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The construction of an axial 8-coil system based on Helmholtz coils is described, which enables a magnetic field with a nonuniformity of not more than 0.1% to be produced at a distance of half the radius from the center of the coil system. The results obtained are confirmed by experimental investigations. [ABSTRACT FROM AUTHOR]

Several pulsar timing array (PTA) collaborations have recently reported the evidence for a stochastic gravitational-wave background (SGWB), which can unveil the formation of primordial seeds of inhomogeneities in the early universe. With the SGWB parameters inferred from PTAs data, we can make a prediction of the seeds for early galaxy formation from the domain walls in the axion-like particles (ALPs) field distribution. This also naturally provides a solution to the observation of high redshifts by the James Webb Space Telescope. The predicted photon coupling of the ALP is within the reach of future experimental searches. [ABSTRACT FROM AUTHOR]

We report first principles quantum-chemical calculations of the electronic structure of pure CaWO4 and CaWO4 containing oxygen vacancies. The calculation results are compared to values extracted from experimental thermoluminescence data. The influence of oxygen vacancies and structural disorder shows up as the presence of additional levels in the band gap of the material. [ABSTRACT FROM AUTHOR]

We study lattice gauge theory with discrete, non-Abelian gauge groups. We extend the formalism of previous studies on D-Wave's quantum annealer as a computing platform to finite, simply reducible gauge groups. As an example, we use the dihedral group D n with n = 3 , 4 on a two plaquette ladder for which we provide proof-of-principle calculations of the ground-state and employ the known time evolution formalism with Feynman clock states. [ABSTRACT FROM AUTHOR]

Quantum annealing has the potential to find low energy solutions of NP-hard problems that can be expressed as quadratic unconstrained binary optimization problems. However, the hardware of the quantum annealer manufactured by D-Wave Systems, which we consider in this work, is sparsely connected and moderately sized (on the order of thousands of qubits), thus necessitating a minor-embedding of a logical problem onto the physical qubit hardware. The combination of relatively small hardware sizes and the necessity of a minor-embedding can mean that solving large optimization problems is not possible on current quantum annealers. In this research, we show that a hybrid approach combining parallel quantum annealing with graph decomposition allows one to solve larger optimization problem accurately. We apply the approach to the Maximum Clique problem on graphs with up to 120 nodes and 6395 edges. [ABSTRACT FROM AUTHOR]

Quantum Annealing (QA) is a metaheuristic for solving optimization problems in a time-efficient manner. Therefore, quantum mechanical effects are used to compute and evaluate many possible solutions of an optimization problem simultaneously. Recent studies have shown the potential of QA for solving such complex assignment problems within milliseconds. This also applies for the field of job shop scheduling, where the existing approaches however focus on small problem sizes. To assess the full potential of QA in this area for industry-scale problem formulations, it is necessary to consider larger problem instances and to evaluate the potentials of computing these job shop scheduling problems while finding a near-optimal solution in a time-efficient manner. Consequently, this paper presents a QA-based job shop scheduling. In particular, flexible job shop scheduling problems in various sizes are computed with QA, demonstrating the efficiency of the approach regarding scalability, solutions quality, and computing time. For the evaluation of the proposed approach, the solutions are compared in a scientific benchmark with state-of-the-art algorithms for solving flexible job shop scheduling problems. The results indicate that QA has the potential for solving flexible job shop scheduling problems in a time efficient manner. Even large problem instances can be computed within seconds, which offers the possibility for application in industry. [ABSTRACT FROM AUTHOR]

In this paper, we propose a scheme for speeding up the generation of steady-state entanglement of two interacting qubits by coupling them with an engineered dissipative ancilla. The coupling strength between the target qubits and the ancilla is tailored by state-based Lyapunov control, which vanishes gradually along with the increasing of the fidelity of steady state. The negativity is adopted to measure the bipartite entanglement, which would not be enhanced by such Lyapunov control. In order to speed up and enhance the bipartite entanglement, we further use the non-vanishing engineered coupling. Numerical simulations indicate that the scheme is robust against the fluctuations of the coupling strength and immune to the system parametric errors. The study shows promising performance of speeding up dissipative generation of quantum states with Lyapunov control. [ABSTRACT FROM AUTHOR]

