Chebyshev real wave packet propagation: H+O-2 (J=0) state-to-state reactive scattering calculations

In this paper we explore the relative performance of two recently developed wave packet methodologies for reactive scattering, namely the real wave packet Chebyshev domain propagation of Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)] and the Lanczos subspace wave packet approach of Smith [J. Chem. Phys. 116, 2354 (2002); Chem. Phys. Lett. 336, 149 (2001)]. In the former method, a modified Schrodinger equation is employed to propagate the real part of the wave packet via the well-known Chebyshev iteration. While the time-dependent wave packet from the modified Schrodinger equation is different from that obtained using the standard Schrodinger equation, time-to-energy Fourier transformation yields wave functions which differ only trivially by normalization. In the Lanczos subspace approach the linear system of equations defining the action of the Green operator may be solved via either time-dependent or time-independent methods, both of which are extremely efficient due to the simple tridiagonal structure of the Hamiltonian in the Lanczos representation. The two different wave packet methods are applied to three dimensional reactive scattering of H+O-2 (total J=0). State-to-state reaction probabilities, product state distributions, as well as initial-state-resolved cumulative reaction probabilities are examined. (C) 2002 American Institute of Physics.

Discrete teleportation protocol of continuum spectra field states

A discrete protocol for teleportation of superpositions of coherent states of optical-cavity fields is presented. Displacement and parity operators are unconventionally used in Bell-like measurement for field states.

Entanglement in the steady state of a collective-angular-momentum (Dicke) model

We model the behavior of an ion trap with all ions driven simultaneously and coupled collectively to a heat bath. The equations for this system are similar to the irreversible dynamics of a collective angular momentum system known as the Dicke model. We show how the steady state of the ion trap as a dissipative many-body system driven far from equilibrium can exhibit quantum entanglement. We calculate the entanglement of this steady state for two ions in the trap and in the case of more than two ions we calculate the entanglement between two ions by tracing over all the other ions. The entanglement in the steady state is a maximum for the parameter values corresponding roughly to a bifurcation of a fixed point in the corresponding semiclassical dynamics. We conjecture that this is a general mechanism for entanglement creation in driven dissipative quantum systems.

Practical scheme for quantum computation with any two-qubit entangling gate

Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-NOT, are universal when assisted by arbitrary one-qubit gates, it has only recently become clear precisely what class of two-qubit gates is universal in this sense. We present an elementary proof that any entangling two-qubit gate is universal for quantum computation, when assisted by one-qubit gates. A proof of this result for systems of arbitrary finite dimension has been provided by Brylinski and Brylinski; however, their proof relies on a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical.

Preparing encoded states in an oscillator

Recently a scheme has been proposed for constructing quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. One of the difficult steps in this scheme is the preparation of the encoded states. We show how these states can be generated by coupling a continuous quantum variable to a single qubit. An ion trap quantum computer provides a natural setting for a continuous system coupled to a qubit. We discuss how encoded states may be generated in an ion trap.

ROM-based computation: Quantum versus classical

We introduce a model of computation based on read only memory (ROM), which allows us to compare the space-efficiency of reversible, error-free classical computation with reversible, error-free quantum computation. We show that a ROM-based quantum computer with one writable qubit is universal, whilst two writable bits are required for a universal classical ROM-based computer. We also comment on the time-efficiency advantages of quantum computation within this model.

A simple formula for the average gate fidelity of a quantum dynamical operation

This Letter presents a simple formula for the average fidelity between a unitary quantum gate and a general quantum operation on a qudit, generalizing the formula for qubits found by Bowdrey et al. [Phys. Lett. A 294 (2002) 258]. This formula may be useful for experimental determination of average gate fidelity. We also give a simplified proof of a formula due to Horodecki et al. [Phys. Rev. A 60 (1999) 1888], connecting average gate fidelity to entanglement fidelity. (C) 2002 Elsevier Science B.V. All rights reserved.

Qudit quantum-state tomography

Recently quantum tomography has been proposed as a fundamental tool for prototyping a few qubit quantum device. It allows the complete reconstruction of the state produced from a given input into the device. From this reconstructed density matrix, relevant quantum information quantities such as the degree of entanglement and entropy can be calculated. Generally, orthogonal measurements have been discussed for this tomographic reconstruction. In this paper, we extend the tomographic reconstruction technique to two new regimes. First, we show how nonorthogonal measurements allow the reconstruction of the state of the system provided the measurements span the Hilbert space. We then detail how quantum-state tomography can be performed for multiqudits with a specific example illustrating how to achieve this in one- and two-qutrit systems.

