We benchmark the quantum processing units of largest annealers to date, 5000+ qubit annealer Advantage and its 2000+ predecessor D-Wave 2000Q, using tail assignment exact cover problems from aircraft scheduling scenarios. The set contains small, intermediate, large with both sparsely connected almost fully instances. find that outperforms 2000Q for all problems, a notable increase in success rate problem size. In particular, is also able solve 120 logical qubits cannot anymore. Furthermore,...

We study the propagation of light through a semi-infinite medium with transverse disorder (that is, in two directions only). show that such system exhibits strong two-dimensional localization by demonstrating on beam expands until length is reached.

We present a detailed numerical study of the electronic properties single-layer graphene with resonant ("hydrogen") impurities and vacancies within framework noninteracting tight-binding model on honeycomb lattice. The algorithms are based solution time-dependent Schr\"{o}dinger equation applied to calculate density states, \textit{quasieigenstates}, AC DC conductivities large samples containing millions atoms. Our results give consistent picture evolution structure transport functionalized...

We study the properties of Suzuki's systematic approximations to exponential operator $\mathrm{exp}(\ensuremath{-}\ensuremath{\beta}H)$ by calculating thermodynamic functions three simple quantum models. demonstrate that path-integral representation partition function obtained from these can be simplified and made more accurate constructing Hermitian versions expressions.

The thermodynamic properties of the small-polaron model are studied by means a discrete version Feynman path-integral representation partition function. This lattice describes fermion interacting with boson field. bosons treated analytically, contribution is calculated using Monte Carlo method. We analyze functions for case one-, two-, and three-dimensional polaron motion. present strong evidence that becomes superlocalized if interaction strength greater than critical value.

Kernel-based support vector machines (SVMs) are supervised machine learning algorithms for classification and regression problems. We introduce a method to train SVMs on D-Wave 2000Q quantum annealer study its performance in comparison trained conventional computers. The is applied both synthetic data real obtained from biology experiments. find that the produces an ensemble of different solutions often generalizes better unseen than single global minimum SVM computer, especially cases where...

Abstract The performance of the quantum approximate optimization algorithm is evaluated by using three different measures: probability finding ground state, energy expectation value, and a ratio closely related to approximation ratio. set problem instances studied consists weighted MaxCut problems 2-satisfiability problems. Ising model representations latter possess unique states highly degenerate first excited states. executed on computer simulators IBM Q Experience. Additionally, data...

Significance Birds-of-paradise are brilliant examples of colorful displays in nature. The dazzling colors the display, used ritualized dances to attract attention mates, arise from interference and diffraction light within photonic nanostructures on their feathers. This study reports a quantitative investigation complex structures by connecting experimental photonics with state art computational model. methods this may be applied numerous applications, e.g., for optimized crystal designs....

A revised version of the massively parallel simulator a universal quantum computer, described in this journal eleven years ago, is used to benchmark various gate-based algorithms on some most powerful supercomputers that exist today. Adaptive encoding wave function reduces memory requirement by factor eight, making it possible simulate computers with up 48 qubits Sunway TaihuLight and K computer. The exhibits close-to-ideal weak-scaling behavior TaihuLight, an IBM Blue Gene/Q, Intel Xeon...

A theoretical analysis is given of the equation motion method, due to Alben et al. [Phys. Rev. B 12, 4090 (1975)], compute eigenvalue distribution (density states) very large matrices. The salient feature this method that for matrices kind encountered in quantum physics memory and CPU requirements scale linearly with dimension matrix. We derive a rigorous estimate statistical error, supporting earlier observations computational efficiency approach increases matrix size. use an imaginary-time...

We demonstrate that the Chebyshev expansion method is a very efficient numerical tool for studying spin-bath decoherence of quantum systems. consider two typical problems arising in systems consisting few coupled spins: (i) determining pointer states system and (ii) temporal decay oscillations. As our results demonstrate, states, Chebyshev-based scheme at least factor 8 faster than existing algorithms based on Suzuki-Trotter decomposition. For second type, approach 3-4 times...

Mature male Calopteryx japonica damselflies have dark-blue wings, due to darkly coloured wing membranes and blue reflecting veins. The contain a high melanin concentration the veins multilayer of chitin. Female immature C. brown wings. We determined refractive index by comparing differently pigmented applying Jamin-Lebedeff interference microscopy. Together with previously measured chitin blue, structural colour could be quantitatively explained an optical model. obtained data will useful in...

We present a comparison of the computer simulation data gyroid nanostructures with optical measurements (reflectivity spectra and scattering diagrams) ventral wing scales Green Hairstreak butterfly, Callophrys rubi . demonstrate that omnidirectional green colour arises from cuticular structure grown in domains different orientation. also show this three-dimensional structure, operating as biophotonic crystal, gives rise to various polarization effects. briefly discuss possible biological...

We present a detailed numerical study of the electronic transport properties bilayer and trilayer graphene within framework single-electron tight-binding model. Various types disorder are considered, such as resonant (hydrogen) impurities, vacancies, short- or long-range Gaussian random potentials, nearest-neighbor hopping. The algorithms based on solution time-dependent Schr\"odinger equation applied to calculate density states conductivities (via Kubo formula) large samples containing...

The cover scales on the wing of Emerald-patched Cattleheart butterfly, Parides sesostris, contain gyroid-type biological photonic crystals that brightly reflect green light. A pigment, which absorbs maximally at approximately 395 nm, is immersed predominantly throughout elaborate upper lamina. This pigment acts as a long-pass filter shaping reflectance spectrum underlying crystals. additional effect filtering spatial distribution scale angle-independent, leading to stable pattern contrast....

The neotropical diamond weevil, Entimus imperialis , is marked by rows of brilliant spots on the overall black elytra. are concave pits with intricate patterns structural-coloured scales, consisting large domains three-dimensional photonic crystals that have a diamond-type structure. Reflectance spectra measured from individual scale perfectly match model spectra, calculated anatomical data and finite-difference time-domain methods. reflections single extremely directional (observed point...

With the advent of public access to small gate-based quantum processors, it becomes necessary develop a benchmarking methodology such that independent researchers can validate operation these processors. We explore usefulness number simple circuits as benchmarks for computing devices and show performing identity operations are very simple, scalable sensitive gate errors therefore well suited this task. illustrate procedure by presenting benchmark results IBM Quantum Experience, cloud-based...

We report on simulations for the molecular-crystal model without dispersion in adiabatic regime all lattice dimensionalities. A discrete version of Feynman path-integral formalism is used to calculate electron properties. compare these results with approximate theories and conclude that continuum versions have little relationship model. In addition, influence phonon transition between "untrapped" "self-trapped" state an a one-dimensional studied within context Holstein's show electron-phonon...

Starting from a genuine discrete version of the Feynman path-integral representation for partition function, calculations have been made energy, specific heat, and static density-density correlation functions one-dimensional lattice model at nonzero temperatures. A Monte Carlo technique has used to calculate temperature-dependent properties. The results are compared with exact short chains, Hartree-Fock approximation, classical model.

In this paper we systemically study the optical conductivity and density of states disordered graphene beyond Dirac cone approximation. The is computed by using Kubo formula, within framework a full $\ensuremath{\pi}$-band tight-binding model. Different types noncorrelated correlated disorder are considered, such as random or Gaussian potentials, nearest-neighbor hopping parameters, randomly distributed vacancies their clusters, adsorbed hydrogen atoms clusters. For large enough...