We benchmark the quantum processing units of the largest quantum annealers to date, the 5000 + qubit quantum annealer Advantage and its 2000+ qubit predecessor D-Wave 2000Q, using tail assignment and exact cover problems from aircraft scheduling scenarios. The benchmark set contains small, intermediate, and large problems with both sparsely connected and almost fully connected instances. We find that Advantage outperforms D-Wave 2000Q for almost all problems, with a notable increase in success rate and problem size. In particular, Advantage is also able to solve the largest problems with 120 logical qubits that D-Wave 2000Q cannot solve anymore. Furthermore, problems that can still be solved by D-Wave 2000Q are solved faster by Advantage. We find, however, that D-Wave 2000Q can achieve better success rates for sparsely connected problems that do not require the many new couplers present on Advantage, so improving the connectivity of a quantum annealer does not per se improve its performance. [ABSTRACT FROM AUTHOR]

The past two decades have witnessed the rapid development of quantum computers. Superconducting circuits are one of the most attractive platforms, and its corresponding precise control system is crucial. Here, a brief review of the room-temperature and cryogenic control systems of superconducting quantum circuits is given. The microwave devices required by the system are introduced, followed by a description of the operation of single-qubit and two-qubit gates, readout techniques, quantum tomography for fidelity characterization, and feedforward and feedback controls. Some future directions are provided for the research and development of control systems for large-scale, fault-tolerant quantum computers. [ABSTRACT FROM AUTHOR]

We benchmark the 5000+ qubit system Advantage coupled with the Hybrid Solver Service 2 released by D-Wave Systems Inc. in September 2020 by using a new class of optimization problems called garden optimization problems known in companion planting. These problems are scalable to an arbitrarily large number of variables and intuitively find application in real-world scenarios. We derive their QUBO formulation and illustrate their relation to the quadratic assignment problem. We demonstrate that the Advantage system and the new hybrid solver can solve larger problems in less time than their predecessors. However, we also show that the solvers based on the 2000+ qubit system DW2000Q sometimes produce more favourable results if they can solve the problems. [ABSTRACT FROM AUTHOR]

Minor-embedding heuristics have become an indispensable tool for compiling problems in quadratically unconstrained binary optimization (QUBO) into the hardware graphs of quantum and CMOS annealing processors. While recent embedding heuristics have been developed for annealers of moderate size (about 2000 nodes), the size of the latest CMOS annealing processor (with 102,400 nodes) poses entirely new demands on the embedding heuristic. This raises the question, if recent embedding heuristics can maintain meaningful embedding performance on hardware graphs of increasing size. Here, we develop an improved version of the probabilistic-swap-shift-annealing (PSSA) embedding heuristic [which has recently been demonstrated to outperform the standard embedding heuristic by D-Wave Systems (Cai et al. in http://arxiv.org/abs/1406.2741, 2014)] and evaluate its embedding performance on hardware graphs of increasing size. For random cubic and Barábasi–Albert graphs we find the embedding performance of improved PSSA to consistently exceed the threshold of the best known complete graph embedding by a factor of 3.2 and 2.8, respectively, up to hardware graphs with 102,400 nodes. On the other hand, for random graphs with constant edge density not even improved PSSA can overcome the deterministic threshold guaranteed by the existence of the best known complete graph embedding. Finally, we prove a new upper bound on the maximal embeddable size of complete graphs into hardware graphs of CMOS annealers and show that the embedding performance of its currently best known complete graph embedding has optimal order for hardware graphs with fixed coordination number. [ABSTRACT FROM AUTHOR]

