Quantum Computers, Factoring, and Decoherence

In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large numbers -- a problem of great practical significance because of its cryptographic applications. Instead of the nearly exponential ($\sim \exp L^{1/3}$, for a number with $L$ digits) time required by the fastest classical algorithm, the quantum algorithm gives factors in a time polynomial in $L$ ($\sim L^2$). This enormous speed-up is possible in principle because quantum computation can simultaneously follow all of the paths corresponding to the distinct classical inputs, obtaining the solution as a result of coherent quantum interference between the alternatives. Hence, a quantum computer is sophisticated interference device, and it is essential for its quantum state to remain coherent in the course of the operation. In this report we investigate the effect of decoherence on the quantum factorization algorithm and establish an upper bound on a ``quantum factorizable'' $L$ based on the decoherence suffered per operational step.Comment: 7 pages,LaTex + 2 postcript figures in a uuencoded fil

Extended Quantum XOR Gate in Terms of Two-Spin Interactions

Considerations of feasibility of quantum computing lead to the study of multispin quantum gates in which the input and output two-state systems (spins) are not identical. We provide a general discussion of this approach and then propose an explicit two-spin interaction Hamiltonian which accomplishes the quantum XOR gate function for a system of three spins: two input and one output.Comment: 15 pages in plain TeX with 1 Postscript figur

Sudden death of effective entanglement

Sudden death of entanglement is a well-known effect resulting from the finite volume of separable states. We study the case when the observer has a limited measurement capability and analyse the effective entanglement, i.e. entanglement minimized over the output data. We show that in the well defined system of two quantum dots monitored by single electron transistors, one may observe a sudden death of effective entanglement when real, physical entanglement is still alive. For certain measurement setups, this occurs even for initial states for which sudden death of physical entanglement is not possible at all. The principles of the analysis may be applied to other analogous scenarios, such as etimation of the parameters arising from quantum process tomography.Comment: final version, 5 pages, 3 figure

Switchable coupling for superconducting qubits using double resonance in the presence of crosstalk

Several methods have been proposed recently to achieve switchable coupling between superconducting qubits. We discuss some of the main considerations regarding the feasibility of implementing one of those proposals: the double-resonance method. We analyze mainly issues related to the achievable effective coupling strength and the effects of crosstalk on this coupling approach. We also find a new, crosstalk-assisted coupling channel that can be an attractive alternative when implementing the double-resonance coupling proposal.Comment: 4 pages, 3 figure

Unified model for vortex-string network evolution

We describe and numerically test the velocity-dependent one-scale (VOS) string evolution model, a simple analytic approach describing a string network with the averaged correlation length and velocity. We show that it accurately reproduces the large-scale behaviour (in particular the scaling laws) of numerical simulations of both Goto-Nambu and field theory string networks. We explicitly demonstrate the relation between the high-energy physics approach and the damped and non-relativistic limits which are relevant for condensed matter physics. We also reproduce experimental results in this context and show that the vortex-string density is significantly reduced by loop production, an effect not included in the usual `coarse-grained' approach.Comment: 5 pages; v2: cosmetic changes, version to appear in PR

Flux-induced isometry gauging in heterotic strings

We study the effect of flux-induced isometry gauging of the scalar manifold in N=2 heterotic string compactification with gauge fluxes. We show that a vanishing theorem by Witten provides the protection mechanism. The other ungauged isometries in hyper moduli space could also be protected, depending on the gauge bundle structure. We also discuss the related issue in IIB settin

Semiconductor superlattice photodetectors

A superlattice photomultiplier and a photodetector based on the real space transfer mechanism were studied. The wavelength for the first device is of the order of a micron or flexible corresponding to the bandgap absorption in a semiconductor. The wavelength for the second device is in the micron range (about 2 to 12 microns) corresponding to the energy of the conduction band edge discontinuity between an Al/(sub x)Ga(sub 1-x)As and GaAs interface. Both devices are described