Quantum simulation using fidelity-profile optimization

Experimental quantum simulation of a Hamiltonian H requires unitary operator decomposition (UOD) of its evolution unitary U = exp(-iHt) in terms of native unitary operators of the experimental system. Here, using a genetic algorithm, we numerically evaluate the most generic UOD (valid over a continuous range of Hamiltonian parameters) of the unitary operator U, termed fidelity-profile optimization. The optimization is obtained by systematically evaluating the functional dependence of experimental unitary operators (such as single-qubit rotations and time-evolution unitaries of the system interactions) to the Hamiltonian (H) parameters. Using this technique, we have solved the experimental unitary decomposition of a controlled-phase gate (for any phase value), the evolution unitary of the Heisenberg XY interaction, and simulation of the Dzyaloshinskii-Moriya (DM) interaction in the presence of the Heisenberg XY interaction. Using these decompositions, we studied the entanglement dynamics of a Bell state in the DM interaction and experimentally verified the entanglement preservation procedure of Hou et al. Ann. Phys. (N.Y.) 327, 292 (2012)] in a nuclear magnetic resonance quantum information processor.

Frustration in Optical Lattices of Interacting Bosons

The realization of optical lattices of cold atoms has opened up the possibility of engineering interacting lattice systems of bosons and fermions, stimulating a frenzy of research over the last decade. More recently, experimental techniques have been developed to apply synthetic gauge fields to these optical lattices. As a result, it has become possible to study quantum Hall physics and the effects of frustration in lattices of cold atoms. In this article we describe the combined effect of frustration and interactions on the superfluidity of bosons. By focussing on a frustrated ladder of interacting bosons, we show that the effect of frustration is for ``chiral'' order to develop, which manifests itself as an alternating pattern of circulating supercurrents. Remarkably, this order persists even when superfluidity is lost and the system enters a Mott phase giving rise to a novel chiral Mott insulator. We describe the combined physics of frustration and interactions by studying a fully frustrated one dimensional model of interacting bosons. The model is studied using mean-field theory, a direct quantum simulation and a higher dimensional classical theory in order to offer a full description of the different quantum phases contained in it and transitions between the different phases. In addition, we provide physical descriptions of the chiral Mott insulator as a vortex-anitvortex super solid and indirect excitonic condensate in addition to obtaining a variational wavefunction for it. We also briefly describe the chiral Mott states arising in other microscopic models.

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.

Quantum clustering and network analysis of MD simulation trajectories to probe the conformational ensembles of protein-ligand interactions

In this article, we present a novel application of a quantum clustering (QC) technique to objectively cluster the conformations, sampled by molecular dynamics simulations performed on different ligand bound structures of the protein. We further portray each conformational population in terms of dynamically stable network parameters which beautifully capture the ligand induced variations in the ensemble in atomistic detail. The conformational populations thus identified by the QC method and verified by network parameters are evaluated for different ligand bound states of the protein pyrrolysyl-tRNA synthetase (DhPylRS) from D. hafniense. The ligand/environment induced re-distribution of protein conformational ensembles forms the basis for understanding several important biological phenomena such as allostery and enzyme catalysis. The atomistic level characterization of each population in the conformational ensemble in terms of the re-orchestrated networks of amino acids is a challenging problem, especially when the changes are minimal at the backbone level. Here we demonstrate that the QC method is sensitive to such subtle changes and is able to cluster MD snapshots which are similar at the side-chain interaction level. Although we have applied these methods on simulation trajectories of a modest time scale (20 ns each), we emphasize that our methodology provides a general approach towards an objective clustering of large-scale MD simulation data and may be applied to probe multistate equilibria at higher time scales, and to problems related to protein folding for any protein or protein-protein/RNA/DNA complex of interest with a known structure.

Subquadratic quantum number dependence and other anomalies of vibrational dephasing in liquid nitrogen: Molecular dynamics simulation study from the triple point to the critical point and beyond

Vibrational phase relaxation near gas-liquid and liquid-solid phase coexistence has been studied by molecular dynamics simulations of N-N stretch in N-2. Experimentally observed pronounced insensitivity of phase relaxation from the triple point to beyond the boiling point is found to originate from a competition between density relaxation and resonant-energy transfer terms. The sharp rise in relaxation rate near the critical point (CP) can be attributed at least partly to the sharp, rise in vibration-rotation coupling contribution. Substantial subquadratic quantum number dependence of overtone dephasing rate is found near the CP and in supercritical fluids. [S0031-9007 (99)09318-7].

Algorithmic approach to simulate Hamiltonian dynamics and an NMR simulation of quantum state transfer

We propose an iterative algorithm to simulate the dynamics generated by any n-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator U (unitary) into a product of different time-step unitaries. The algorithm product-decomposes U in a chosen operator basis by identifying a certain symmetry of U that is intimately related to the number of gates in the decomposition. We illustrate the algorithm by first obtaining a polynomial decomposition in the Pauli basis of the n-qubit quantum state transfer unitary by Di Franco et al. [Phys. Rev. Lett. 101, 230502 (2008)] that transports quantum information from one end of a spin chain to the other, and then implement it in nuclear magnetic resonance to demonstrate that the decomposition is experimentally viable. We further experimentally test the resilience of the state transfer to static errors in the coupling parameters of the simulated Hamiltonian. This is done by decomposing and simulating the corresponding imperfect unitaries.

