In the current fields of quantum information processing and quantum computing, fast and accurate quantum state manipulation and preparation have been of keen interest to researchers, and their potential applications are mainly in quantum measurement, quantum information, quantum communication, and quantum sensing.In this paper, the Hilbert space of a bipartite state system is unfolded by four Bell state entanglement bases and the result is projected to the subsystem to obtain a mixed state.A quantum approximation algorithm is proposed to provide a solution to the combinatorial optimization problem, and based on the workflow of the quantum approximation optimization algorithm, an improvement is proposed to the quantum approximation optimization algorithm to solve the constrained problem using the quadratic unconstrained binary optimization method.Based on the theory of cavity magnetism, the hybrid quantum system model is constructed, and the calculation method of Hamiltonian quantity is proposed.Combined with the quantum entanglement optimal path calculation of UQAOA algorithm, the optimal value of time-microwave entanglement ac E is obtained at r=0.234, so the compression parameter r=0.2 is used in the calculation.Based on the UQAOA algorithm for the analysis of the transmission characteristics of the generated OMA wave in air and the transmission optimization problem, the simulation obtains the reflection coefficient is slightly lower than that of the test, and the maximal error error is controlled at ±7.5dB around, and the two results are basically in agreement.
In the current fields of quantum information processing and quantum computing, fast and accurate quantum state manipulation and preparation have been of keen interest to researchers, and their potential applications are mainly in quantum measurement, quantum information, quantum communication, and quantum sensing.In this paper, the Hilbert space of a bipartite state system is unfolded by four Bell state entanglement bases and the result is projected to the subsystem to obtain a mixed state.A quantum approximation algorithm is proposed to provide a solution to the combinatorial optimization problem, and based on the workflow of the quantum approximation optimization algorithm, an improvement is proposed to the quantum approximation optimization algorithm to solve the constrained problem using the quadratic unconstrained binary optimization method.Based on the theory of cavity magnetism, the hybrid quantum system model is constructed, and the calculation method of Hamiltonian quantity is proposed.Combined with the quantum entanglement optimal path calculation of UQAOA algorithm, the optimal value of time-microwave entanglement ac E is obtained at r=0.234, so the compression parameter r=0.2 is used in the calculation.Based on the UQAOA algorithm for the analysis of the transmission characteristics of the generated OMA wave in air and the transmission optimization problem, the simulation obtains the reflection coefficient is slightly lower than that of the test, and the maximal error error is controlled at ±7.5dB around, and the two results are basically in agreement.
Recent advances in quantum computing have shown great potential for solving combinatorial optimization problems. A notable example is the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum-inspired algorithms require Quadratic Unconstrained Binary Optimization (QUBO) formulations. Transforming constrained optimization into QUBO impacts the algorithms' speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess them by using Simulated Annealing (SA), and find that three of our approaches outperform existing methods in terms of execution time as well as quality and quantity of feasible solutions found. Also, we tested these transformations on a quantum annealer, which was unable to solve even small instances, due to limitations in connectivity and error rates. In general, our results highlight the advantages of the new approaches, which reduce the number of variables in the QUBO representation.
Quantum entanglement, a fundamental aspect of quantum mechanics, holds immense potential for secure communication and advanced computation. However, the practical challenges associated with maintaining and manipulating entangled states, particularly over long distances, remain significant. This paper explores the potential of quantum entanglement transmission optimization, focusing on leveraging quantum mechanics to enhance the fidelity and efficiency of entangled state creation and transfer. We investigate a novel approach utilizing a quantum-enhanced model to guide the quantum process, aiming to minimize decoherence and maximize entanglement generation. The core claim is that by optimizing the entanglement creation and transfer process using this quantum model, we can substantially improve transmission efficiency and security. The study details the proposed model and its impact on the observed entanglement properties.
Quantum Entanglement Optimization Algorithm (QCOA) is a novel optimization algorithm that leverages the unique properties of quantum entanglement to discover optimal solutions for complex mathematical problems. Traditional optimization methods typically rely on classical computation, but QCOA introduces a fundamentally new approach by encoding optimization problems into entangled states, allowing for the detection of optimal solutions through quantum mechanics. This paper presents a comprehensive overview of QCOA, detailing its core mechanism, why it is new, and its potential impact across diverse mathematical domains.
