Vacancies in graphene: an application of adiabatic quantum optimization

Quantum annealers have grown in complexity to the point that quantum computations involving few thousands of qubits are now possible. In this paper, \textcolor{black}{with the intentions to show the feasibility of quantum annealing to tackle problems of physical relevance, we used a simple model, compatible with the capability of current quantum annealers, to study} the relative stability of graphene vacancy defects. By mapping the crucial interactions that dominate carbon-vacancy interchange onto a quadratic unconstrained binary optimization problem, our approach exploits \textcolor{black}{the ground state as well the excited states found by} the quantum annealer to extract all the possible arrangements of multiple defects on the graphene sheet together with their relative formation energies. This approach reproduces known results and provides a stepping stone towards applications of quantum annealing to problems of physical-chemical interest

Investigating the Chinese Postman Problem on a Quantum Annealer

The recent availability of quantum annealers has fueled a new area of information technology where such devices are applied to address practically motivated and computationally difficult problems with hardware that exploits quantum mechanical phenomena. D-Wave annealers are promising platforms to solve these problems in the form of quadratic unconstrained binary optimization. Here we provide a formulation of the Chinese postman problem that can be used as a tool for probing the local connectivity of graphs and networks. We treat the problem classically with a tabu algorithm and using a D-Wave device. We systematically analyze computational parameters associated with the specific hardware. Our results clarify how the interplay between the embedding due to limited connectivity of the Chimera graph, the definition of logical qubits, and the role of spin-reversal controls the probability of reaching the expected solution

GPU-accelerated algorithms for many-particle continuous-time quantum walks

Many-particle continuous-time quantum walks (CTQWs) represent a resource for several tasks in quantum technology, including quantum search algorithms and universal quantum computation. In order to design and implement CTQWs in a realistic scenario, one needs effective simulation tools for Hamiltonians that take into account static noise and fluctuations in the lattice, i.e. Hamiltonians containing stochastic terms. To this aim, we suggest a parallel algorithm based on the Taylor series expansion of the evolution operator, and compare its performances with those of algorithms based on the exact diagonalization of the Hamiltonian or a 4th order Runge–Kutta integration. We prove that both Taylor-series expansion and Runge–Kutta algorithms are reliable and have a low computational cost, the Taylor-series expansion showing the additional advantage of a memory allocation not depending on the precision of calculation. Both algorithms are also highly parallelizable within the SIMT paradigm, and are thus suitable for GPGPU computing. In turn, we have benchmarked 4 NVIDIA GPUs and 3 quad-core Intel CPUs for a 2-particle system over lattices of increasing dimension, showing that the speedup provided by GPU computing, with respect to the OPENMP parallelization, lies in the range between 8x and (more than) 20x, depending on the frequency of post-processing. GPU-accelerated codes thus allow one to overcome concerns about the execution time, and make it possible simulations with many interacting particles on large lattices, with the only limit of the memory available on the device. Program summary Program Title: cuQuWa Licensing provisions: GNU General Public License, version 3 Program Files doi: http://dx.doi.org/10.17632/vjpnjgycdj.1 Programming language: CUDA C Nature of problem: Evolution of many-particle continuous-time quantum-walks on a multidimensional grid in a noisy environment. The submitted code is specialized for the simulation of 2-particle quantum-walks with periodic boundary conditions. Solution method: Taylor-series expansion of the evolution operator. The density-matrix is calculated by averaging multiple independent realizations of the system. External routines: cuBLAS, cuRAND Unusual features: Simulations are run exclusively on the graphic processing unit within the CUDA environment. An undocumented misbehavior in the random-number generation routine (cuRAND package) can corrupt the simulation of large systems, though no problems are reported for small and medium-size systems. Compiling the code with the -arch=sm_30 flag for compute capability 3.5 and above fixes this issue

