Sampling binary sparse coding QUBO models using a spiking neuromorphic processor

Low-density parity-check (LDPC) codes have previously been considered as combinatorial optimization problems (COPs) in respect to its decoding. However, after defining it as such, none have gone so far as to convert the LDPC code into a quadratic unconstrained binary optimization (QUBO) problem. Thus, a new method is created: one that converts the LDPC code to a QUBO problem, inputs the QUBO problem into Ising machines (computers based on the Ising model that are designed to solve the QUBO problem), obtains the QUBO solution and converts it to a LDPC solution. By utilizing an actual Ising machine, LDPC solutions with code length of 256-bits have been obtained with an accuracy of 93.9% by average annealing time 214.0ms. The benefit of this newfound methodology goes beyond its theoretical imprint of obtaining LDPC solutions more accurately. It has only been a few years since the Ising machine has been developed. Therefore, in formulating this method, one expands the currently scope of studies involving Ising machines, helping current and future researchers unlock its full range of capabilities and possibilities.

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.

With the recent advancements in the field of combinatorial optimization, QUBO (quadratic unconstrained binary optimization) has become a topic of intense interest, as a problem format acceptable to several hardware heuristics such as quantum and digital annealers. Accordingly, transforming hard mathematical problems into QUBO problems is of particular importance. In this paper, we restate three problems in NP-complete and NP-hard classes as QUBO problems with proofs of equivalence. Our problems of interest are the numerical three-dimensional matching problem, the monochromatic triangle problem and the optimum facility location problem. Furthermore, we comment on the feasibility of these formulations on sophisticated QUBO solving platforms.

Steric clashes pose a challenge when exploring dense protein systems using conventional explicit-chain methods. A minimal example is a single lattice protein confined on a minimal grid, with no free sites. Finding its minimum energy is a hard optimization problem, with similarities to scheduling problems. It can be recast as a quadratic unconstrained binary optimization (QUBO) problem amenable to classical and quantum approaches. We show that this problem in its QUBO form can be swiftly and consistently solved for chain length 48, using either classical simulated annealing or hybrid quantum-classical annealing on a D-Wave system. In fact, the latter computations required about 10 s. We also test linear and quadratic programming methods, which work well for a lattice gas but struggle with chain constraints. All methods are benchmarked against exact results obtained from exhaustive structure enumeration, at a high computational cost.

We propose a new kernel that quantifies success for the task of computing a core-periphery partition for an undirected network. Finding the associated optimal partitioning may be expressed in the form of a quadratic unconstrained binary optimization (QUBO) problem, to which a state-of-the-art quantum annealer may be applied. We therefore make use of the new objective function to (a) judge the performance of a quantum annealer, and (b) compare this approach with existing heuristic core-periphery partitioning methods. The quantum annealing is performed on a commercially available D-Wave machine. The QUBO problem involves a full matrix even when the underlying network is sparse. Hence, we develop and test a sparsified version of the original QUBO which increases the available problem dimension for the quantum annealer. Results are provided on both synthetic and real data sets, and we conclude that the QUBO/quantum annealing approach offers benefits in terms of optimizing this new quantity of interest.

Quantum computations are very important branch of modern cryptology. According to the number of working physical qubits available in general-purpose quantum computers and in quantum annealers, there is no coincidence, that nowadays quantum annealers allow to solve larger problems. In this paper we focus on solving discrete logarithm problem (DLP) over binary fields using quantum annealing. It is worth to note, that however solving DLP over prime fields using quantum annealing has been considered before, no author, until now, has considered DLP over binary fields using quantum annealing. Therefore, in this paper, we aim to bridge this gap. We present a polynomial transformation of the discrete logarithm problem over binary fields to the Quadratic Unconstrained Binary Optimization (QUBO) problem, using approximately 3n2 logical variables for the binary field F2n. In our estimations, we assume the existence of an optimal normal base in the given fields. Such a QUBO instance can then be solved using quantum annealing.

One of the biggest obstacles to creating precise machine learning models is choosing representative and pertinent characteristics from big, unbalanced datasets. While too many features raise the risk of overfitting and computational expense, class imbalance frequently results in decreased accuracy and bias. The Simulated Annealing technique is used in this study to tackle a Quadratic Unconstrained Binary Optimization (QUBO) problem that is formulated as a quantum-assisted feature selection method to handle these problems. The technique seeks to reduce inter-feature redundancy and the number of selected features. There are 102,487 samples in the majority class and 11,239 in the minority class, totaling 28 characteristics in the experimental dataset. Nine ideal features were found during the feature selection method (12, 14, 15, 22, 23, 24, 25, 27, and 28). Ten-fold cross-validation was used to assess a Random Forest Classifier that was trained using an 80:20 split. With precision, recall, f1-score, and accuracy all hitting 1.00, the suggested QUBO+SMOTE method demonstrated exceptional performance. Comparatively, QUBO without SMOTE performed worse with accuracy 0.95 and minority-class f1-score of only 0.71, whereas a traditional Recursive Feature Elimination (RFE) approach obtained accuracy 0.97 with minority-class f1-score of 0.94. These findings indicate that QUBO can reduce dimensionality and address class imbalance which requires its integration with SMOTE. This study demonstrates how quantum computing can enhance the effectiveness and efficiency of machine learning, especially for large-scale imbalanced datasets

