A method for mapping quadratic unconstrained binary optimizations expressed as nearest neighbor stencils onto contemporary quantum annealing machines is developed. The method is shown to be scalable in providing higher utilization of annealing hardware resources than prior work. Applying the technique to the problem of determining an effective fuel loading pattern for nuclear reactors shows that densely mapped quantum stencils result in higher fidelity solutions of optimization problems then the sparser default solutions. These results are likely to generalize to quadratic unconstrained binary optimizations that can be expressed as dense quantum stencils, thereby improving optimization results obtained from noisy quantum devices.
A method for mapping quadratic unconstrained binary optimizations expressed as nearest neighbor stencils onto contemporary quantum annealing machines is developed. The method is shown to be scalable in providing higher utilization of annealing hardware resources than prior work. Applying the technique to the problem of determining an effective fuel loading pattern for nuclear reactors shows that densely mapped quantum stencils result in higher fidelity solutions of optimization problems then the sparser default solutions. These results are likely to generalize to quadratic unconstrained binary optimizations that can be expressed as dense quantum stencils, thereby improving optimization results obtained from noisy quantum devices.
Abstract Operation management of nuclear power plants consists of several computationally hard problems. Searching for an in-core fuel loading pattern is among them. The main challenge of this combinatorial optimization problem is the exponential growth of the search space with a number of loading elements. Here we study a reloading problem in a Quadratic Unconstrained Binary Optimization (QUBO) form. Such a form allows us to apply various techniques, including quantum annealing, classical simulated annealing, and quantum-inspired algorithm in order to find fuel reloading patterns for several realistic configurations of nuclear reactors. We present the results of benchmarking the in-core fuel management problem in the QUBO form using the aforementioned computational techniques. This work demonstrates potential applications of quantum computers and quantum-inspired algorithms in the energy industry.
Abstract : One approach to solving planning problems is to compile them to another problem for which powerful off-the-shelf solvers are available; common targets include SAT, CSP, and MILP. Recently, a novel optimization technique has become available: quantum annealing (QA). QA takes as input problem instances encoded as Quadratic Unconstrained Binary Optimization (QUBO). Early quantum annealers are now available, and more sophisticated quantum annealers will likely be built over the next decades. Specific quantum annealing hardware implementations have specific constraints, restricting the types of QUBOs each can take as input. In this paper, we introduce the planning community to the key steps involved in compiling planning problems to quantum annealing hardware: a hardware-independent step, mapping, and a hardware-dependent step, embedding. After describing two approaches to mapping general planning problems to QUBO, we provide preliminary results from running an early quantum annealer on a parameterized family of hard planning problems. The results show that different mappings can lead to a substantial difference in performance, even when many superficial features of the resulting instances are similar. We also provide some insights gained from this early study, and suggest directions for future work.
This paper explores the application of Quantum Annealing (QA) to the field of combinatorial optimization. The core idea is to leverage the principles of quantum mechanics, specifically quantum tunneling, to efficiently solve complex optimization problems. We present a framework for utilizing QA to tackle problems represented as quadratic unconstrained binary optimization (QUBO) models. The methodology focuses on mapping the problem's constraints and objective function into a form suitable for QA hardware. We discuss the challenges involved in this mapping process, including the limitations of current QA devices and the need for careful problem formulation. Furthermore, we analyze the potential advantages of QA over classical optimization techniques, particularly concerning the exploration of a wider solution space. The research highlights the promise of QACO as a viable approach for tackling computationally demanding combinatorial optimization tasks, offering a novel method to enhance optimization efficiency.
To date, conventional computers have never been able to efficiently handle certain tasks, where the number of computation steps is likely to blow up as the problem size increases. As an emerging technology and new computing paradigm, quantum computing has a great potential to tackle those hard tasks efficiently. Among all the existing quantum computation models, quantum annealing has drawn significant attention in recent years due to the realization of the commercialized quantum annealer, sparking research interests in developing applications to solve problems that are intractable for classical computers.However, designing and implementing algorithms that manage to harness the enormous computation power from quantum annealer remains a challenging task. Generally, it requires mapping of the given optimization problem into quadratic unconstrained binary optimization(QUBO) problem and embedding the subsequent QUBO onto the physical architecture of quantum annealer. Additionally, practical quantum annealers are susceptible to errors leading to low probability of the correct solution.In this study, we focus on solving Boolean satisfiability (SAT) problem using quantum annealer while addressing practical limitations. We have proposed a mapping technique that maps SAT problem to QUBO, and we have further devised a tool flow that embeds the QUBO onto the architecture of a quantum annealing device. Additionally, We have optimized the proposed embedding flow to reduce run-time in addition to shortening the qubit chain length, leading to robust quantum annealing. To further improve the reliability of quantum annealing, we have also developed a post processing embedding technique that enlarges the energy gap between ground state and the first excited state. To demonstrate the effectiveness of proposed methods, we have conducted experiments on real quantum annealing devices manufactured by D-Wave Systems, showing compelling result of using quantum annealer to solve SAT problem.
This paper explores the application of quantum annealing to the challenging domain of combinatorial optimization within large-scale networks. Specifically, it investigates the feasibility of utilizing quantum annealing for problems such as network routing and scheduling, where traditional classical algorithms often struggle due to computational complexity. The core approach involves formulating the network optimization problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem. This transformation enables the mapping of the problem onto the quantum annealing hardware, leveraging the quantum annealing process – characterized by its adiabatic evolution – to discover the optimal solution. We argue that this method presents a potential advantage over conventional algorithms for large-scale network scenarios, offering a pathway to tackling problems previously considered intractable. The theoretical framework and underlying principles are thoroughly discussed, outlining the methodology and highlighting the anticipated benefits.
Quantum annealing device has shown a great potential in solving discrete problems that are theoretically and empirically hard. Boolean Satisfiability (SAT) problem, determining if there is an assignment of variables that satisfies a given Boolean function, is the first proven NP-complete problem widely used in various domains. Here, we present a novel mapping of the SAT problem to the quadratic unconstrained binary optimization problem (QUBO), and further develop a tool flow embedding the proposed QUBO to the architecture of the commercialized quantum computer D-Wave. By leveraging electronic design automation techniques including synthesis, placement and routing, this is not only the first work providing the detail flow that embeds the QUBO, but also a technique scalable for real world applications and some hard SAT problems with over 6000 variables in QUBO. Based on our results, we discuss the challenges in solving SAT using the current generation of annealing device, and explore the problem solving capability of future quantum annealing computers.