Quantum-Ohmic Resistance Fluctuation In Disordered Conductors - An Invariant Imbedding Approach

It is now well known that in extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c. resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have re-examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one-dimensional continuum with a Gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive the d-dimensional generalization of the above probability distribution, or rather the associated cumulant function –‘the free energy’. For d=3, our analysis shows that the dispersion dominates the mobilitly edge phenomena in that (i) a one-parameter B-function depending on the mean conductance only does not exist, (ii) an approximate treatment gives a diffusion-correction involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge ‘first-order’. We also report some analytical results for the case of the one dimensional system in the presence of a finite electric fiekl. We find a cross-over from the exponential to the power-low length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors.

Quantum Threshold Voltage Modeling of Short Channel Quad Gate Silicon Nanowire Transistor

In this paper, a physically based analytical quantum linear threshold voltage model for short channel quad gate MOSFETs is developed. The proposed model, which is suitable for circuit simulation, is based on the analytical solution of 3-D Poisson and 2-D Schrodinger equation. Proposed model is fully validated against the professional numerical device simulator for a wide range of device geometries and also used to analyze the effect of geometry variation on the threshold voltage.

Necessity for quatum simulation for 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.

Computationally Efficient Model for Simulation of Boost Converter

This paper presents a computationally efficient model for a dc-dc boost converter, which is valid for continuous and discontinuous conduction modes; the model also incorporates significant non-idealities of the converter. Simulation of the dc-dc boost converter using an average model provides practically all the details, which are available from the simulation using the switching (instantaneous) model, except for the quantum of ripple in currents and voltages. A harmonic model of the converter can be used to evaluate the ripple quantities. This paper proposes a combined (average-cum-harmonic) model of the boost converter. The accuracy of the combined model is validated through extensive simulations and experiments. A quantitative comparison of the computation times of the average, combined and switching models are presented. The combined model is shown to be more computationally efficient than the switching model for simulation of transient and steady-state responses of the converter under various conditions.

Efficient simulation of unitary operators by combining two numerical algorithms: An NMR simulation of the mirror-inversion propagator of an XY spin chain

Precise experimental implementation of unitary operators is one of the most important tasks for quantum information processing. Numerical optimization techniques are widely used to find optimized control fields to realize a desired unitary operator. However, finding high-fidelity control pulses to realize an arbitrary unitary operator in larger spin systems is still a difficult task. In this work, we demonstrate that a combination of the GRAPE algorithm, which is a numerical pulse optimization technique, and a unitary operator decomposition algorithm Ajoy et al., Phys. Rev. A 85, 030303 (2012)] can realize unitary operators with high experimental fidelity. This is illustrated by simulating the mirror-inversion propagator of an XY spin chain in a five-spin dipolar coupled nuclear spin system. Further, this simulation has been used to demonstrate the transfer of entangled states from one end of the spin chain to the other end.

An efficient design of serial and parallel memory using Quantum dot cellular automata

Quantum cellular automata (QCA) is a new technology in the nanometer scale and has been considered as one of the alternative to CMOS technology. In this paper, we describe the design and layout of a serial memory and parallel memory, showing the layout of individual memory cells. Assuming that we can fabricate cells which are separated by 10nm, memory capacities of over 1.6 Gbit/cm2 can be achieved. Simulations on the proposed memories were carried out using QCADesigner, a layout and simulation tool for QCA. During the design, we have tried to reduce the number of cells as well as to reduce the area which is found to be 86.16sq mm and 0.12 nm2 area with the QCA based memory cell. We have also achieved an increase in efficiency by 40%.These circuits are the building block of nano processors and provide us to understand the nano devices of the future.

Investigations on the physical origin of lateral photovoltage in PbS-colloidal quantum dot/Si heterojunctions

Restricted area heterojunctions, an array of lead sulfide colloidal quantum dots (PbS-CQDs) and crystalline silicon, are studied with a non-destructive remote contact light beam induced current (RC-LBIC) technique. As well as getting good quality active area images we observed an anomalous unipolar signal response for the PbS-CQD/n-Si devices and a conventionally expected bipolar signal profile for the PbS-CQD/p-Si devices. Interestingly, our simulation results consistently yielded a unipolar and bipolar nature in the signals related to the PbSCQD/n-Si and PbS-CQD/p-Si heterostructures, respectively. In order to explain the physical mechanism involved in the unipolar signal response of the PbS-CQD/n-Si devices, we propose a model based on the band alignment in the heterojunctions, in addition to the distribution of photo-induced excess majority carriers across the junction. Given that the RC-LBIC technique is well suited to this context, the presence of these two distinct mechanisms (the bipolar and unipolar nature of the signals) needs to be considered in order to have a better interpretation of the data in the characterization of an array of homo/heterojunctions.

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.

Influence of friction during forming processes-a study using a numerical simulation technique

Friction has an important influence in metal forming operations, as it contributes to the success or otherwise of the process. In the present investigation, the effect of friction on metal forming was studied by simulating compression tests on cylindrical Al-Mg alloy using the finite element method (FEM) technique. Three kinds of compression tests were considered wherein a constant coefficient of friction was employed at the upper die-work-piece interface. However, the coefficient of friction between the lower die-work-piece interfaces was varied in the tests. The simulation results showed that a difference in metal flow occurs near the interfaces owing to the differences in the coefficient of friction. It was concluded that the variations in the coefficient of friction between the dies and the work-piece directly affect the stress distribution and shape of the work-piece, having implications on the microstructure of the material being processed.