NMR analogue of the generalized Grover‘s algorithm of multiple marked states and its application

The generalized Grover's algorithm for the case in which there are multiple marked states is demonstrated on a nuclear magnetic resonance (NMR) quantum computer. The Walsh－Hadamard transform and the phase inversion are all replaced. NMR analogues of Einstein－Podolsky－Rosen states (pseudo-EPR states) are synthesized using the above algorithm.     

Dense coding scheme using superpositions of Bell-states and its NMR implementation

Dense coding using superpositions of Bell-states is proposed. The generalized Grover's algorithm is used to prepare the initial entangled states, and the reverse process of the quantum algorithm is used to determine the entangled state in the decoding measurement. Compared with the previous schemes, the superpositions of two Bell-states are exploited. Our scheme is demonstrated using a nuclear magnetic resonance (NMR) quantum computer. The corresponding manipulations are obtained. Experimental results show a good agreement between theory and experiment. We also generalize the scheme to transmit eight messages by introducing an additional two-state system.     

A Robust Scheme for Two－Qubit Grover Quantum Search Alogrithm Based on the Motional and Internal States of a Single Cold Trapped Ion

We propose a scheme to implement a two-qubit Grover quantum search algorithm. The novelty in the proposal is that the motional state is introduced into the computation and the internal state within a single cold trapped ion.The motional and internal states of the ion are manipulated as two qubits by the laser pulses to accomplish anexample of a Grover algorithm based on the two qubits. The composite laser pulses that are applied to implementthe Grover algorithm have been designed in detail. The issues concerning measurement and decoherence arediscussed.     

Degree of fourth-order coherence by double Hanbury Brown—Twiss detections

<正>Photon quantum statistics of light can be shown by the high-order coherence.The fourth-order coherences of various quantum states including Fock states,coherent states,thermal states and squeezed vacuum states are investigated based on a double Hanbury Brown-Twiss(HBT) scheme.The analytical results are obtained by taking the overall efficiency and background into account.     

Highly accurate theoretical study on spectroscopic properties of SH including spin–orbit coupling

The multi-reference configuration interaction method plus Davidson correction(MRCI+Q) are adopted to study the low-lying states of SH with consideration of scalar relativistic effect, core-valence(CV) electron correlation, and spin–orbit coupling(SOC) effect. The SOC effect on the low-lying states is considered by utilizing the full Breit–Pauli operator. The potential energy curves(PECs) of 10 Λ–S states and 18 ? states are calculated. The dipole moments of 10 Λ–S states are calculated, and the variation along the internuclear distance is explained by the electronic configurations. With the help of calculated SO matrix elements, the possible predissociation channels of A~2Σ+, c4Σ-and F~2Σ-are discussed. The Franck–Condon factors of A~2Σ~+–X~2Π, F~2Σ~-–X~2Π and E~2Σ~+–X~2Π transitions are determined, and the radiative lifetimes of A~2Σ+and F~2Σ-states are evaluated, which are in good agreement with previous experimental results.     

Low-lying electronic states of aluminum monoiodide

High-level ab initio calculations of aluminum monoiodide(AlI) molecule are performed by utilizing the multireference configuration interaction plus Davidson correction(MRCI+Q) method. The core-valence correlation(CV) and spin–orbit coupling(SOC) effect are considered. The adiabatic potential energy curves(PECs) of a total of 13 Λ–S states and 24 ? states are computed. The spectroscopic constants of bound states are determined, which are in accordance with the results of the available experimental and theoretical studies. The interactions between the Λ–S states are analyzed with the aid of the spin–orbit matrix elements. Finally, the transition properties including transition dipole moment(TDM),Frank–Condon factors(FCF) and radiative lifetime are obtained based on the computed PEC. Our study sheds light on the electronic structure and spectroscopy of low-lying electronic states of the AlI molecule.     

Preparation of the W State of Atoms in a Single Cavity or N Distant Cavities by Photon Interference

We suggest two schemes to generate the W state of N A-type three-level atoms. In the schemes, identical N three-level atoms are trapped in a cavity or N distant cavities. The success or failure of the generation of the W state can be determined by detecting the polarization of photon leaking out of the cavity. The result demonstrates that the W state is free from both the cavity loss and the spontaneous emission due to the fact that the two ground states (left and right) of the three-level atoms are stable states (or metastable states).     

Axis-symmetric Onsager clustered states of point vortices in a bounded domain

We study axis-symmetric Onsager clustered states of a neutral point vortex system confined to a two-dimensional disc. Our analysis is based on the mean field of bounded point vortices in the microcanonical ensemble. The clustered vortex states are specified by the inverse temperature β and the rotation frequency ω, which are the conjugate variables of energy E and angular momentum L,respectively. The formation of the axis-symmetric clustered vortex states(azimuthal angle independent) involves th...     

