The Optimal Single Copy Measurement for the Hidden Subgroup Problem

The optimization of measurements for the state distinction problem has recently been applied to the theory of quantum algorithms with considerable successes, including efficient new quantum algorithms for the non-abelian hidden subgroup problem. Previous work has identified the optimal single copy measurement for the hidden subgroup problem over abelian groups as well as for the non-abelian problem in the setting where the subgroups are restricted to be all conjugate to each other. Here we describe the optimal single copy measurement for the hidden subgroup problem when all of the subgroups of the group are given with equal a priori probability. The optimal measurement is seen to be a hybrid of the two previously discovered single copy optimal measurements for the hidden subgroup problem.Comment: 8 pages. Error in main proof fixe

Close Approach during Hard Binary--Binary Scattering

We report on an extensive series of numerical experiments of binary--binary scattering, analysing the cross--section for close approach during interactions for a range of hard binary parameters of interest in globular cluster cores. We consider the implied rate for tidal interactions for different globular clusters and compare our results with previous, complementary estimates of stellar collision rates in globular clusters. We find that the collision rate for binary--binary encounters dominates in low density clusters if the binary fraction in the cluster is larger than $0.2$ for wide main--sequence binaries. In dense clusters binary--single interactions dominate the collision rate and the core binary fraction must be \ltorder 0.1 per decade in semi--major axis or too many collisions take place compared to observations. The rates are consistent if binaries with semi--major axes $\sim 100 AU$ are overabundant in low density clusters or if breakup and ejection substantially lowers the binary fraction in denser clusters. Given reasonable assumptions about fractions of binaries in the cores of low density clusters such as NGC~5053, we cannot account for all the observed blue stragglers by stellar collisions during binary encounters, suggesting a substantial fraction may be due to coalescence of tight primordial binaries.Comment: 13 pages including 13 ps figures. MNRAS in pres

Coherence-Preserving Quantum Bits

Real quantum systems couple to their environment and lose their intrinsic quantum nature through the process known as decoherence. Here we present a method for minimizing decoherence by making it energetically unfavorable. We present a Hamiltonian made up solely of two-body interactions between four two-level systems (qubits) which has a two-fold degenerate ground state. This degenerate ground state has the property that any decoherence process acting on an individual physical qubit must supply energy from the bath to the system. Quantum information can be encoded into the degeneracy of the ground state and such coherence-preserving qubits will then be robust to local decoherence at low bath temperatures. We show how this quantum information can be universally manipulated and indicate how this approach may be applied to a quantum dot quantum computer.Comment: 5 pages, 1 figur

The Effect on Rudder Control of Slip Stream Body, and Ground Interference

This investigation was undertaken to determine the relative effects of those factors which may interfere with the rudder control of an airplane, with especial reference to the process of landing. It shows that ground interference is negligible, but that the effects of a large rounded body and of the slip stream may combine to interfere seriously with rudder control at low flying speeds and when taxiing

Adiabatic Gate Teleportation

The difficulty in producing precisely timed and controlled quantum gates is a significant source of error in many physical implementations of quantum computers. Here we introduce a simple universal primitive, adiabatic gate teleportation, which is robust to timing errors and many control errors and maintains a constant energy gap throughout the computation above a degenerate ground state space. Notably this construction allows for geometric robustness based upon the control of two independent qubit interactions. Further, our piecewise adiabatic evolution easily relates to the quantum circuit model, enabling the use of standard methods from fault-tolerance theory for establishing thresholds.Comment: 4 pages, 1 figure, with additional 3 pages and 2 figures in an appendix. v2 Refs added. Video abstract available at http://www.quantiki.org/video_abstracts/0905090

Recurrence rates for SIDS - the importance of risk stratification

Objective: To investigate the importance of stratification by risk factors in computing the probability of a second SIDS in a family. Design: Simulation Study Background: The fact that a baby dies suddenly and unexpectedly means that there is a raised probability that the baby’s family have risk factors associated with Sudden Infant Death Syndrome (SIDS). Thus one cannot consider the risk of a subsequent death to be that of the general population. The Confidential Enquiry into Stillbirths and Deaths in Infancy (CESDI)6 identified three major social risk factors: smoking, age1, and unemployed/unwaged as major risk factors. It gave estimates of risk for families with different numbers of these risk factors. We investigate whether it is reasonable to assume that, conditional on these risk factors, the risk of a second event is independent of the risk of the first and as a consequence one can square the risks to get the risk of two SIDS in a family. We have used CESDI data to estimate the probability of a second SID in a family under different plausible scenarios of the prevalence of the risk factors. We have applied the model to make predictions in the Care of Next Infant (CONI) study7. Results: The model gave plausible predictions. The CONI study observed 18 second SIDS. Our model predicted 14 (95% prediction interval 7 to 21). Conclusion: When considering the risk of a subsequent SIDS in a family one should always take into account the known risk factors. If all risks have been identified, then conditional on these risks, the risk of two events is the product of the individual risks However for a given family we cannot quantify the magnitude of the increased risk because of other possible risk factors not accounted for in the model