From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz

The next few years will be exciting as prototype universal quantum processors emerge, enabling implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware for their evaluation, and which have the potential to significantly expand the breadth of quantum computing applications. A leading candidate is Farhi et al.'s Quantum Approximate Optimization Algorithm, which alternates between applying a cost-function-based Hamiltonian and a mixing Hamiltonian. Here, we extend this framework to allow alternation between more general families of operators. The essence of this extension, the Quantum Alternating Operator Ansatz, is the consideration of general parametrized families of unitaries rather than only those corresponding to the time-evolution under a fixed local Hamiltonian for a time specified by the parameter. This ansatz supports the representation of a larger, and potentially more useful, set of states than the original formulation, with potential long-term impact on a broad array of application areas. For cases that call for mixing only within a desired subspace, refocusing on unitaries rather than Hamiltonians enables more efficiently implementable mixers than was possible in the original framework. Such mixers are particularly useful for optimization problems with hard constraints that must always be satisfied, defining a feasible subspace, and soft constraints whose violation we wish to minimize. More efficient implementation enables earlier experimental exploration of an alternating operator approach to a wide variety of approximate optimization, exact optimization, and sampling problems. Here, we introduce the Quantum Alternating Operator Ansatz, lay out design criteria for mixing operators, detail mappings for eight problems, and provide brief descriptions of mappings for diverse problems.Comment: 51 pages, 2 figures. Revised to match journal pape

Demographic Studies on Hawaii's Endangered Tree Snails: Partulina proxima

Populations of the tree snail Partulina proxima, endemic to higher elevations of Molokai, Hawaiian Islands, were studied for 3 years. Analyses of the data derived from 17bimonthly mark-recapture events determined that each tree harbors a small, mostly nonmigratory population of 8-26 snails of which 2-4 are adults; the snails average 4.2 mm long at birth and 21.3 mm long when growth stops; growth is slow, with maturity reached in 5-7 years; annual fecundity averages 6.2 offspring per adult; and mortality is about 98% over the first 4 years of life. Given the high rate of juvenile mortality, adult snails must reproduce for at least 12 years to replace themselves. From this we calculate a minimum maximal life-span of 18-19 years. We conclude that the current high rate of unexplained juvenile mortality, combined with lat e age at first reproduction and low fecundity, place this species at very high risk to any sort of perturbation, particularly any selective predation on adults

Analysis of a distributed fiber-optic temperature sensor using single-photon detectors

We demonstrate a high-accuracy distributed fiber-optic temperature sensor using superconducting nanowire single-photon detectors and single-photon counting techniques. Our demonstration uses inexpensive single-mode fiber at standard telecommunications wavelengths as the sensing fiber, which enables extremely low-loss experiments and compatibility with existing fiber networks. We show that the uncertainty of the temperature measurement decreases with longer integration periods, but is ultimately limited by the calibration uncertainty. Temperature uncertainty on the order of 3 K is possible with spatial resolution of the order of 1 cm and integration period as small as 60 seconds. Also, we show that the measurement is subject to systematic uncertainties, such as polarization fading, which can be reduced with a polarization diversity receiver

Population genetics and the effects of a severe bottleneck in an ex situ population of critically endangered Hawaiian tree snails

As wild populations decline, ex situ propagation provides a potential bank of genetic diversity and a hedge against extinction. These programs are unlikely to succeed if captive populations do not recover from the severe bottleneck imposed when they are founded with a limited number of individuals from remnant populations. In small captive populations allelic richness may be lost due to genetic drift, leading to a decline in fitness. Wild populations of the Hawaiian tree snail Achatinella lila,a hermaphroditic snail with a long life history, have declined precipitously due to introduced predators and other human impacts. A captive population initially thrived after its founding with seven snails, exceeding 600 captive individuals in 2009, but drastically declined in the last five years. Measures of fitness were examined from 2,018 captive snails that died between 1998 and 2012, and compared with genotypic data for six microsatellite loci from a subset of these deceased snails (N5335), as well as live captive snails (N5198) and wild snails (N592). Surprisingly, the inbreeding coefficient (Fis) declined over time in the captive population, and is now approaching values observed in the 2013 wild population, despite a significant decrease in allelic richness. However, adult annual survival and fecundity significantly declined in the second generation. These measures of fitness were positively correlated with heterozygosity. Snails with higher measures of heterozygosity had more offspring, and third generation offspring with higher measures of heterozygosity were more likely to reach maturity. These results highlight the importance of maintaining genetic diversity in captive populations, particularly those initiated with a small number of individuals from wild remnant populations. Genetic rescue may allow for an increase in genetic diversity in the captive population, as measures of heterozygosity and rarified allelic richness were higher in wild tree snails

