Quantum Fidelity Decay of Quasi-Integrable Systems

We show, via numerical simulations, that the fidelity decay behavior of quasi-integrable systems is strongly dependent on the location of the initial coherent state with respect to the underlying classical phase space. In parallel to classical fidelity, the quantum fidelity generally exhibits Gaussian decay when the perturbation affects the frequency of periodic phase space orbits and power-law decay when the perturbation changes the shape of the orbits. For both behaviors the decay rate also depends on initial state location. The spectrum of the initial states in the eigenbasis of the system reflects the different fidelity decay behaviors. In addition, states with initial Gaussian decay exhibit a stage of exponential decay for strong perturbations. This elicits a surprising phenomenon: a strong perturbation can induce a higher fidelity than a weak perturbation of the same type.Comment: 11 pages, 11 figures, to be published Phys. Rev.

Energetic Suppression of Decoherence in Exchange-Only Quantum Computation

Universal quantum computation requiring only the Heisenberg exchange interaction and suppressing decoherence via an energy gap is presented. The combination of an always-on exchange interaction between the three physical qubits comprising the encoded qubit and a global magnetic field generates an energy gap between the subspace of interest and all other states. This energy gap suppresses decoherence. Always-on exchange couplings greatly simplify hardware specifications and the implementation of inter-logical-qubit gates. A controlled phase gate can be implemented using only three Heisenberg exchange operations all of which can be performed simultaneously.Comment: 4 pages, 4 figure

A Scalable Architecture for Coherence-Preserving Qubits

We propose scalable architectures for the coherence-preserving qubits introduced by Bacon, Brown, and Whaley [Phys. Rev. Lett. {\bf 87}, 247902 (2001)]. These architectures employ extra qubits providing additional degrees of freedom to the system. We show that these extra degrees of freedom can be used to counter errors in coupling strength within the coherence-preserving qubit and to combat interactions with environmental qubits. The presented architectures incorporate experimentally viable methods for inter-logical-qubit coupling and can implement a controlled phase gate via three simultaneous Heisenberg exchange operations. The extra qubits also provide flexibility in the arrangement of the physical qubits. Specifically, all physical qubits of a coherent-preserving qubit lattice can be placed in two spatial dimensions. Such an arrangement allows for universal cluster state computation.Comment: 4 pages, 4 figure

Quantum Cellular Automata Pseudo-Random Maps

Quantum computation based on quantum cellular automata (QCA) can greatly reduce the control and precision necessary for experimental implementations of quantum information processing. A QCA system consists of a few species of qubits in which all qubits of a species evolve in parallel. We show that, in spite of its inherent constraints, a QCA system can be used to study complex quantum dynamics. To this aim, we demonstrate scalable operations on a QCA system that fulfill statistical criteria of randomness and explore which criteria of randomness can be fulfilled by operators from various QCA architectures. Other means of realizing random operators with only a few independent operators are also discussed.Comment: 7 pages, 8 figures, submitted to PR

Bayesian Value-of-Information Analysis: An Application to a Policy Model of Alzheimer's Disease

A framework is presented which distinguishes the conceptually separate decisions of which treatment strategy is optimal from the question of whether more information is required to inform this choice in the future. The authors argue that the choice of treatment strategy should be based on expected utility and the only valid reason to characterise the uncertainty surrounding outcomes of interest is to establish the value of acquiring additional information. A Bayesian decision theoretic approach is demonstrated though a probabilistic analysis of a published policy model of Alzheimer’s disease. The expected value of perfect information is estimated for the decision to adopt a new pharmaceutical for the population of US Alzheimer’s disease patients. This provides an upper bound on the value of additional research. The value of information is also estimated for each of the model inputs. This analysis can focus future research by identifying those parameters where more precise estimates would be most valuable, and indicating whether an experimental design would be required. We also discuss how this type of analysis can also be used to design experimental research efficiently (identifying optimal sample size and optimal sample allocation) based on the marginal cost and marginal benefit of sample information. Value-of-information analysis can provide a measure of the expected payoff from proposed research, which can be used to set priorities in research and development. It can also inform an efficient regulatory framework for new health care technologies: an analysis of the value of information would define when a claim for a new technology should be deemed “substantiated” and when evidence should be considered “competent and reliable” when it is not cost-effective to gather anymore information.stochastic CEA; Bayesian decision theory; value of information.

Fidelity Decay as an Efficient Indicator of Quantum Chaos

Recent work has connected the type of fidelity decay in perturbed quantum models to the presence of chaos in the associated classical models. We demonstrate that a system's rate of fidelity decay under repeated perturbations may be measured efficiently on a quantum information processor, and analyze the conditions under which this indicator is a reliable probe of quantum chaos and related statistical properties of the unperturbed system. The type and rate of the decay are not dependent on the eigenvalue statistics of the unperturbed system, but depend on the system's eigenvector statistics in the eigenbasis of the perturbation operator. For random eigenvector statistics the decay is exponential with a rate fixed precisely by the variance of the perturbation's energy spectrum. Hence, even classically regular models can exhibit an exponential fidelity decay under generic quantum perturbations. These results clarify which perturbations can distinguish classically regular and chaotic quantum systems.Comment: 4 pages, 3 figures, LaTeX; published version (revised introduction and discussion

The Effects of Symmetries on Quantum Fidelity Decay

We explore the effect of a system's symmetries on fidelity decay behavior. Chaos-like exponential fidelity decay behavior occurs in non-chaotic systems when the system possesses symmetries and the applied perturbation is not tied to a classical parameter. Similar systems without symmetries exhibit faster-than-exponential decay under the same type of perturbation. This counter-intuitive result, that extra symmetries cause the system to behave in a chaotic fashion, may have important ramifications for quantum error correction.Comment: 5 pages, 3 figures, to be published Phys. Rev. E Rapid Communicatio

Entanglement Generation of Nearly-Random Operators

We study the entanglement generation of operators whose statistical properties approach those of random matrices but are restricted in some way. These include interpolating ensemble matrices, where the interval of the independent random parameters are restricted, pseudo-random operators, where there are far fewer random parameters than required for random matrices, and quantum chaotic evolution. Restricting randomness in different ways allows us to probe connections between entanglement and randomness. We comment on which properties affect entanglement generation and discuss ways of efficiently producing random states on a quantum computer.Comment: 5 pages, 3 figures, partially supersedes quant-ph/040505

The Lattice Schwinger Model: Confinement, Anomalies, Chiral Fermions and All That

In order to better understand what to expect from numerical CORE computations for two-dimensional massless QED (the Schwinger model) we wish to obtain some analytic control over the approach to the continuum limit for various choices of fermion derivative. To this end we study the Hamiltonian formulation of the lattice Schwinger model (i.e., the theory defined on the spatial lattice with continuous time) in $A_0=0$ gauge. We begin with a discussion of the solution of the Hamilton equations of motion in the continuum, we then parallel the derivation of the continuum solution within the lattice framework for a range of fermion derivatives. The equations of motion for the Fourier transform of the lattice charge density operator show explicitly why it is a regulated version of this operator which corresponds to the point-split operator of the continuum theory and the sense in which the regulated lattice operator can be treated as a Bose field. The same formulas explicitly exhibit operators whose matrix elements measure the lack of approach to the continuum physics. We show that both chirality violating Wilson-type and chirality preserving SLAC-type derivatives correctly reproduce the continuum theory and show that there is a clear connection between the strong and weak coupling limits of a theory based upon a generalized SLAC-type derivative.Comment: 27 pages, 3 figures, revte