Quadratic unconstrained binary optimization (QUBO) has gained popularity over the past ten years both for the wide range of problems that can be expressed in this form and for its compatibility with many quantum computing architectures. More recently, quantum annealers have advanced to the point where the scaling of qubits makes real-world applications increasingly feasible; however, current architectures remain restricted to solving quadratic unconstrained binary optimization problems, which can represent at most two-body interactions. Here we systematically examine the shortcomings of the QUBO framework and modern quantum annealers through the lens of the high-dimensional, exponentially scaling problem of RNA structure prediction, and find results that are generalizable to QUBO formalisms writ large. We find that using the QUBO framework to predict RNA structures results in poor accuracy, which becomes worse as system size scales. We determine that the fundamental constraint of two-body interactions prevents emergent correlations in the system, which are crucial to accurate structure prediction. Furthermore, we highlight that explicit, higher-order, empirical terms that are needed to improve structure prediction are incompatible with a QUBO framework. Finally, we show that our energy landscape has many deep local minima, which lead to local minima trapping and prevent permutation invariance. The relevance of these findings to other applications of QUBO, and therefore to modern quantum annealers more broadly, are discussed, with our work providing the first explicit explanation of why these formalisms have failed and will continue to fail in high-dimensional systems with similar constraints.

Recent hardware advances in quantum and quantum-inspired annealers promise substantial speedup for solving NP-hard combinatorial optimization problems compared to general-purpose computers. These special-purpose hardware are built for solving hard instances of Quadratic Unconstrained Binary Optimization (QUBO) problems. In terms of number of variables and precision of these hardware are usually resource-constrained and they work either in Ising space {-1,1} or in Boolean space {0,1}. Many naturally occurring problem instances are higher-order in nature. The known method to reduce the degree of a higher-order optimization problem uses Rosenberg's polynomial. The method works in Boolean space by reducing the degree of one term by introducing one extra variable. In this work, we prove that in Ising space the degree reduction of one term requires the introduction of two variables. Our proposed method of degree reduction works directly in Ising space, as opposed to converting an Ising polynomial to Boolean space and applying previously known Rosenberg's polynomial. For sparse higher-order Ising problems, this results in a more compact representation of the resultant QUBO problem, which is crucial for utilizing resource-constrained QUBO solvers.

Quantum annealing is a model for quantum computing that is aimed at solving hard optimization problems by representing them as quadratic unconstrained binary optimization (QUBO) problems. Although many NP-hard problems can easily be formulated as binary-variable problems with a quadratic objective function, such formulations typically also include constraints, which are not allowed in a QUBO. Hence, such constraints are usually incorporated in the objective function as additive penalty terms. While there is substantial previous work on implementing linear equality constraints, the case of inequality constraints has not much been studied. In this paper, we propose a new approach for formulating and embedding inequality constraints as penalties and describe early implementation results.

A max-flow approach to improved lower bounds for quadratic unconstrained binary optimization (QUBO)

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.

In the field of microlithography, conventional computers are widely used for mask optimization. Recent progress of quantum and quantum-inspired computers has encouraged the development of quantum algorithms for numerous applications. So far, no method has been established for solving mask optimization problems with quantum computers. We introduced a simple model that describes the mask optimization problem as a quadratic unconstrained binary optimization (QUBO) problem, which is easily implemented on these computers. For simplicity, we assume there exists a target image profile on the wafer. The target can be the image of an existing mask or a virtual ideal mask which may be designed as a pixelated mask having a continuous transmission distribution. The solution is evaluated as the difference between the simulated image profile on the wafer surface and the target profile.

Resource allocation of wide-area internet networks is inherently a combinatorial optimization problem that if solved quickly, could provide near real-time adaptive control of internet-protocol traffic ensuring increased network efficacy and robustness, while minimizing energy requirements coming from power-hungry transceivers. In recent works we demonstrated how such a problem could be cast as a quadratic unconstrained binary optimization (QUBO) problem that can be embedded onto the D-Wave Advantage™ quantum annealer system, demonstrating proof of principle. Our initial studies left open the possibility for improvement of D-Wave solutions via judicious choices of system run parameters. Here we report on our investigations for optimizing these system parameters, and how we incorporate machine learning (ML) techniques to further improve on the quality of solutions. In particular, we use the Hamming distance to investigate correlations between various system-run parameters and solution vectors. We then apply a decision tree neural network (NN) to learn these correlations, with the goal of using the neural network to provide further guesses to solution vectors. We successfully implement this NN in a simple integer linear programming (ILP) example, demonstrating how the NN can fully map out the solution space that was not captured by D-Wave. We find, however, for the 3-node network problem the NN is not able to enhance the quality of space of solutions.

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.