Absorption and dispersion by a multiple driven two-level atom

We investigate the absorption and dispersion properties of a two-level atom driven by a polychromatic field. The driving field is composed of a strong resonant (carrier) frequency component and a large number of symmetrically detuned sideband fields (modulators). A rapid increase in the absorption at the central frequency and the collapse of the response of the system from multiple frequencies to a single frequency are predicted to occur when the Rabi frequency of the modulating fields is equal to the Rabi frequency of the carrier field. These are manifestations of the undressing or a disentanglement of the atomic and driving field states, that leads to a collapse of the atom to its ground state. Our calculation permits consideration of the question of the undressing of the driven atom by a multiple-modulated field and the predicted spectra offer a method of observing undressing. Moreover, we find that the absorption and dispersion spectra split into multiplets whose structures depend on the Rabi frequency of the modulating fields. The spectral features can jump between different resonance frequencies by changing the Rabi frequency of the modulating fields or their initial phases, which can have potential applications as a quantum frequency filter.

Quantum Parrondo's games

Parrondo's paradox arises when two losing games are combined to produce a winning one. A history-dependent quantum Parrondo game is studied where the rotation operators that represent the toss of a classical biased coin are replaced by general SU(2) operators to transform the game into the quantum domain. In the initial state, a superposition of qubits can be used to couple the games and produce interference leading to quite different payoffs to those in the classical case. (C) 2002 Elsevier Science B.V. All rights reserved.

Combined chemical separation of Lu, Hf, Sm, Nd, and REEs from a single rock digest: Precise and accurate isotope Determinations of Lu-Hf and Sm-Nd using multicollector-ICPMS

A combined procedure for separating Lu, Hf, Sm, Nd, and rare earth elements (REEs) from a single sample digest is presented. The procedure consists of the following five steps: (1) sample dissolution via sodium peroxide sintering; (2) separation of the high field strength elements from the REEs and other matrix elements by a HF-free anion-exchange column procedure; (3) purification of Hf on a cation-exchange resin; (4) separation of REEs from other matrix elements by cation exchange; (5) Lu, Sm, and Nd separation from the other REEs by reversed-phase ion chromatography. Analytical reproducibilities of Sm-Nd and Lu-Hf isotope systematics are demonstrated for standard solutions and international rock reference materials. Results show overall good reproducibilities for Sm-Nd systematics independent of the rock type analyzed. For the Lu-Hf systematics, the reproducibility of the parent/daughter ratio is much better for JB-1 (basalt) than for two analyzed felsic crustal rocks (DR-N and an Archaean granitoid). It is demonstrated that this poorer reproducibility of the Lu/Hf ratio is truly caused by sample heterogeneity; thus, results are geologically reasonable.

A cassette ligation strategy with thioether replacement of three Gly-Gly peptide bonds: Total chemical synthesis of the 101 residue protein early pregnancy factor [psi(CH2S)(28-29,56-57,76-77)]

The 101 residue protein early pregnancy factor (EPF), also known as human chaperonin 10, was synthesized from four functionalized, but unprotected, peptide segments by a sequential thioether ligation strategy. The approach exploits the differential reactivity of a peptide-NHCH2CH2SH thiolate with XCH2CO-peptides, where X = Cl or I/Br. Initial model studies with short functionalized (but unprotected) peptides showed a significantly faster reaction of a peptide-NHCH2CH2SH thiolate with a BrCH2CO-peptide than with a CICH2CO-peptide, where thiolate displacement of the halide leads to chemoselective formation of a thioether surrogate for the Gly-Gly peptide bond. This rate difference was used as the basis of a novel sequential ligation approach to the synthesis of large polypeptide chains. Thus, ligation of a model bifunctional N-alpha-chloroacetyl, C-terminal thiolated peptide with a second N-alpha-bromoacetyl peptide demonstrated chemoselective bromide displacement by the thiol group. Further investigations showed that the relatively unreactive N-alpha-chloroacetyl peptides could be activated by halide exchange using saturated KI solutions to yield the highly reactive No-iodoacetyl peptides. These findings were used to formulate a sequential thioether ligation strategy for the synthesis of EPF, a 101 amino acid protein containing three Gly-Gly sites approximately equidistantly spaced within the peptide chain. Four peptide segments or cassettes comprising the EPF protein sequence (BrAc-[EPF 78-101] 12, ClAc-[EPF 58-75]-[NHCH2CH2SH] 13, ClAc-[EPF 30-55]-[NHCH2CH2SH] 14, and Ac-[EPF 1-27]-[NHCH2CH2SH] 15) of EPF were synthesized in high yield and purity using Boc SPPS chemistry. In the stepwise sequential ligation strategy, reaction of peptides 12 and 13 was followed by conversion of the N-terminal chloroacetyl functional group to an iodoacetyl, thus activating the product peptide for further ligation with peptide 14. The process of ligation followed by iodoacetyl activation was repeated to yield an analogue of EPF (EPF psi(CH2S)(28-29,56-57,76-77)) 19 in 19% overall yield.