjelmslev plane defined over a Galois ring of characteristic p^2 and rank r. The q vectors of a basis of H\_q correspond to the q points of a (so-called) neighbour class and the q+1 MUBs answer to the total number of (pairwise disjoint) neighbour classes on the conic.Comment: 4 pages, 1 figure; extended list of references, figure made more illustrative and in colour; v3 - one more figure and section added, paper made easier to follow, references update