GPU-accelerated algorithms for many-particle continuous-time quantum walks

Many-particle continuous-time quantum walks (CTQWs) represent a resource for several tasks in quantum technology, including quantum search algorithms and universal quantum computation. In order to design and implement CTQWs in a realistic scenario, one needs effective simulation tools for Hamiltonians that take into account static noise and fluctuations in the lattice, i.e.\ua0Hamiltonians containing stochastic terms. To this aim, we suggest a parallel algorithm based on the Taylor series expansion of the evolution operator, and compare its performances with those of algorithms based on the exact diagonalization of the Hamiltonian or a 4th order Runge\u2013Kutta integration. We prove that both Taylor-series expansion and Runge\u2013Kutta algorithms are reliable and have a low computational cost, the Taylor-series expansion showing the additional advantage of a memory allocation not depending on the precision of calculation. Both algorithms are also highly parallelizable within the SIMT paradigm, and are thus suitable for GPGPU computing. In turn, we have benchmarked 4 NVIDIA GPUs and 3 quad-core Intel CPUs for a 2-particle system over lattices of increasing dimension, showing that the speedup provided by GPU computing, with respect to the OPENMP parallelization, lies in the range between 8x and (more than) 20x, depending on the frequency of post-processing. GPU-accelerated codes thus allow one to overcome concerns about the execution time, and make it possible simulations with many interacting particles on large lattices, with the only limit of the memory available on the device. Program summary Program Title: cuQuWa Licensing provisions: GNU General Public License, version 3 Program Files doi: http://dx.doi.org/10.17632/vjpnjgycdj.1 Programming language: CUDA C Nature of problem: Evolution of many-particle continuous-time quantum-walks on a multidimensional grid in a noisy environment. The submitted code is specialized for the simulation of 2-particle quantum-walks with periodic boundary conditions. Solution method: Taylor-series expansion of the evolution operator. The density-matrix is calculated by averaging multiple independent realizations of the system. External routines: cuBLAS, cuRAND Unusual features: Simulations are run exclusively on the graphic processing unit within the CUDA environment. An undocumented misbehavior in the random-number generation routine (cuRAND package) can corrupt the simulation of large systems, though no problems are reported for small and medium-size systems. Compiling the code with the -arch=sm_30 flag for compute capability 3.5 and above fixes this issue

Quantum metrology at level anticrossing

We address parameter estimation in two-level systems exhibiting level anticrossing and prove that universally optimal strategies for parameter estimation may be designed. In fact, we find a parameter-independent measurement scheme, leading to the ultimate quantum precision, independently of the value of the parameter of interest. Optimal estimationmay be achieved also at high temperature, depending on the structure of the two-level Hamiltonian. Finally, we discuss parameter estimation based on dynamical strategies, and a number of specific applications

Quantum walks of two interacting particles on percolation graphs

We address the dynamics of two indistinguishable interacting particles moving on a dynamical percolation graph, i.e., a graph where the edges are independent random telegraph processes whose values jump between 0 and 1, thus mimicking percolation. The interplay between the particle interaction strength, initial state and the percolation rate determine different dynamical regimes for the walkers. We show that, whenever the walkers are initially localised within the interaction range, fast noise enhances the particle spread compared to the noiseless case

Advanced modeling of materials with PAOFLOW 2.0:New features and software design

Recent research in materials science opens exciting perspectives to design novel quantum materials and devices, but it calls for quantitative predictions of properties which are not accessible in standard first principles packages. PAOFLOW, is a software tool that constructs tight-binding Hamiltonians from self consistent electronic wavefunctions by projecting onto a set of atomic orbitals. The electronic structure provides numerous materials properties that otherwise would have to be calculated via phenomenological models. In this paper, we describe recent re-design of the code as well as the new features and improvements in performance. In particular, we have implemented symmetry operations for unfolding equivalent k-points, which drastically reduces the runtime requirements of first principles calculations, and we have provided internal routines of projections onto atomic orbitals enabling generation of real space atomic orbitals. Moreover, we have included models for non-constant relaxation time in electronic transport calculations, doubling the real space dimensions of the Hamiltonian as well as the construction of Hamiltonians directly from analytical models. Importantly, PAOFLOW has been now converted into a Python package, and is streamlined for use directly within other Python codes. The new object oriented design treats PAOFLOW's computational routines as class methods, providing an API for explicit control of each calculation.</p

Quantum entanglement in heterometallic wheels

Molecular nanomagnets are widely engineerable, low-dimensional spin systems, and typically exhibit strongly correlated ground states. This makes them an ideal playground for investigating quantum entanglement. Here, we present a theoretical investigation of entanglement in a relevant class of nanomagntes, namely the Cr-based wheels. We use exchange energy as a simple means for detecting spin-pair and multi-spin entanglement, and derive the temperature range where such correlations are present in the equilibrium state of the molecules

Relaxation time approximations in PAOFLOW 2.0

Regardless of its success, the constant relaxation time approximation has limited validity. Temperature and energy dependent effects are important to match experimental trends even in simple situations. We present the implementation of relaxation time approximation models in the calculation of Boltzmann transport in PAOFLOW 2.0 and apply those to model band-structures. In addition, using a self-consistent fitting of the model parameters to experimental conductivity data, we provide a flexible tool to extract scattering rates with high accuracy. We illustrate the approximations using simple models and then apply the method to GaAs, Si, Mg3Sb2, and CoSb3.Comment: 20 pages, 7 figure