Quantum Algorithm for Variant Maximum Satisfiability

In this paper, we proposed a novel quantum algorithm for the maximum satisfiability problem. Satisfiability (SAT) is to find the set of assignment values of input variables for the given Boolean function that evaluates this function as TRUE or prove that such satisfying values do not exist. For a POS SAT problem, we proposed a novel quantum algorithm for the maximum satisfiability (MAX-SAT), which returns the maximum number of OR terms that are satisfied for the SAT-unsatisfiable function, providing us with information on how far the given Boolean function is from the SAT satisfaction. We used Grover’s algorithm with a new block called quantum counter in the oracle circuit. The proposed circuit can be adapted for various forms of satisfiability expressions and several satisfiability-like problems. Using the quantum counter and mirrors for SAT terms reduces the need for ancilla qubits and realizes a large Toffoli gate that is then not needed. Our circuit reduces the number of ancilla qubits for the terms T of the Boolean function from T of ancilla qubits to ≈⌈log2⁡T⌉+1. We analyzed and compared the quantum cost of the traditional oracle design with our design which gives a low quantum cost

Exploring ab initio machine synthesis of quantum circuits

Gate-level quantum circuits are often derived manually from higher level algorithms. While this suffices for small implementations and demonstrations, ultimately automatic circuit design will be required to realise complex algorithms using hardware-specific operations and connectivity. Therefore, ab initio creation of circuits within a machine, either a classical computer or a hybrid quantum–classical device, is of key importance. We explore a range of established and novel techniques for the synthesis of new circuit structures, the optimisation of parameterised circuits, and the efficient removal of low-value gates via the quantum geometric tensor. Using these techniques we tackle the tasks of automatic encoding of unitary processes and translation (recompilation) of a circuit from one form to another. Using emulated quantum computers with various noise-free gate sets we provide simple examples involving up to 10 qubits, corresponding to 20 qubits in the augmented space we use. Further applications of specific relevance to chemistry modelling are considered in a sister paper, 'Exploiting subspace constraints and ab initio variational methods for quantum chemistry'. The emulation environments used were QuEST, QuESTlink and pyQuEST. All resources will be made openly accessible and are currently available upon request

Application of the Matlab® Linprog function to plan the short term operation of hydro stations considered as price makers

The restructuring of power systems induced newchallenges to generation companies in terms of adequatelyplanning the operation of power stations in order to maximizetheir profits. In this scope, hydro resources are becomingextremely valuable given the revenues that their operation cangenerate. In this paper we describe the application of theMatlab® Linprog optimization function to solve the Short TermHydro Scheduling Problem, HSP, admitting that some stationsare installed in the same cascade and that some of them havepumping capabilities. The optimization module to solve the HSPproblem is then integrated in an iterative process to take intoaccount the impact that the operation decisions regarding thehydro stations under analysis have on the market prices. Theupdated market prices are then used to run again the HSPproblem thus enabling considering the hydro stations as pricemakers. The developed approach is illustrated using a systembased on the Portuguese Douro River cascade that includes 9hydro stations (4 of them are pumping stations) and a totalinstalled capacity of 1485 MW

Quantum Algorithm for Maximum Biclique Problem

Identifying a biclique with the maximum number of edges bears considerable implications for numerous fields of application, such as detecting anomalies in E-commerce transactions, discerning protein-protein interactions in biology, and refining the efficacy of social network recommendation algorithms. However, the inherent NP-hardness of this problem significantly complicates the matter. The prohibitive time complexity of existing algorithms is the primary bottleneck constraining the application scenarios. Aiming to address this challenge, we present an unprecedented exploration of a quantum computing approach. Efficient quantum algorithms, as a crucial future direction for handling NP-hard problems, are presently under intensive investigation, of which the potential has already been proven in practical arenas such as cybersecurity. However, in the field of quantum algorithms for graph databases, little work has been done due to the challenges presented by the quantum representation of complex graph topologies. In this study, we delve into the intricacies of encoding a bipartite graph on a quantum computer. Given a bipartite graph with n vertices, we propose a ground-breaking algorithm qMBS with time complexity O^*(2^(n/2)), illustrating a quadratic speed-up in terms of complexity compared to the state-of-the-art. Furthermore, we detail two variants tailored for the maximum vertex biclique problem and the maximum balanced biclique problem. To corroborate the practical performance and efficacy of our proposed algorithms, we have conducted proof-of-principle experiments utilizing IBM quantum simulators, of which the results provide a substantial validation of our approach to the extent possible to date

Optimization of medical image steganography using n-decomposition genetic algorithm

Protecting patients' confidential information is a critical concern in medical image steganography. The Least Significant Bits (LSB) technique has been widely used for secure communication. However, it is susceptible to imperceptibility and security risks due to the direct manipulation of pixels, and ASCII patterns present limitations. Consequently, sensitive medical information is subject to loss or alteration. Despite attempts to optimize LSB, these issues persist due to (1) the formulation of the optimization suffering from non-valid implicit constraints, causing inflexibility in reaching optimal embedding, (2) lacking convergence in the searching process, where the message length significantly affects the size of the solution space, and (3) issues of application customizability where different data require more flexibility in controlling the embedding process. To overcome these limitations, this study proposes a technique known as an n-decomposition genetic algorithm. This algorithm uses a variable-length search to identify the best location to embed the secret message by incorporating constraints to avoid local minimum traps. The methodology consists of five main phases: (1) initial investigation, (2) formulating an embedding scheme, (3) constructing a decomposition scheme, (4) integrating the schemes' design into the proposed technique, and (5) evaluating the proposed technique's performance based on parameters using medical datasets from kaggle.com. The proposed technique showed resistance to statistical analysis evaluated using Reversible Statistical (RS) analysis and histogram. It also demonstrated its superiority in imperceptibility and security measured by MSE and PSNR to Chest and Retina datasets (0.0557, 0.0550) and (60.6696, 60.7287), respectively. Still, compared to the results obtained by the proposed technique, the benchmark outperforms the Brain dataset due to the homogeneous nature of the images and the extensive black background. This research has contributed to genetic-based decomposition in medical image steganography and provides a technique that offers improved security without compromising efficiency and convergence. However, further validation is required to determine its effectiveness in real-world applications