The local environment of Mo6+ ions in the structures of scheelite-type crystals (space group I41/a) with the initial compositions (Na1/2Gd1/2)MoO4 (NGM 1:1) and (Na2/7Gd4/7□1/7)MoO4 (NGM 1:2; □ - vacancies) was determined by X-ray absorption spectroscopy (XAS) for the first time. Different coordination environments of Na1+ and Gd3+ ions caused primarily by the difference in their formal charges have been established based on the comparison of Mo–Gd and Mo–Na interatomic distances. According to resent results and structural data known for the (Na1-хREx)MO4 crystals (RE3+ = rare-earth cations), the character of distribution of different Na1+ and RE3+ polyhedra over NGM crystal structures is influenced by the sizes and electronegativities of Na1+, RE3+, and М6+ (M6+ = Mo, W) ions, the Na1+:RE3+ ratio, and vacancies in the M site. Disordered distribution of Na1+ and RE3+ polyhedra in NGM occurs without changing the symmetry of crystals (space group I41/a) and ordered one is accompanied by reduction of crystal symmetry. [ABSTRACT FROM AUTHOR]

Optimization problems with Boolean variables that fall into the nondeterministic polynomial (NP) class when cast as decision problems are of fundamental importance in computer science, mathematics, physics and industrial applications. Most notably, solving constraint-satisfaction problems, which are related to spin-glass-like Hamiltonians in physics, remains a difficult numerical task. As such, there has been great interest in designing efficient heuristics to solve these computationally difficult problems. Inspired by parallel tempering Monte Carlo in conjunction with the rejection-free isoenergetic cluster algorithm developed for Ising spin glasses, we present a generalized global update optimization heuristic that can be applied to different NP-complete problems with Boolean variables. The global cluster updates allow for a wide-spread sampling of phase space, thus considerably speeding up optimization. By carefully tuning the pseudo-temperature (needed to randomize the configurations) of the problem, we show that the method can efficiently tackle optimization problems with over-constraints or on topologies with a large site percolation threshold. We illustrate the efficiency of the heuristic on paradigmatic optimization problems, such as the maximum satisfiability problem and the vertex cover problem. Because this physics-based algorithm is an algorithm that searches solutions globally, it performs best for random Max-k-SAT instances. [ABSTRACT FROM AUTHOR]

Optimization Modulo Theories (OMT ) is an extension of SMT which allows for finding models that optimize given objectives. OptiMathSAT is an OMT solver which allows for solving a list of optimization problems on SMT formulas with linear objective functions—on the Boolean, the rational and the integer domains, and on their combination thereof—including (partial weighted) MaxSMT. Multiple and heterogeneous objective functions can be combined together and handled either independently, or lexicographically, or in linear or min–max /max–min combinations. OptiMathSAT provides an incremental interface, it supports both an extended version of the SMT-LIBv2 language and a subset of the FlatZinc language, and can be interfaced via an API. In this paper we describe OptiMathSAT and its usage in full detail. [ABSTRACT FROM AUTHOR]

Quantum Bridge Analytics relates generally to methods and systems for hybrid classical-quantum computing, and more particularly is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the first of a two-part tutorial that surveys key elements of Quantum Bridge Analytics and its applications, with an emphasis on supplementing models with numerical illustrations. In Part 1 (the present paper) we focus on the Quadratic Unconstrained Binary Optimization model which is presently the most widely applied optimization model in the quantum computing area, and which unifies a rich variety of combinatorial optimization problems. [ABSTRACT FROM AUTHOR]

Superconducting coplanar waveguide resonators and Josephson junctions are crucial components of superconducting quantum information processing chips. Resonators are usually fabricated through lift-off or etching, while Josephson junctions are made by trilayer process or double-angle evaporation. To simplify the fabrication process, we propose a scheme that uses the same process steps for both Josephson junctions and resonators. Simulations and experiments are conducted to confirm that resonators fabricated via the proposed process have quality factor comparable to those via traditional process. This work paves the way for quantum information processing on superconducting large-scale integrated circuits. [ABSTRACT FROM AUTHOR]

