Quantum Algorithms with Fixed Points: The Case of Database Search

The standard quantum search algorithm lacks a feature, enjoyed by many classical algorithms, of having a fixed-point, i.e. a monotonic convergence towards the solution. Here we present two variations of the quantum search algorithm, which get around this limitation. The first replaces selective inversions in the algorithm by selective phase shifts of $\frac{\pi}{3}$. The second controls the selective inversion operations using two ancilla qubits, and irreversible measurement operations on the ancilla qubits drive the starting state towards the target state. Using $q$ oracle queries, these variations reduce the probability of finding a non-target state from $\epsilon$ to $\epsilon^{2q+1}$, which is asymptotically optimal. Similar ideas can lead to robust quantum algorithms, and provide conceptually new schemes for error correction.

Search on a hypercubic lattice using a quantum random walk. I. d > 2

Random walks describe diffusion processes, where movement at every time step is restricted to only the neighboring locations. We construct a quantum random walk algorithm, based on discretization of the Dirac evolution operator inspired by staggered lattice fermions. We use it to investigate the spatial search problem, that is, to find a marked vertex on a d-dimensional hypercubic lattice. The restriction on movement hardly matters for d > 2, and scaling behavior close to Grover's optimal algorithm (which has no restriction on movement) can be achieved. Using numerical simulations, we optimize the proportionality constants of the scaling behavior, and demonstrate the approach to that for Grover's algorithm (equivalent to the mean-field theory or the d -> infinity limit). In particular, the scaling behavior for d = 3 is only about 25% higher than the optimal d -> infinity value.

Search on a hypercubic lattice using a quantum random walk. II. d = 2

We investigate the spatial search problem on the two-dimensional square lattice, using the Dirac evolution operator discretized according to the staggered lattice fermion formalism. d = 2 is the critical dimension for the spatial search problem, where infrared divergence of the evolution operator leads to logarithmic factors in the scaling behavior. As a result, the construction used in our accompanying article A. Patel and M. A. Rahaman, Phys. Rev. A 82, 032330 (2010)] provides an O(root N ln N) algorithm, which is not optimal. The scaling behavior can be improved to O(root N ln N) by cleverly controlling the massless Dirac evolution operator by an ancilla qubit, as proposed by Tulsi Phys. Rev. A 78, 012310 (2008)]. We reinterpret the ancilla control as introduction of an effective mass at the marked vertex, and optimize the proportionality constants of the scaling behavior of the algorithm by numerically tuning the parameters.

Search on a Hypercubic Lattice using Quantum Random Walk

We investigate the spatial search problem on the two-dimensional square lattice, using the Dirac evolution operator discretized according to the staggered lattice fermion formalism. d=2 is the critical dimension for the spatial search problem, where infrared divergence of the evolution operator leads to logarithmic factors in the scaling behavior. As a result, the construction used in our accompanying article [ A. Patel and M. A. Rahaman Phys. Rev. A 82 032330 (2010)] provides an O(√NlnN) algorithm, which is not optimal. The scaling behavior can be improved to O(√NlnN) by cleverly controlling the massless Dirac evolution operator by an ancilla qubit, as proposed by Tulsi Phys. Rev. A 78 012310 (2008). We reinterpret the ancilla control as introduction of an effective mass at the marked vertex, and optimize the proportionality constants of the scaling behavior of the algorithm by numerically tuning the parameters.

Search on a fractal lattice using a quantum random walk

The spatial search problem on regular lattice structures in integer number of dimensions d >= 2 has been studied extensively, using both coined and coinless quantum walks. The relativistic Dirac operator has been a crucial ingredient in these studies. Here, we investigate the spatial search problem on fractals of noninteger dimensions. Although the Dirac operator cannot be defined on a fractal, we construct the quantum walk on a fractal using the flip-flop operator that incorporates a Klein-Gordon mode. We find that the scaling behavior of the spatial search is determined by the spectral (and not the fractal) dimension. Our numerical results have been obtained on the well-known Sierpinski gaskets in two and three dimensions.