Analysis of ATS photographs using a specially designed electronic console, phase 1 Final report, 8 Oct. 1969 - 8 Oct. 1970

Evaluation of capabilities of electronic display system used in analysis of ATS cloud photograph

Novel Josephson Junction Geometries in NbCu bilayers fabricated by Focused Ion Beam Microscope

We explore novel junction configurations as an extension of our established Focused Ion Beam-based low TC SNS Junction fabrication technique. By milling a circular trench (diameter 1 micron, width 50 nm) in a 125 nm Nb 75 nm Cu bilayer we define a superconducting island connected to the bulk of the film by a normal metal barrier and entirely enclosed in-plane by the superconducting film. The circular junction properties can be probed by depositing an insulating layer over the device and drilling a 0.3 micron diameter hole down to the island to allow a Nb via to be deposited. Device behavior has been studied at 4.2 K. An SNS-like current voltage characteristic and Shapiro steps are observed. It is in terms of magnetic field behavior that the device exhibits novel characteristics: as the device is entirely enclosed in type II superconductor, when a magnetic field is applied perpendicular to the plane of the film, only quantized flux can enter the junction. Hence as applied magnetic field is increased the junction critical current is unchanged, then abruptly suppressed as soon as a flux quantum enters (close to the expected value of lower critical field for the film).Comment: 10 pages including 6 figures Minor Corrections inlight of referees' comment

A Hydrodynamic-Sediment Transport Numerical Model for the Waipaoa Shelf, New Zealand: Model Archive

These files are compressed versions of input files, model code, and output used for two publications: Moriarty, J. M., Harris, C. K., and Hadfield, M. G. (2014). A hydrodynamic and sediment transport model for the Waipaoa Shelf, New Zealand: Sensitivity of fluxes to spatially-varying erodibility and model nesting. Journal of Marine Science and Engineering, 2 (2): 336-369. Doi:10.3390/jmse2020336 Moriarty, J. M., Harris, C. K., and Hadfield, M. G. (2015). Event-to-seasonal sediment dispersal on the Waipaoa River Shelf, New Zealand: A numerical modeling study. Continental Shelf Research, 110: 108-123. Doi: 10.1016/j.csr2015.10.005 Compressed files with the .gz file extension can be opened with Gzip GNU software (open source). Compressed files with the .tar file extension can be opened with Gzip Tar software (open source). Many of the input / output files use the NetCDF (Network Common Data Form) file format. These have "nc" as a file extension and can be read using a variety of open source tools: see http://www.unidata.ucar.edu/software/netcdf/docs/ . For information about the Regional Ocean Modeling System (ROMS), its model code and input / output, see www.myroms.org

Design and characterisation of titanium nitride sub-arrays of kinetic inductance detectors for passive terahertz imaging

We report on the investigation of titanium nitride (TiN) thin films deposited via atomic layer deposition (ALD) for microwave kinetic inductance detectors (MKID). Using our in-house ALD process, we have grown a sequence of TiN thin films (thickness 15, 30, 60 nm). The films have been characterised in terms of superconducting transition temperature Tc , sheet resistance Rs and microstructure. We have fabricated test resonator structures and characterised them at a temperature of 300 mK. At 350 GHz, we report an optical noise equivalent power NEPopt≈2.3×10−15 W/√Hz , which is promising for passive terahertz imaging applications

Exploring Network-Related Optimization Problems Using Quantum Heuristics

Network-related connectivity optimization problems are underlying a wide range of applications and are also of high computational complexity. We consider studying network optimization problems using two types of quantum heuristics.One is quantum annealing, and the other Quantum Alternating Operator Ansatz, an extension of the Quantum Approximate Optimization Algorithms for gate-model quantum computation, in which a cost-function based unitary and a non-commuting mixing unitary are applied alternately. We present problem mappings for problems of finding the spanning-tree or spanning-graph of a graph that optimizes certain costs, and a variant that further requires the spanning-tree be degree-bounded. With quantum annealing, all constraints are cast into penalty terms in the cost Hamiltonian, and the solution is encoded as the ground state of the Hamiltonian. We provide three mappings to the quadratic unconstrained binary optimization (QUBO) form, compare the resource requirements, and analyze the tradeoffs. For QAOA, we give special focus on the design of mixers based on the constraints presented in the problem, such that the system evolution remains in a subspace of the full Hilbert space where all constraints are satisfied. In the spanning-tree problem, one such hard constraint is that a mixer applied to a spanning-tree needs also be a spanning tree. This involves checking the connectivity of a subgraph, which is a global condition common for most network-related problems. We show how this feature can be efficiently represented in the mixer in a quantum coherent way, based on manipulation of a descendant-matrix and an adjacent matrix. We further develop a mixer for the spanning-graphs based on the spanning-tree mixer