This paper assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is quite small (usually around 45 vertices), we also consider decomposition algorithms intended for larger graphs and analyze their performance. For smaller graphs that fit DW, we provide formulations of the maximum clique problem as a quadratic unconstrained binary optimization (QUBO) problem, which is one of the two input types (together with the Ising model) acceptable by the machine, and compare several quantum implementations to current classical algorithms such as simulated annealing, Gurobi, and third-party clique finding heuristics. We further estimate the contributions of the quantum phase of the quantum annealer and the classical post-processing phase typically used to enhance each solution returned by DW. We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms. On the other hand, for instances specifically designed to fit well the DW qubit interconnection network, we observe substantial speed-ups in computing time over classical approaches. [ABSTRACT FROM AUTHOR]

We realize tunable coupling between two superconducting transmission line resonators. The coupling is mediated by a non-hysteretic rf SQUID acting as a flux-tunable mutual inductance between the resonators. We present a spectroscopic characterization of the device. In particular, we observe couplings $g/2\pi$ ranging between −320 MHz and 37 MHz. In the case of $g \simeq 0$, the microwave power cross transmission between the two resonators is reduced by almost four orders of magnitude as compared to the case where the coupling is switched on. [ABSTRACT FROM AUTHOR]

In order to formulate mathematical conjectures likely to be true, a number of base cases must be determined. However, many combinatorial problems are NP-hard and the computational complexity makes this research approach difficult using a standard brute force approach on a typical computer. One sample problem explored is that of finding a minimum identifying code. To work around the computational issues, a variety of methods are explored and consist of a parallel computing approach using MATLAB, an adiabatic quantum optimization approach using a D-Wave quantum annealing processor, and lastly using satisfiability modulo theory (SMT) and corresponding SMT solvers. Each of these methods requires the problem to be formulated in a unique manner. In this paper, we address the challenges of computing solutions to this NP-hard problem with respect to each of these methods. [ABSTRACT FROM AUTHOR]

Based on the quantum Zeno dynamics, a scheme is presented to implement a Toffoli gate of three separated superconducting qubits (SQs) by one step. Three separated SQs are connected by two resonators. The scheme is insensitive to the resonator decay because the Zeno subspace does not include the state of the resonators being excited. Numerical simulations indicate that the scheme is robust to the fluctuation of the parameters and the Toffoli gate can be implemented with high fidelity. [ABSTRACT FROM AUTHOR]

Quantum annealing is a promising approach for solving optimization problems, but like all other quantum information processing methods, it requires error correction to ensure scalability. In this work, we experimentally compare two quantum annealing correction (QAC) codes in the setting of antiferromagnetic chains, using two different quantum annealing processors. The lower-temperature processor gives rise to higher success probabilities. The two codes differ in a number of interesting and important ways, but both require four physical qubits per encoded qubit. We find significant performance differences, which we explain in terms of the effective energy boost provided by the respective redundantly encoded logical operators of the two codes. The code with the higher energy boost results in improved performance, at the expense of a lower-degree encoded graph. Therefore, we find that there exists an important trade-off between encoded connectivity and performance for quantum annealing correction codes. [ABSTRACT FROM AUTHOR]

The current generation of D-Wave quantum annealing processor is designed to minimize the energy of an Ising spin configuration whose pairwise interactions lie on the edges of a Chimera graph $${\mathcal {C}}_{M,N,L}$$ . In order to solve an Ising spin problem with arbitrary pairwise interaction structure, the corresponding graph must be minor-embedded into a Chimera graph. We define a combinatorial class of native clique minors in Chimera graphs with vertex images of uniform, near minimal size and provide a polynomial-time algorithm that finds a maximum native clique minor in a given induced subgraph of a Chimera graph. These minors allow improvement over recent work and have immediate practical applications in the field of quantum annealing. [ABSTRACT FROM AUTHOR]

