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

Deutsch-Jozsa algorithm as a test of quantum computation

A redundancy in the existing Deutsch-Jozsa quantum algorithm is removed and a refined algorithm, which reduces the size of the register and simplifies the function evaluation, is proposed. The refined version allows a simpler analysis of the use of entanglement between the qubits in the algorithm and provides criteria for deciding when the Deutsch-Jozsa algorithm constitutes a meaningful test of quantum computation.Comment: 10 pages, 2 figures, RevTex, Approved for publication in Phys Rev

Approximate quantum error correction can lead to better codes

We present relaxed criteria for quantum error correction which are useful when the specific dominant noise process is known. These criteria have no classical analogue. As an example, we provide a four-bit code which corrects for a single amplitude damping error. This code violates the usual Hamming bound calculated for a Pauli description of the error process, and does not fit into the GF(4) classification.Comment: 7 pages, 2 figures, submitted to Phys. Rev.

Prescription for experimental determination of the dynamics of a quantum black box

We give an explicit prescription for experimentally determining the evolution operators which completely describe the dynamics of a quantum mechanical black box -- an arbitrary open quantum system. We show necessary and sufficient conditions for this to be possible, and illustrate the general theory by considering specifically one and two quantum bit systems. These procedures may be useful in the comparative evaluation of experimental quantum measurement, communication, and computation systems.Comment: 6 pages, Revtex. Submitted to J. Mod. Op

Electronic bandstructure and optical gain of lattice matched III-V dilute nitride bismide quantum wells for 1.55 μ\mum optical communication systems

Dilute nitride bismide GaNBiAs is a potential semiconductor alloy for near- and mid-infrared applications, particularly in 1.55 $\mu$m optical communication systems. Incorporating dilute amounts of Bismuth (Bi) into GaAs reduces the effective bandgap rapidly, while significantly increasing the spin-orbit-splitting energy. Additional incorporation of dilute amounts of Nitrogen (N) helps to attain lattice matching with GaAs, while providing a route for flexible bandgap tuning. Here we present a study of the electronic bandstructure and optical gain of the lattice matched GaN$_x$Bi$_y$As$_{1-x-y}$/GaAs quaternary alloy quantum well (QW) based on the 16-band k$\cdot$p model. We have taken into consideration the interactions between the N and Bi impurity states with the host material based on the band anticrossing (BAC) and valence band anticrossing (VBAC) model. The optical gain calculation is based on the density matrix theory. We have considered different lattice matched GaNBiAs QW cases and studied their energy dispersion curves, optical gain spectrum, maximum optical gain and differential gain; and compared their performances based on these factors. The thickness and composition of these QWs were varied in order to keep the emission peak fixed at 1.55 $\mu$m. The well thickness has an effect on the spectral width of the gain curves. On the other hand, a variation in the injection carrier density has different effects on the maximum gain and differential gain of QWs of varying thicknesses. Among the cases studied, we found that the 6.3 nm thick GaN$_3$Bi$_{5.17}$As$_{91.83}$ lattice matched QW was most suited for 1.55 $\mu$m (0.8 eV) GaAs-based photonic applications.Comment: Accepted in AIP Journal of Applied Physic

Normal modes in an overmoded circular waveguide coated with lossy material

The normal modes in an overmoded waveguide coated with a lossy material are analyzed, particularly for their attenuation properties as a function of coating material, layer thickness, and frequency. When the coating material is not too lossy, the low-order modes are highly attenuated even with a thin layer of coating. This coated guide serves as a mode suppressor of the low-order modes, which can be particularly useful for reducing the radar cross section (RCS) of a cavity structure such as a jet inlet. When the coating material is very lossy, low-order modes fall into two distinct groups: highly and lowly attenuated modes. However, as a/lambda (a = radius of the cylinder; lambda = the free-space wavelength) increases, the separation between these two groups becomes less distinctive. The attenuation constants of most of the low-order modes become small, and decrease as a function of lambda sup 2/a sup 3