Determination of the vapor–liquid transition of square-well particles using a novel generalized-canonical-ensemble-based method

The square-well(SW) potential is one of the simplest pair potential models and its phase behavior has been clearly revealed, therefore it has become a benchmark for checking new theories or numerical methods. We introduce the generalized canonical ensemble(GCE) into the isobaric replica exchange Monte Carlo(REMC) algorithm to form a novel isobaric GCE-REMC method, and apply it to the study of vapor–liquid transition of SW particles. It is validated that this method can reproduce the vapor–liquid diagram of SW particles by comparing the estimated vapor–liquid binodals and the critical point with those from the literature. The notable advantage of this method is that the unstable vapor–liquid coexisting states,which cannot be detected using conventional sampling techniques, are accessed with a high sampling efficiency. Besides,the isobaric GCE-REMC method can visit all the possible states, including stable, metastable or unstable states during the phase transition over a wide pressure range, providing an effective pathway to understand complex phase transitions during the nucleation or crystallization process in physical or biological systems.     

The effect of the rotational excitation of NO on the stereodynamics for the reaction C(~3P)+NO(X~2Π)→CN(X~2Σ~+)+O(~3P)

The stereodynamic properties of the reaction C(3P)+NO(X2Π)→CN(X2Σ+)+O(3P) in different rotational states of reactant NO are studied theoretically by using the quasiclassical trajectory method on 2A' and 2A' potential energy surfaces(PESs) at a collision energy of 0.06 eV.The vector properties in different rotational states on the two surfaces are discussed in detail.The results indicate that the rotational excitation of NO has considerable influence on the stereodynamic property of the reaction occurring on the two surfaces.At the same time,the calculated polarization-dependent differential cross sections(PDDCSs) in different initial rotational states manifest that products are strongly polarized at three scattering angles.     

Analysis of Relaxed States in Coaxial Helicity Injection Tokamaks on the Basis of Analytical Solutions

The principle of the minimum energy dissipation rate is applied to toroidal plasmas with a coaxial direct current helicity injection.The relaxed states are analysed based on the analytical solutions of the resulting Euler-Lagrangian equations.Three typical states are found.The relaxed states are close to the Taylor state if the ratio of current density to magnetic field on the boundary is small enough.The states will deviate from the Taylor state when the ratio increases,but when it approaches a critical value the central part of relaxed plasmas may approach a force free state,and above the critical value both current and magnetic field may reverse in the central part.     

Quantum Properties of Two-Mode Squeezed Even and Odd Coherent States

Two new types of quantum states are constructed by applying the operator s(ξ) = exp(ξ*ab - ξa b ) on the two-mode even and odd coherent states.The mathematical and quantum statistical properties of such states are investigated.Various nonclassical features of these states,such as squeezing properties,the inter-mode photon bunching,and the violation of Cauchy-Schwarz inequality,are discussed.The Wigner function in these states are studied in detail.     

Entanglement for a two-parameter class of states in a high-dimension bipartite quantum system

The entanglement for a two-parameter class of states in a high-dimension (m  n,n≥m≥3) bipartite quantum system is discussed.The negativity (N) and the relative entropy of entanglement (Er) are calculated,and the analytic expressions are obtained.Finally the relation between the negativity and the relative entropy of entanglement is discussed.The result demonstrates that all PPT states of the two-parameter class of states are separable,and all entangled states are NPT states.Different from the 2 ? n quantum system,the negativity for a two-parameter class of states in high dimension is not always greater than or equal to the relative entropy of entanglement.The more general relation expression is mN/2≥Er.     

Design of quantum VQ iteration and quantum VQ encoding algorithm taking O（√N） steps for data compression

Vector quantization (VQ) is an important data compression method. The key of the encoding of VQ is to find the closest vector among N vectors for a feature vector. Many classical linear search algorithms take $O(N)$ steps of distance computing between two vectors. The quantum VQ iteration and corresponding quantum VQ encoding algorithm that takes $O(\sqrt N )$ steps are presented in this paper. The unitary operation of distance computing can be performed on a number of vectors simultaneously because the quantum state exists in a superposition of states. The quantum VQ iteration comprises three oracles, by contrast many quantum algorithms have only one oracle, such as Shor's factorization algorithm and Grover's algorithm. Entanglement state is generated and used, by contrast the state in Grover's algorithm is not an entanglement state. The quantum VQ iteration is a rotation over subspace, by contrast the Grover iteration is a rotation over global space. The quantum VQ iteration extends the Grover iteration to the more complex search that requires more oracles. The method of the quantum VQ iteration is universal.     

Excitation Energies of 1s^2 ns （6 ≤ n ≤ 9） States for Lithium-Like Systems from Z = 11 to 20

The non-relativistic energies of 1s^2 ns (6 ≤ n ≤ 9) states for the lithium-like systems from Z = 11 to 20 are calculated by using a full-core-plus-correlation (FCPC) method. The relativistic and mass-polarization effects on the energy are calculated by the first-order perturbation corrections. The correction from the quantumelectrodynamics effect is also included using effective nuclear charge. Based on these results and the quantum defect theory, the quantum defects of 1s^2ns series for these ions, as a function of energy, are determined. The comparisons between the ionization potentials for 1s^2ns states (6 ≤ n ≤ 9) obtained by the FCPC method and the semi-empirical method are carried out. The results show that their agreement is very well and the energies of all discrete states (n ≥ 10) below the ionization threshold of this series for the ions can be predicted by using their quantum defects.     