In this paper, we address the field of quantum information processing and analyze the prospects of applying quantum computation concepts to image processing tasks. Specifically, we discuss the development of a quantum version for the image segmentation operation. This is an important technique that comes up in many image processing applications. We consider the threshold-based segmentation and show that a quantum circuit to achieve this operation can be built using a quantum oracle that implements the thresholding function. We discuss the circuit implementation of the oracle operator and provide examples of segmenting synthetic and real images. The main advantage of the quantum version for image segmentation over the classical approach is its speedup and is provided by the special properties of quantum information processing: superposition of states and inherent parallelism. [ABSTRACT FROM AUTHOR]

Electronic components which are able to work at cryogenic temperatures are demanded in cryogenic instruments, high sensitivity measurement systems, space missions, medical diagnosis among other applications. Different non-cryogenic commercial electronic components have been characterized between room temperature and −196°C. A simple measurement technique, taking advantage of the temperature gradient inside a partially empty LN Dewar vessel has been used. The results of the electrical characterization show that some of these components can be used at cryogenic temperatures with a reasonable performance even if their specifications datasheets state the contrary. [ABSTRACT FROM AUTHOR]

We develop an approach to machine learning and anomaly detection via quantum adiabatic evolution. This approach consists of two quantum phases, with some amount of classical preprocessing to set up the quantum problems. In the training phase we identify an optimal set of weak classifiers, to form a single strong classifier. In the testing phase we adiabatically evolve one or more strong classifiers on a superposition of inputs in order to find certain anomalous elements in the classification space. Both the training and testing phases are executed via quantum adiabatic evolution. All quantum processing is strictly limited to two-qubit interactions so as to ensure physical feasibility. We apply and illustrate this approach in detail to the problem of software verification and validation, with a specific example of the learning phase applied to a problem of interest in flight control systems. Beyond this example, the algorithm can be used to attack a broad class of anomaly detection problems. [ABSTRACT FROM AUTHOR]

Most realistic solid state devices considered as qubits are not true two-state systems. If the energy separation of the upper energy levels from the lowest two levels is not large, then these upper states may affect the evolution of the ground state over time and therefore cannot be neglected. In this work, we study the effect of energy levels beyond the lowest two energy levels on adiabatic quantum optimization in a device with a double-well potential as the basic logical element. We show that the extra levels can be modeled by adding additional ancilla qubits coupled to the original logical qubits, and that the presence of upper levels has no effect on the final ground state. We also study the influence of upper energy levels on the minimum gap for a set of 8-qubit spin glass instances. [ABSTRACT FROM AUTHOR]

The ratio J[ T( x, y, t)]/ J[ T( x, y, t)] of critical current densities ( t indicating start of a disturbance) integrated over sample cross section serves to calculate the 'stability function', Φ( t), to predict under which conditions zero-loss transport current is possible. Critical current density and stability function are correlated with (conventional) timescale, t, in the superconductor (the 'phonon aspect'). However, the stability problem is not simply restricted to coupled conduction/radiation heat transfer. It is questionable whether decay of electron pairs and subsequent recombination of excited electron states to a new dynamic equilibrium (the 'electron aspect' under a disturbance) proceeds on the same timescale. A sequential model has been defined to calculate lifetimes of the excited electron states. These are estimated from analogy to the nucleon-nucleon, pion-mediated Yukawa interaction, from an aspect of the Racah-problem (expansion of an antisymmetric N-particle wave function from a N−1 parent state) and from the uncertainty principle, all in dependence of the local (transient) temperature field; with these approximations, the sequential model accounts for the retarded electron-phonon interaction. The numerical analysis is applied to NbTi and YBaCuO filaments in a standard matrix. As a result, the difference between both timescales can be significant, in particular near the phase transition: in the NbTi filament, a minimum distance of at least 60 μm (in this example) from the location of a disturbance should be observed for reliable stability analysis. This difference could have consequences also for safe operation of a resistive fault current limiter. [ABSTRACT FROM AUTHOR]

