Implementation of measurement reduction for the variational quantum eigensolver

One limitation of the variational quantum eigensolver algorithm is the large number of measurement steps required to estimate different terms in the Hamiltonian of interest. Unitary partitioning reduces this overhead by transforming the problem Hamiltonian into one containing fewer terms. We explore two different circuit constructions of the transformation required - one built by a sequence of rotations and the other built by a linear combination of unitaries (LCU). To assess performance, we simulated chemical Hamiltonians and studied the ground states of H2 and LiH. Both implementations are successful even in the presence of noise. The sequence-of-rotations realization offers the greatest benefit to calculations, whereas the probabilistic nature of LCU reduces its effectiveness. This work also demonstrates an experimental implementation of LCU on quantum hardware

Unitary partitioning and the contextual subspace variational quantum eigensolver

The contextual subspace variational quantum eigensolver (CS-VQE) is a hybrid quantum-classical algorithm that approximates the ground-state energy of a given qubit Hamiltonian. It achieves this by separating the Hamiltonian into contextual and noncontextual parts. The ground-state energy is approximated by classically solving the noncontextual problem, followed by solving the contextual problem using VQE, constrained by the noncontextual solution. In general, computation of the contextual correction needs fewer qubits and measurements compared with solving the full Hamiltonian via traditional VQE. We simulate CS-VQE on different tapered molecular Hamiltonians and apply the unitary partitioning measurement reduction strategy to further reduce the number of measurements required to obtain the contextual correction. Our results indicate that CS-VQE combined with measurement reduction is a promising approach to allow feasible eigenvalue computations on noisy intermediate-scale quantum devices. We also provide a modification to the CS-VQE algorithm; the CS-VQE algorithm previously could cause an exponential increase in Hamiltonian terms but with this modification now at worst will scale quadratically

A Comparison of the Bravyi-Kitaev and Jordan-Wigner Transformations for the Quantum Simulation of Quantum Chemistry

The ability to perform classically intractable electronic structure calculations is often cited as one of the principal applications of quantum computing. A great deal of theoretical algorithmic development has been performed in support of this goal. Most techniques require a scheme for mapping electronic states and operations to states of and operations upon qubits. The two most commonly used techniques for this are the Jordan-Wigner transformation and the Bravyi-Kitaev transformation. However, comparisons of these schemes have previously been limited to individual small molecules. In this paper, we discuss resource implications for the use of the Bravyi-Kitaev mapping scheme, specifically with regard to the number of quantum gates required for simulation. We consider both small systems, which may be simulatable on near-future quantum devices, and systems sufficiently large for classical simulation to be intractable. We use 86 molecular systems to demonstrate that the use of the Bravyi-Kitaev transformation is typically at least approximately as efficient as the canonical Jordan-Wigner transformation and results in substantially reduced gate count estimates when performing limited circuit optimizations

An intergenerational study of perceptions of changes in active free play among families from rural areas of Western Canada

Background: Children's engagement in active free play has declined across recent generations. Therefore, the purpose of this study was to examine perceptions of intergenerational changes in active free play among families from rural areas. We addressed two research questions: (1) How has active free play changed across three generations? (2) What suggestions do participants have for reviving active free play? Methods: Data were collected via 49 individual interviews with members of 16 families (15 grandparents, 16 parents, and 18 children) residing in rural areas/small towns in the Province of Alberta (Canada). Interview recordings were transcribed verbatim and subjected to thematic analysis guided by an ecological framework of active free play. Results: Factors that depicted the changing nature of active free play were coded in the themes of less imagination/more technology, safety concerns, surveillance, other children to play with, purposeful physical activity, play spaces/organized activities, and the good parenting ideal. Suggestions for reviving active free play were coded in the themes of enhance facilities to keep kids entertained, provide more opportunities for supervised play, create more community events, and decrease use of technology. Conclusions: These results reinforce the need to consider multiple levels of social ecology in the study of active free play, and highlight the importance of community-based initiatives to revive active free play in ways that are consistent with contemporary notions of good parentin

Bioavailable iron in the Southern Ocean: the significance of the iceberg conveyor belt

Productivity in the Southern Oceans is iron-limited, and the supply of iron dissolved from aeolian dust is believed to be the main source from outside the marine reservoir. Glacial sediment sources of iron have rarely been considered, as the iron has been assumed to be inert and non-bioavailable. This study demonstrates the presence of potentially bioavailable Fe as ferrihydrite and goethite in nanoparticulate clusters, in sediments collected from icebergs in the Southern Ocean and glaciers on the Antarctic landmass. Nanoparticles in ice can be transported by icebergs away from coastal regions in the Southern Ocean, enabling melting to release bioavailable Fe to the open ocean. The abundance of nanoparticulate iron has been measured by an ascorbate extraction. This data indicates that the fluxes of bioavailable iron supplied to the Southern Ocean from aeolian dust (0.01–0.13 Tg yr-1) and icebergs (0.06–0.12 Tg yr-1) are comparable. Increases in iceberg production thus have the capacity to increase productivity and this newly identified negative feedback may help to mitigate fossil fuel emissions

A comparison of methods for temporal analysis of aoristic crime

Objectives: To test the accuracy of various methods previously proposed (and one new method) to estimate offence times where the actual time of the event is not known. Methods: For 303 thefts of pedal cycles from railway stations, the actual offence time was determined from closed-circuit television and the resulting temporal distribution compared against commonly-used estimated distributions using circular statistics and analysis of residuals. Results: Aoristic analysis and allocation of a random time to each offence allow accurate estimation of peak offence times. Commonly-used deterministic methods were found to be inaccurate and to produce misleading results. Conclusions: It is important that analysts use the most accurate methods for temporal distribution approximation to ensure any resource decisions made on the basis of peak times are reliable