Prototype-Based Classifiers and Vector Quantization on a Quantum Computer-Implementing Integer Arithmetic Oracles for Nearest Prototype Search.

While the ultimate goal of solving computationally intractable problems is to find a provably optimal solutions, practical constraints of real-world scenarios often necessitate focusing on efficiently obtaining high-quality, near-optimal solutions. The Quantum Approximate Optimization Algorithm (QAOA) is a state-of-the-art hybrid quantum-classical approach for tackling these challenging problems that are encoded using quadratic and higher-order unconstrained binary optimization problems (QUBO and HUBO). We present SCOOP, a novel QAOAbased framework for solving constrained optimization problems. SCOOP transforms a constrained problem into an unconstrained counterpart, forming SCOOP problem twins. The QAOA quantum algorithm operates on the unconstrained twin to identify potential optimal and near-optimal solutions. Effective classical post-processing reduces the solution set to the constrained problem space. Our SCOOP approach is solution-enhanced, objective-function-compatible, and scalable. We demonstrate the framework on three NP-hard problems, Minimum Dominating Set, Minimum Maximal Matching, and Minimum Set Cover appearing in practical application domains such as resource allocation, communication networks, and machine learning. We validate SCOOP's feasibility and effectiveness on Xanadu PennyLane simulators.

The assignment of resources dynamically is a decisive issue in the new paradigms of computations including cloud, edge, fog computing, and the Internet of Things (IoT). These are heterogeneous resource environments, decentralized control environments, and overload environments that vary at a rapid pace and require adaptive and intelligent allocation schemes. The paper suggests a hybrid quantum-game-theoretic model, which combines quantum optimization approaches and multi-agent game theory to solve the problems of multi-agent resource allocation in dynamic systems. Using the quantum concept of superposition and entanglement, the framework can explore the solution spaces in parallel and therefore increase convergence speed and allocation efficiency.A quantum game-theoretic model is developed, which entails price-motivated system to control the strategic interaction of rational agents, in addition to maintaining stability, autonomy and equilibrium. The resource allocation problem is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem and solved with the Quantum Approximate Optimization Algorithm (QAOA) algorithm. The proposed approach is proved to be useful as simulation results show significant gains to classical baselines in terms of utility gain, fairness, and system throughput. The results highlight the possibilities of the quantum-game-theoretic paradigm as a fundamental engine of next-generation computing infrastructures, including networked cloud, edge and IoT with networked computing nodes in VPN-enabled networks.

The principle of superposition of states requires that the states of a dynamical system form a linear vector space. This hypothesis of linearity has usually been regarded as a fundamental postulate in quantum mechanics, of a kind that cannot be explained by classical concepts. Indeed, Dirac [2, p. 14] comments that "the superposition that occurs in quantum mechanics is of an essentially different nature from any occurring in the classical theory, as is shown by the fact that the quantum superposition principle demands indeterminacy in the results of observations in order to be capable of a sensible physical interpretation."

Current hardware limitations restrict the potential when solving quadratic unconstrained binary optimization (QUBO) problems via the quantum approximate optimization algorithm (QAOA) or quantum annealing (QA). Thus, we consider training neural networks in this context. We first discuss QUBO problems that originate from translated instances of the traveling salesman problem (TSP): Analyzing this representation via autoencoders shows that there is way more information included than necessary to solve the original TSP. Then we show that neural networks can be used to solve TSP instances from both QUBO input and autoencoders' hidden state representation. We finally generalize the approach and successfully train neural networks to solve arbitrary QUBO problems, sketching means to use neuromorphic hardware as a simulator or an additional co-processor for quantum computing.

A large class of isolated quantum systems in a pure state can equilibrate and serve as a heat bath. We show that, once equilibrium is reached, any of its subsystems, which are much smaller than the isolated system, can be thermalized such that the subsystem is governed by the Gibbs distribution. Within this theoretical framework, the celebrated superposition principle of quantum mechanics leads to a prediction of a thermalized subsystem with multiple temperatures when the isolated system is in a superposition state of energy eigenstates of multiple distinct energy scales. This multiple-temperature state is at equilibrium, completely different from a non-equilibrium state that has multiple temperatures at different parts. Feasible experimental schemes, in particular with ultra-cold atoms, to verify this prediction are discussed.

We have made the first demonstration that low error rate quantum cryptography over long distances (14km) of installed optical fiber in a real-world environment, subject to uncontrolled temperature and mechanical influences, representing an important new step towards incorporation of quantum cryptography into existing information security systems. We also point out that the high visibility single-photon interference in our experiment allows us to infer a test of the superposition principle of quantum mechanics: a photon reaching the detector has traveled over 14km of optical fiber in a wavepacket comprising a coherent superposition of two components that are spatially separated by about 2m. In principle, there are decoherence processes (or even possible modifications of quantum mechanics) that could cause the photon`s wavefunction to collapse into one component or the other during propagation, leading to a reduction in visibility. However, our results are consistent with no such loss of quantum coherence during the 67-{mu}s propagation time.

In this paper the superpositions of two arbitrary coherent states |Ψ〉 = a|β〉 + beiϕ|mβeiδ〉 are constructed by using the superposition principle of quantum mechanics. The entropic squeezing effects of the quantum states are studied. The numerical results indicate that the amplitudes, the ratio between the amplitudes of two coherent states, the phase difference between the two components and the relative phase of the two coefficients play important roles in the squeezing effects of the position entropy and momentum entropy.

