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.

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.

Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

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.

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.

Young children's performance on the balance scale: The influence of relational complexity

Three experiments investigated the effect of complexity on children's understanding of a beam balance. In nonconflict problems, weights or distances varied, while the other was held constant. In conflict items, both weight and distance varied, and items were of three kinds: weight dominant, distance dominant, or balance (in which neither was dominant). In Experiment 1, 2-year-old children succeeded on nonconflict-weight and nonconflict-distance problems. This result was replicated in Experiment 2, but performance on conflict items did not exceed chance. In Experiment 3, 3- and 4-year-olds succeeded on all except conflict balance problems, while 5- and 6-year-olds succeeded on all problem types. The results were interpreted in terms of relational complexity theory. Children aged 2 to 4 years succeeded on problems that entailed binary relations, but 5- and 6-year-olds also succeeded on problems that entailed ternary relations. Ternary relations tasks from other domains-transitivity and class inclusion-accounted for 93% of the age-related variance in balance scale scores. (C) 2002 Elsevier Science (USA).

A cognitive complexity metric applied to cognitive development

Two experiments tested predictions from a theory in which processing load depends on relational complexity (RC), the number of variables related in a single decision. Tasks from six domains (transitivity, hierarchical classification, class inclusion, cardinality, relative-clause sentence comprehension, and hypothesis testing) were administered to children aged 3-8 years. Complexity analyses indicated that the domains entailed ternary relations (three variables). Simpler binary-relation (two variables) items were included for each domain. Thus RC was manipulated with other factors tightly controlled. Results indicated that (i) ternary-relation items were more difficult than comparable binary-relation items, (ii) the RC manipulation was sensitive to age-related changes, (iii) ternary relations were processed at a median age of 5 years, (iv) cross-task correlations were positive, with all tasks loading on a single factor (RC), (v) RC factor scores accounted for 80% (88%) of age-related variance in fluid intelligence (compositionality of sets), (vi) binary- and ternary-relation items formed separate complexity classes, and (vii) the RC approach to defining cognitive complexity is applicable to different content domains. (C) 2002 Elsevier Science (USA). All rights reserved.

One-dimensional quantum walk with unitary noise

The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution P-t(n) at time t is very different from the Gaussian distribution obtained for the classical random walk. Furthermore, its standard deviation, sigma(t) scales as sigma(t)similar tot, unlike the classical random walk for which sigma(t)similar toroott. It is shown that when the quantum walk is exposed to unitary noise, it exhibits a crossover from quantum behavior for short times to classical-like behavior for long times. The crossover time is found to be Tsimilar toalpha(-2), where alpha is the standard deviation of the noise.

Computational differentiation of N-terminal signal peptides and transmembrane helices

Signal peptides and transmembrane helices both contain a stretch of hydrophobic amino acids. This common feature makes it difficult for signal peptide and transmembrane helix predictors to correctly assign identity to stretches of hydrophobic residues near the N-terminal methionine of a protein sequence. The inability to reliably distinguish between N-terminal transmembrane helix and signal peptide is an error with serious consequences for the prediction of protein secretory status or transmembrane topology. In this study, we report a new method for differentiating protein N-terminal signal peptides and transmembrane helices. Based on the sequence features extracted from hydrophobic regions (amino acid frequency, hydrophobicity, and the start position), we set up discriminant functions and examined them on non-redundant datasets with jackknife tests. This method can incorporate other signal peptide prediction methods and achieve higher prediction accuracy. For Gram-negative bacterial proteins, 95.7% of N-terminal signal peptides and transmembrane helices can be correctly predicted (coefficient 0.90). Given a sensitivity of 90%, transmembrane helices can be identified from signal peptides with a precision of 99% (coefficient 0.92). For eukaryotic proteins, 94.2% of N-terminal signal peptides and transmembrane helices can be correctly predicted with coefficient 0.83. Given a sensitivity of 90%, transmembrane helices can be identified from signal peptides with a precision of 87% (coefficient 0.85). The method can be used to complement current transmembrane protein prediction and signal peptide prediction methods to improve their prediction accuracies. (C) 2003 Elsevier Inc. All rights reserved.

Numerical study of hydrogenic effective mass theory for an impurity P donor in Si in the presence of an electric field and interfaces

In this paper we examine the effects of varying several experimental parameters in the Kane quantum computer architecture: A-gate voltage, the qubit depth below the silicon oxide barrier, and the back gate depth to explore how these variables affect the electron density of the donor electron. In particular, we calculate the resonance frequency of the donor nuclei as a function of these parameters. To do this we calculated the donor electron wave function variationally using an effective-mass Hamiltonian approach, using a basis of deformed hydrogenic orbitals. This approach was then extended to include the electric-field Hamiltonian and the silicon host geometry. We found that the phosphorous donor electron wave function was very sensitive to all the experimental variables studied in our work, and thus to optimize the operation of these devices it is necessary to control all parameters varied in this paper.

Quantum dynamical characterization of unimolecular resonances

We give a selective review of quantum mechanical methods for calculating and characterizing resonances in small molecular systems, with an emphasis on recent progress in Chebyshev and Lanczos iterative methods. Two archetypal molecular systems are discussed: isolated resonances in HCO, which exhibit regular mode and state specificity, and overlapping resonances in strongly bound HO2, which exhibit irregular and chaotic behavior. Future directions in this field are also discussed.