Quasiparticle structure of superheavy nuclei in α-decay chains of ~(285)Fl and ~(291,293)Lv

Two mean-field potentials, Woods-Saxon and Skyrme based potentials, are used to calculate the energies of low-lying one-quasiparticle states. The spectra of the low-lying states and the α-decay spectra of nuclei belonging to the α-decay chains of ~(285)Fl and ~(291,293)Lv are calculated and compared with the available experimental data. Dependence of the splitting of the pseudospin doublets and of the energies of the unique parity neutron one-quasiparticle states on the mean field potential are discussed. As shown, the α-decay spectra could be different in the α-decay chain and at the direct production of the nucleus in a fusion reaction.     

Experimental quantum deletion in an NMR quantum information processor

We report an NMR experimental realization of a rapid quantum deletion algorithm that deletes marked states in an unsorted database.Unlike classical deletion,where search and deletion are equivalent,quantum deletion can be implemented with only a single query,which achieves exponential speed-up compared to the optimal classical analog.In the experimental realization,the GRAPE algorithm was used to obtain an optimized NMR pulse sequence,and the efficient method of maximum-likelihood has been used to reconstruct the experimental output state.     

Configuration interaction calculations on the spectroscopic and transition properties of magnesium chloride

The potential energy curves(PECs) of 14 Λ–S states for magnesium chloride(Mg Cl) have been calculated by using multi-reference configuration interaction method with Davidson correction(MRCI + Q). The core-valence correlation(CV), scalar relativistic effect, and spin–orbit coupling(SOC) effect are considered in the electronic structure computations.The spectroscopic constants of X~2Σ~+ and A ~2Π states have been obtained, which are in good agreement with the existing theoretical and experimental results. Furthermore, other higher electronic states are also characterized. The permanent dipole moments(PDMs) of Λ–S states and the spinorbit(SO) matrix elements between Λ–S states are also computed. The results indicate that the abrupt changes of PDMs and the SO matrix elements are attributed to the avoided crossing between the states with the same symmetry. The SOC effect is taken into account with Breit–Pauli operator, which makes the 14Λ–S states split into 30 ? states, and leads to a double-well potential of the ? =(3)1/2 state. The energy splitting for the A2Π is calculated to be 53.61 cm~(-1) and in good agreement with the experimental result 54.47 cm~(-1). The transition dipole moments(TDMs), Franck–Condon factors(FCFs), and the corresponding radiative lifetimes of the selected transitions from excited ? states to the ground state X~2Σ + 1/2 have been reported. The computed radiative lifetimes τν of low-lying excites ? states are all on the order of 10 ns. Finally, the feasibility of laser cooling of Mg Cl molecule has been analyzed.     

An adaptive time delay estimati on algorithm based onquadratic weighting of the frequency domain

Time delay estimation (TDE) plays an important role in many engineering appli-cations. A new time delay estimation configuration, the quadratic weighting of the frequency domain adaptive TDE model, is put forward. The quadratic weighting of the frequency domainSCOT (Smoothed Coherence Transform) and ML (Maximum Likelihood) adaptive TDE algo-rithms are presented, respectively. The variance of the quadratic weighting of the frequency domain SCOT algorithm is derived. Then the proposed algorithms are applied in the TDE of helicopter passive acoustic location. The simulation results are presented which verify that the proposed algorithm has better performance in the low signal to noise ratio.     

Quantum Mechanical Nature in Liquid NMR Quantum Computing

The quantum nature of bulk ensemble NMR quantum computing-the center of recent heated debate,is addressed.Concepts of the mixed state and entanglement are examined,and the data in a two-qubit liquid NMR quantum computation are analyzed.the main points in this paper are;i) Density matrix describes the “state“ of an average particle in an ensemble.It does not describe the state of an individual particle in an ensemble;ii) Entanglement is a property of the wave function of a microscopic particle(such as a molecule in a liquid NMR sample),and separability of the density matrix canot be used to measure the entanglement of mixed ensemble;iii) The state evolution in bulkensemble NMR quantum computation is quantum-mechanical;iv) The coefficient before the effective pure state density matrix,ε,is a measure of the simultaneity of the molecules in an ensemble,It reflets the intensity of the NMR signal and has no significance in quantifying the entanglement in the bulk ensemble NMR system.The decomposition of the density matrix into product states is only an indication that the ensemble can be prepared by an ensemble with the particles unentangeld.We conclude that effective-pure-state NMR quantum computation is genuine,not just classical simulations.