This dissertation addresses fundamental challenges in solving constrained combinatorial optimization problems using hybrid quantum-classical computing approaches. Quantum computing shows promise for tackling computationally intractable problems, current approaches face significant limitations. The path forward in computing involves combining quantum and classical computing approaches. Quantum processing units (QPUs) will play a key role in accelerating algorithms in optimization, simulation, and machine learning applications beyond what classical computers can achieve on their own, similar to how graphical processing units (GPUs) have become integral to general-purpose computing. The current generation of quantum devices is limited by noise and circuit depth constraints, making it challenging to gain practical utility. Hybrid quantum-classical approaches, which combine quantum computing resources with classical computing resources, are essential for addressing these limitations on near-term devices. In the area of combinatorial optimization, current practical state-of-the-art hybrid approaches are variational in nature, relying on parameterized quantum circuits to encode solutions and classical optimization techniques to find optimal parameters. While the ultimate goal of solving computationally intractable problems is to find 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 hybrid quantum-classical approach for tackling these challenging problems that are encoded using quadratic and higher-order unconstrained binary optimization problems (QUBO and HUBO). QAOA alternates between two operators: a problem-specific cost Hamiltonian that encodes the optimization objective, and a mixer Hamiltonian that explores the solution space. The algorithm's parameters are iteratively optimized using classical methods to maximize the probability of sampling high-quality solutions. However, these methods often struggle with solution feasibility, especially for problems where the solutions must satisfy specific constraints. Penalty-based encodings require careful parameter tuning and risk producing infeasible solutions, while feasibility-preserving methods demand deeper quantum circuits that are challenging to implement on near-term quantum devices. In this dissertation, we present novel strategies that reduce or omit dependency on penalty parameters while maintaining solution quality, effectively capturing both optimal and near-optimal solutions, and balancing the trade-offs between circuit depth and solution feasibility. We present SCOOP, a novel QAOA-based framework for solving constrained optimization problems. SCOOP transforms a constrained problem into an unconstrained counterpart, forming SCOOP problem twins. QAOA 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 effectiveness of the SCOOP framework on selected NP-hard problems, some of which can be encoded quadratically (such as Minimum Vertex Cover and Maximum Independent Set), and some that can be encoded using higher-order terms (such as Minimum Dominating Set, Minimum Maximal Matching, and Minimum Set Cover). We also apply our framework to constrained combinatorial optimization problems that can be solved in polynomial time, such as Minimum Edge Cover and Maximum Matching. Experimental results on full statevector simulators and tensor network simulators show that SCOOP significantly improves the probability of finding high-quality feasible solutions across various problem classes, on problems that can be encoded quadratically as well as problems that can be encoded using higher-order terms. We also demonstrate the effectiveness of SCOOP on real quantum hardware, specifically IBM Quantum Heron R2 processors with 156 qubits, showing that SCOOP can be applied to practical problems with current quantum hardware limitations. This work makes significant contributions toward achieving quantum utility by enabling systematic investigation of constrained optimization problems on quantum devices. While current quantum computing research primarily focuses on unconstrained problems like MaxCut, real-world applications typically involve constraints. SCOOP provides a scalable framework for encoding constrained problems, extending quantum computing's practical utility beyond simple unconstrained cases. By eliminating dependency on penalty parameters and providing natural problem formulations, SCOOP makes it feasible to explore quantum solutions for constrained problems where classical exact methods become intractable. This capability is crucial for identifying promising avenues for demonstrating quantum utility across diverse constrained optimization problems, advancing the practical applicability of quantum computing approaches.
Quantum entanglement, a bizarre phenomenon in which two or more particles become linked in such a way that they share the same fate, holds immense promise for quantum computing and quantum information processing. However, harnessing entanglement effectively requires precise control over its quantum states. This paper explores the application of physics simulation techniques to optimize quantum entanglement states, specifically focusing on a novel geometric optimization method leveraging the unique properties of entanglement. Traditional optimization methods struggle to fully capture the intricacies of entangled states, necessitating a shift towards a more sophisticated approach. We propose a new method that utilizes entanglement to guide the search for optimal quantum states, resulting in enhanced efficiency and control over quantum computation. The core claim is that this method provides a significant improvement in the performance of quantum algorithms by effectively manipulating entangled states. The mechanism involves the exploitation of entanglement's non-classical correlation to generate a more complex and structured quantum state, facilitating faster and more accurate computations. This research presents a theoretical framework and preliminary results demonstrating the effectiveness of this approach.
Recent advancements in quantum computing have demonstrated significant potential for solving combinatorial optimization problems, like the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum and quantum-inspired algorithms often require transforming these constrained problems into an unconstrained form, known as Quadratic Unconstrained Binary Optimization (QUBO). Such transformations can significantly impact the algorithms’ speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess all nine methods using Simulated Annealing and find that three of our approaches outperform existing methods in terms of execution time and the quality and quantity of feasible solutions found. Additionally, we tested these transformations on quantum annealers, which were unable to solve even small problem instances, due to limitations in connectivity and error rates. However, our results highlight the advantages of the new approaches, which reduce the total number of variables in the QUBO representation. This is a critical factor for enhanced performance on emerging quantum hardware, since it also reduces the required number of qubits and the embedding chain lengths.