We design a nearest-neighbor architectural layout that uses fixed positive and negative couplings between qubits, to overcome the effects of relative phases due to qubit precessions, both during idle times and gate operations. The scheme uses decoherence-free subspaces, and we show how to realize gate operations on these encoded qubits. The main advantage of our scheme is that most gate operations are realized by only varying a single control parameter, which greatly reduces the circuit complexity. Moreover, the scheme is robust against phase errors occurring as a result of finite rise and fall times due to non-ideal pulses. [ABSTRACT FROM AUTHOR]

review of the principles of operation of quantum computers and their elements is presented. The radical advantage of quantum algorithms for processing information over the classical ones is discussed, quantum entanglement is considered as the basic resource of quantum computations, and the most promising and interesting proposals on realization of quantum computers on the basis of trapped ions, nuclear spins, quantum dots, superconducting structures, and others are described. This review reflects the materials of the report presented at the scientific session of the Department of Nanotechnologies and Information Technologies of the Russian Academy of Sciences on February 25, 2010. [ABSTRACT FROM AUTHOR]

Scheelite CaWO4 doped with rare earth ions (Eu3+, Sm3+, Dy3+) were fabricated via a facile solvothermal process without further heat treatment, which used sodium oleate and oleylamine as capping reagent. The structure, morphology, and optical properties of the samples were well characterized by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FT-IR), transmission electron microscopy (TEM), high-resolution transmission electron microscope (HRTEM), X-ray photoelectron spectra (XPS), photoluminescence (PL) spectra and cathodoluminescence (CL). The XRD results reveal that all the doped samples are well assigned to the scheelite structure of the CaWO4 phase. Upon excitation by ultraviolet radiation, the CaWO4:Eu3+ phosphors show the characteristic 5D0–7F1–3 emission lines of Eu3+, and the CaWO4:Sm3+ phosphors demonstrate the characteristic 4G5/2–6H5/2–9/2 emission line of Sm3+, and the CaWO4:Dy3+ phosphors demonstrate the characteristic 4F9/2–6H13/2–15/2 emission line of Dy3+. [ABSTRACT FROM AUTHOR]

In this review we summarize our recent experiments on the investigation on superconducting qubits. Instead of strong projective measurement used by other groups in their first pioneering experiments we have proposed and realized a weak continuous readout which belongs to the class of quantum non-demolition measurements. Moreover, our scheme enables to measure a superconducting qubit at the so called sweet (or magic) point where a qubit is in a superposition of two classical states and its sensitivity to external noise is minimized. In this scheme, which is widely used nowadays, the superconducting oscillator coupled to superconducting qubit is used as a detector of the qubit’s state. Such system is analogue to a system of a single atom interacting with photons in a cavity, which allows to study quantum electrodynamics in artificial macroscopic systems. Pushing this analogy we demonstrate Sisyphus cooling and amplification caused by energy exchange between an oscillator and a flux qubit. Using the Sisyphus effect we show consistency between the adiabatic weak continuous measurement in the ground state and the spectroscopic measurement. This allows us to characterize the more complicated system of coupled qubits by making use of the same method. We have realized and studied fixed ferromagnetic, antiferromagnetic as well as tunable qubit–qubit coupling. We argue that ground state measurements can be used for characterization of entangled states in coupled flux qubits. [ABSTRACT FROM AUTHOR]

We report measurements of coherence times of an rf SQUID qubit using pulsed microwaves and rapid flux pulses. The modified rf SQUID, described by an double-well potential, has independent, in situ, controls for the tilt and barrier height of the potential. The decay of coherent oscillations is dominated by the lifetime of the excited state and low frequency flux noise and is consistent with independent measurement of these quantities obtained by microwave spectroscopy, resonant tunneling between fluxoid wells and decay of the excited state. The oscillation’s waveform is compared to analytical results obtained for finite decay rates and detuning and averaged over low frequency flux noise. [ABSTRACT FROM AUTHOR]