The role of lysine-41 in RNase A catalysis - A quantum chemical study on the active site ligand complex

Several mechanisms have been proposed to explain the action of enzymes at the atomic level. Among them, the recent proposals involving short hydrogen bonds as a step in catalysis by Gerlt and Gassman [1] and proton transfer through low barrier hydrogen bonds (LBHBs) [2, 3] have attracted attention. There are several limitations to experimentally testing such hypotheses, Recent developments in computational methods facilitate the study of active site-ligand complexes to high levels of accuracy, Our previous studies, which involved the docking of the dinucleotide substrate UpA to the active site of RNase A [4, 5], enabled us to obtain a realistic model of the ligand-bound active site of RNase A. From these studies, based on empirical potential functions, we were able to obtain the molecular dynamics averaged coordinates of RNase A, bound to the ligand UpA. A quantum mechanical study is required to investigate the catalytic process which involves the cleavage and formation of covalent bonds. In the present study, we have investigated the strengths of some of the hydrogen bonds between the active site residues of RNase A and UpA at the ab initio quantum chemical level using the molecular dynamics averaged coordinates as the starting point. The 49 atom system and other model systems were optimized at the 3-21G level and the energies of the optimized systems were obtained at the 6-31G* level. The results clearly indicate the strengthening of hydrogen bonds between neutral residues due to the presence of charged species at appropriate positions. Such a strengthening manifests itself in the form of short hydrogen bonds and a low barrier for proton transfer. In the present study, the proton transfer between the 2'-OH of ribose (from the substrate) and the imidazole group from the H12 of RNase A is influenced by K41, which plays a crucial role in strengthening the neutral hydrogen bond, reducing the barrier for proton transfer.

Structural and optical investigation of semiconductor CdSe/CdS core-shell quantum dot thin films

Highly luminescent CdSe/CdS core-shell nanocrystals have been assembled on indium tin oxide (ITO) coated glass substrates using a wet synthesis route. The physical properties of the quantum dots (QD) have been investigated using X-ray diffraction, transmission electron microscopy and optical absorption spectroscopy techniques. These quantum dots showed a strong enhancement in the near band edge absorption. The in situ luminescence behavior has been interpreted in the light of the quantum confinement effect and induced strain in the core-shell structure.

Electroluminescence from modulation-doped pseudomorphic AlGaAs/InGaAs/GaAs quantum wells

Low-temperature electroluminescence (EL) is observed in n-type modulation-doped AlGaAs/InGaAs/GaAs quantum well samples by applying a positive voltage between the semitransparent Au gate and alloyed Au–Ge Ohmic contacts made on the top surface of the samples. We attribute impact ionization in the InGaAs QW to the observed EL from the samples. A redshift in the EL spectra is observed with increasing gate bias. The observed redshift in the EL spectra is attributed to the band gap renormalization due to many-body effects and quantum-confined Stark effect.

Efficient Hg and Ag ion detection with luminescent PbS quantum dots grown in poly vinyl alcohol and capped with mercaptoethanol

PbS quantum dots capped with mercaptoethanol (C2H5OSH) have been synthesized in poly vinyl alcohol and used to investigate their photoluminescence (PL) response to various ions such as zinc (Zn), cadmium (Cd), mercury (Hg), silver (Ag), copper (Cu), iron (Fe), manganese (Mn), cobalt (Co), chromium (Cr) and nickel (Ni). The enhancement in the PL intensity was observed with specific ions namely Zn, Cd, Hg and Ag. Among these four ions, the PL response to Hg and Ag even at sub-micro-molar concentrations was quite high, compared to that of Zn and Cd. It was observed that the change in Pb and S molar ratio has profound effect on the sensitivity of these ions. These results indicate that the sensitivity of these QDs could be fine-tuned by controlling the S concentration at the surface. Contrary to the above, Cu quenched the photoluminescence. In Cd based QDs related ion probing, Hg and Cu was found to have quenching properties, however, our PbS QDs have quenching property only for Cu ions. This was attributed to the formation HgS at the surface that has bandgap higher than PbS. Another interesting property of PbS in PVA observed is photo-brightening mechanism due to the curing of the polymer with laser. However, the presence of excess ions at the surface changes its property to photo-darkening/brightening that depends on the direction of carrier transfer mechanism (from QDs to the surface adsorbed metal ions or vice-versa). which is an interesting feature for metal ion detectivity.

Multiple-quantum artifacts in single-quantum two-dimensional correlated NMR spectra of strongly coupled spins

Artifacts in the form of cross peaks have been observed along two- and three-quantum diagonals in single-quantum two-dimensional correlated (COSY) spectra of several peptides and oligonucleotides. These have been identified as due to the presence of a non-equilibrium state of kind I (a state describable by populations which differ from equilibrium) of strongly coupled spins carried over from one experiment to the next in the COSY algorithm.