A generalization of the superposition principle of quantum mechanics is proposed introducing the concept of maximal state of a logic.

The double slit experiment is iconic and widely used in classrooms to demonstrate the fundamental mystery of quantum physics. The puzzling feature is that the probability of an electron arriving at the detector when both slits are open is not the sum of the probabilities when the slits are open separately. The superposition principle of quantum mechanics tells us to add amplitudes rather than probabilities and this results in interference. This experiment defies our classical intuition that the probabilities of exclusive events add. In understanding the emergence of the classical world from the quantum one, there have been suggestions by Feynman, Diosi and Penrose that gravity is responsible for suppressing interference. This idea has been pursued in many different forms ever since, predominantly within Newtonian approaches to gravity. In this paper, we propose and theoretically analyse two ‘gedanken’ or thought experiments which lend strong support to the idea that gravity is responsible for decoherence. The first makes the point that thermal radiation can suppress interference. The second shows that in an accelerating frame, Unruh radiation does the same. Invoking the Einstein equivalence principle to relate acceleration to gravity, we support the view that gravity is responsible for decoherence.

ObjectivesCausal reasoning should have an explicit formal structure.MethodSuch a structure can be provided with the help of counterfactuals. This approach allocates different versions (factual and non-factual) of exposures and responses...

As the volume of data for classification tasks in machine learning grows, feature selection plays an increasingly crucial role in enhancing the efficiency and effectiveness of these tasks. Existing classical feature selection algorithms often encounter challenges, such as high computational complexity and vulnerability to local optima. Quantum algorithms have been proposed to overcome these limitations. Here, our work proposes a new approach that combines the Quantum Approximate Optimization Algorithm (QAOA) with the classical feature selection algorithm Maximum Relevance-Minimum Redundancy (MRMR). First, we transform the feature selection problem into the Quadratic Unconstrained Binary Optimization (QUBO) problem. Then, we map the QUBO formulation to Hamiltonian with the Ising model. Finally, we employ QAOA with a shallow circuit to search this Hamiltonian's ground state, which matches the specific solution for feature selection. We conducted numerical experiments on eight real-world datasets for classification tasks from diverse domains, including finance, medicine, and natural hazards. Experiment results suggest that QAOA-selected feature subsets size are typically less than half the complete set while achieving comparable or better classification accuracy than classical MRMR, demonstrating its preference for smaller, more efficient feature subsets.

We are looking for a way of combining experimentally determined probabilities that should yield maximum predictive power. This concept is defined as permitting calculation of the accuracy of future experimental results solely on the basis of the number of runs whose data will serve as input for making the prediction. Each probability is transformed to an associated variable whose uncertainty interval depends only on the amount of data and strictly decreases with it. We find that for a probability which is a function of two other probabilities maximum predictive power is achieved when linearly summing their associated variables and transforming back to a probability. This recovers the quantum mechanical superposition principle.

The selection of crude oil feedstock is a critical, high-impact optimization problem in the petrochemical industry, directly influencing refinery profitability and environmental footprint. Traditional optimization methods face scalability challenges as the complexity and number of constraints increase. This paper presents an initial study on the application of quantum computing to solve a binary feedstock optimization model. We formulate the problem as a Quadratic Unconstrained Binary Optimization (QUBO) model and employ the Quantum Approximate Optimization Algorithm (QAOA) to find low-cost solutions. To manage the probabilistic nature of quantum results, we introduce Conditional Value at Risk (CVaR) as a post-processing technique to select robust, high-quality solutions. Our results on a representative small-scale problem demonstrate the viability of this hybrid quantum-classical approach, showing its potential to identify near-optimal solutions. We conclude with a discussion of current limitations and an open call for collaboration to further explore quantum computing applications in the energy sector.

Although many efficient heuristics have been developed to solve binary optimization problems, these typically produce correlated solutions for degenerate problems. Most notably, transverse-field quantum annealing-the heuristic employed in current commercially available quantum annealing machines-has been shown to often be exponentially biased when sampling the solution space. Here we present an approach to sample ground-state (or low-energy) configurations for binary optimization problems. The method samples degenerate states with almost equal probability and is based on a combination of parallel tempering Monte Carlo with isoenergetic cluster moves. We illustrate the approach using two-dimensional Ising spin glasses, as well as spin glasses on the D-Wave Systems quantum annealer chimera topology. In addition, a simple heuristic to approximate the number of solutions of a degenerate problem is introduced.

We present an integrated model for Bayesian learning of sparse representation and classifier training, and apply it for the task of visual recognition. Most previous work learns the sparse representation and trains the classifier on top of it in two separate steps. We cast these two into a unified probabilistic model. This way, the supervised labels can effectively affect the learning of the sparse representation. In the training phase, the inference of the joint expectation for dictionary, code, classifier and other variables under the observation of descriptors and labels is carried out by Gibbs Sampling. In the testing phase, based on the learned parameters, the sparse code and the class label of the image are obtained by Bayesian inference. The proposed model is evaluated on Caltech 101 dataset and its efficacy is demonstrated by a careful analysis of the experimental results.