Abstract Although first hints of the existence of Dark Matter were observed by the Swiss astronomer Zwicky already in the 1930s, only in recent years has it become known that the universe, in fact, is dominated by particles whose nature is almost unknown and which have never been directly observed. Meanwhile, as the existence of these particles is postulated not only by astronomy, but also cosmology and theoretical particle physics, there is significant effort to detect them in a laboratory experiment and determine their physical properties. However, as the interaction rate between Dark Matter particles and ordinary matter is extremely low, detectors have to be extremely sensitive. Low temperature detectors have been available for more than a decade and have now reached the highest sensitivity for direct Dark Matter detection. In this article, we give a short overview of observational results that suggest the existence of Dark Matter particles and what physicists have learned so far about their properties. The main focus is on the experimental challenges and effort for their direct detection. [ABSTRACT FROM AUTHOR]

In classical computing, analog approaches have sometimes appeared to be more powerful than they really are. This occurs when resources, particularly precision, are not appropriately taken into account. While the same should also hold for analog quantum computing, precision issues are often neglected from the analysis. In this work, we present a classical analog algorithm for unstructured search that can be viewed as analogous to the quantum adiabatic unstructured search algorithm devised by Roland and Cerf (Phys Rev A 65:042308, 2002). We show that similarly to its quantum counterpart, the classical construction may also provide a quadratic speedup over standard digital unstructured search. We discuss the meaning and the possible implications of this result in the context of adiabatic quantum computing. [ABSTRACT FROM AUTHOR]

Recent advancements in quantum annealing hardware and numerous studies in this area suggest that quantum annealers have the potential to be effective in solving unconstrained binary quadratic programming problems. Naturally, one may desire to expand the application domain of these machines to problems with general discrete variables. In this paper, we explore the possibility of employing quantum annealers to solve unconstrained quadratic programming problems over a bounded integer domain. We present an approach for encoding integer variables into binary ones, thereby representing unconstrained integer quadratic programming problems as unconstrained binary quadratic programming problems. To respect some of the limitations of the currently developed quantum annealers, we propose an integer encoding, named bounded-coefficient encoding, in which we limit the size of the coefficients that appear in the encoding. Furthermore, we propose an algorithm for finding the upper bound on the coefficients of the encoding using the precision of the machine and the coefficients of the original integer problem. We experimentally show that this approach is far more resilient to the noise of the quantum annealers compared to traditional approaches for the encoding of integers in base two. In addition, we perform time-to-solution analysis of various integer encoding strategies with respect to the size of integer programming problems and observe favorable performance from the bounded-coefficient encoding relative to that of the unary and binary encodings. [ABSTRACT FROM AUTHOR]

We investigate the dynamics of entanglement, decoherence and quantum discord in a system of three non-interacting superconducting flux qubits (fqubits) initially prepared in a Greenberger-Horne-Zeilinger (GHZ) state and subject to static noise in different, bipartite and common environments, since it is recognized that different noise configurations generally lead to completely different dynamical behavior of physical systems. The noise is modeled by randomizing the single fqubit transition amplitude. Decoherence and quantum correlations dynamics are strongly affected by the purity of the initial state, type of system-environment interaction and the system-environment coupling strength. Specifically, quantum correlations can persist when the fqubits are commonly coupled to a noise source, and reaches a saturation value respective to the purity of the initial state. As the number of decoherence channels increases (bipartite and different environments), decoherence becomes stronger against quantum correlations that decay faster, exhibiting sudden death and revival phenomena. The residual entanglement can be successfully detected by means of suitable entanglement witness, and we derive a necessary condition for entanglement detection related to the tunable and non-degenerated energy levels of fqubits. In accordance with the current literature, our results further suggest the efficiency of fqubits over ordinary ones, as far as the preservation of quantum correlations needed for quantum processing purposes is concerned. [ABSTRACT FROM AUTHOR]