Visualization of enantiomers using natural abundant 13C-filtered single and double quantum selective refocusing experiments: Application to small chiral molecules

The routine use of proton NMR for the visualization of enantiomers, aligned in the chiral liquid crystal solvent poly-γ-benzyl-l-glutamate (PBLG), is restricted due to severe loss of resolution arising from large number of pair wise interaction of nuclear spins. In the present study, we have designed two experimental techniques for their visualization utilizing the natural abundance 13C edited selective refocusing of single quantum (CH-SERF) and double quantum (CH-DQSERF) coherences. The methods achieve chiral discrimination and aid in the simultaneous determination of homonuclear couplings between active and passive spins and heteronuclear couplings between the excited protons and the participating 13C spin. The CH-SERF also overcomes the problem of overlap of central transitions of the methyl selective refocusing (SERF) experiment resulting in better chiral discrimination. Theoretical description of the evolution of magnetization in both the sequences has been discussed using polarization operator formalism.

Simple theoretical analysis of the Einstein's photoemission from quantum confined superlattices

In this paper, we study the Einstein's photoemission from III-V, II-VI, IV-VI and HgTe/CdTe quantum well superlattices (QWSLs) with graded interfaces and quantum well effective mass superlattices in the presence of a quantizing magnetic field on the basis of newly formulated dispersion relations in the respective cases. Besides, the same has been studied from the afore-mentioned quantum dot superlattices and it appears that the photoemission oscillates with increasing carrier degeneracy and quantizing magnetic field in different manners. In addition, the photoemission oscillates with film thickness and increasing photon energy in quantum steps together with the fact that the solution of the Boltzmann transport equation will introduce new physical ideas and new experimental findings under different external conditions. The influence of band structure is apparent from all the figures and we have suggested three applications of the analyses of this paper in the fields of superlattices and microstructures.

Thermoelectric power in ultrathin films, quantum wires and carbon nanotubes under classically large magnetic field: Simplified theory and relative comparison

We study the thermoelectric power under classically large magnetic field (TPM) in ultrathin films (UFs), quantum wires (QWs) of non-linear optical materials on the basis of a newly formulated electron dispersion law considering the anisotropies of the effective electron masses, the spin-orbit splitting constants and the presence of the crystal field splitting within the framework of k.p formalism. The results of quantum confined III-V compounds form the special cases of our generalized analysis. The TPM has also been studied for quantum confined II-VI, stressed materials, bismuth and carbon nanotubes (CNs) on the basis of respective dispersion relations. It is found taking quantum confined CdGeAs2, InAs, InSb, CdS, stressed n-InSb and Bi that the TPM increases with increasing film thickness and decreasing electron statistics exhibiting quantized nature for all types of quantum confinement. The TPM in CNs exhibits oscillatory dependence with increasing carrier concentration and the signature of the entirely different types of quantum systems are evident from the plots. Besides, under certain special conditions, all the results for all the materials gets simplified to the well-known expression of the TPM for non-degenerate materials having parabolic energy bands, leading to the compatibility test. (C) 2009 Elsevier B.V. All rights reserved.

Experimental implementation of a three qubit quantum game with corrupt source using nuclear magnetic resonance quantum information processor

In a three player quantum `Dilemma' game each player takes independent decisions to maximize his/her individual gain. The optimal strategy in the quantum version of this game has a higher payoff compared to its classical counterpart. However, this advantage is lost if the initial qubits provided to the players are from a noisy source. We have experimentally implemented the three player quantum version of the `Dilemma' game as described by Johnson, [N.F. Johnson, Phys. Rev. A 63 (2001) 020302(R)] using nuclear magnetic resonance quantum information processor and have experimentally verified that the payoff of the quantum game for various levels of corruption matches the theoretical payoff. (c) 2007 Elsevier Inc. All rights reserved.

Necessity for quantum mechanical simulation for the future technology nodes

In this paper we present and compare the results obtained from semi-classical and quantum mechanical simulation for a Double Gate MOSFET structure to analyze the electrostatics and carrier dynamics of this device. The geometries like gate length, body, thickness of this device have been chosen according to the ITRS specification for the different technology nodes. We have shown the extent of deviation between the semi-classical and quantum mechanical results and hence the need of quantum simulations for the promising nanoscale devices in the future technology nodes predicted in ITRS.