Cluster-state quantum computation

This article is a short introduction to and review of the cluster-state model of quantum computation, in which coherent quantum information processing is accomplished via a sequence of single-qubit measurements applied to a fixed quantum state known as a cluster state. We also discuss a few novel properties of the model, including a proof that the cluster state cannot occur as the exact ground state of any naturally occurring physical system, and a proof that measurements on any quantum state which is linearly prepared in one dimension can be efficiently simulated on a classical computer, and thus are not candidates for use as a substrate for quantum computation.Comment: 15 pages, resubmitted version accepted to Rev. Math. Phy

A 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 (CNOT), 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. Here 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 important result for systems of arbitrary finite dimension has been provided by J. L. and R. Brylinski [arXiv:quant-ph/0108062, 2001]; however, their proof relies upon a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical [C. M. Dawson and A. Gilchrist, online implementation of the procedure described herein (2002), http://www.physics.uq.edu.au/gqc/].Comment: 3 pages, online implementation of procedure described can be found at http://www.physics.uq.edu.au/gqc

Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, subriemannian, and Finslerian manifolds. These results generalize the results of Nielsen, Dowling, Gu, and Doherty, Science 311, 1133-1135 (2006), which showed that the gate complexity can be related to distances on a Riemannian manifoldComment: 7 Pages Added Full Names to Author

Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? We provide an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling n-qubit Hamiltonian and local unitaries. It follows that universal quantum computation can be performed using any entangling interaction and local unitary operations.Comment: Added references to NMR refocusing and to earlier work by Leung et al and Jones and Knil

Quantum privacy and quantum coherence

We derive a simple relation between a quantum channel's capacity to convey coherent (quantum) information and its usefulness for quantum cryptography.Comment: 6 pages RevTex; two short comments added 7 October 199

Elementary gates for quantum computation

We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values $(x,y)$ to $(x,x \oplus y)$) is universal in the sense that all unitary operations on arbitrarily many bits $n$ (U($2^n$)) can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical AND of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two-and three-bit quantum gates, the asymptotic number required for $n$-bit Deutsch-Toffoli gates, and make some observations about the number required for arbitrary $n$-bit unitary operations.Comment: 31 pages, plain latex, no separate figures, submitted to Phys. Rev. A. Related information on http://vesta.physics.ucla.edu:7777

Vacuum Polarization and Energy Conditions at a Planar Frequency Dependent Dielectric to Vacuum Interface

The form of the vacuum stress-tensor for the quantized scalar field at a dielectric to vacuum interface is studied. The dielectric is modeled to have an index of refraction that varies with frequency. We find that the stress-tensor components, derived from the mode function expansion of the Wightman function, are naturally regularized by the reflection and transmission coefficients of the mode at the boundary. Additionally, the divergence of the vacuum energy associated with a perfectly reflecting mirror is found to disappear for the dielectric mirror at the expense of introducing a new energy density near the surface which has the opposite sign. Thus the weak energy condition is always violated in some region of the spacetime. For the dielectric mirror, the mean vacuum energy density per unit plate area in a constant time hypersurface is always found to be positive (or zero) and the averaged weak energy condition is proven to hold for all observers with non-zero velocity along the normal direction to the boundary. Both results are found to be generic features of the vacuum stress-tensor and not necessarily dependent of the frequency dependence of the dielectric.Comment: 16 pages, 4 figures, Revtex style Minor typographic corrections to equations and tex

Temporal and Space-Use Changes by Rats in Response to Predation by Feral Cats in an Urban Ecosystem

Feral cats (Felis catus) are predators that cause widespread loss of native wildlife in urban ecosystems. Despite these risks, cats are commonly released as control agents for city rats (Rattus spp.). Cats can influence their prey directly by killing or indirectly through changes to feeding or space-use. However, cats prefer defenseless prey, and there are no data suggesting that cats influence large (>300 g) urban rats. We used a pre-existing radiofrequency identification assay (microchipped rats and field cameras) and ethograms to assess the impact of cats, including temporal and space use patterns, on an active rat colony. From Dec 27, 2017 through May 28, 2018 we captured 306 videos of pre-identified cats and/or rats that shared the same space. There were three instances of predation and 20 stalking events. Logistic regression showed the likelihood of a rat being seen on a particular day is associated with the number of cats seen on the same day (OR = 0.1, p < 0.001) or previous day (OR = 0.15, p < 0.001). Space-use was also impacted. For every additional cat sighting, a rat is 1.19 times more likely to move in the direction of shelter. Our findings of low levels of predation support why ecologists believe the risks to native wildlife outweighs any benefits of releasing cats. Even though rats were less likely to be seen, they simply shifted their movements and remained present in the system. Our findings that cat presence led to fewer rat sightings may explain the common perception of their value as rat-predators despite the associated risks

Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism

This essay examines the philosophical significance of $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of $\Omega$-logical validity can then be countenanced within a coalgebraic logic, and $\Omega$-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of $\Omega$-logical validity correspond to those of second-order logical consequence, $\Omega$-logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets

From alcohol initiation to tolerance to problems: Discordant twin modeling of a developmental process

AbstractThe current study examined a stage-based alcohol use trajectory model to test for potential causal effects of earlier drinking milestones on later drinking milestones in a combined sample of two cohorts of Australian monozygotic and same-sex dizygotic twins (N= 7,398, ageM= 30.46,SD= 2.61, 61% male, 56% monozygotic twins). Ages of drinking, drunkenness, regular drinking, tolerance, first nontolerance alcohol use disorder symptom, and alcohol use disorder symptom onsets were assessed retrospectively. Ages of milestone attainment (i.e., age-of-onset) and time between milestones (i.e., time-to-event) were examined via frailty models within a multilevel discordant twin design. For age-of-onset models, earlier ages of onset of antecedent drinking milestones increased hazards for earlier ages of onset for more proximal subsequent drinking milestones. For the time-to-event models, however, earlier ages of onset for the “starting” milestone decreased risk for a shorter time period between the starting and the “ending” milestone. Earlier age of onset of intermediate milestones between starting and ending drinking milestones had the opposite effect, increasing risk for a shorter time period between the starting and ending milestones. These results are consistent with a causal effect of an earlier age of drinking milestone onset on temporally proximal subsequent drinking milestones.</jats:p