Abstract One approach to solving planning problems is to compile them to other problems 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 of quadratic unconstrained binary optimization (QUBO) problem. Early quantum annealers are now available, though their constraints restrict the types of QUBOs they can take as input. Here, we introduce the planning community to the key steps in compiling planning problems to QA hardware: a hardware-independent step, mapping, and a hardware-dependent step, embedding. After describing two approaches to mapping general planning problems to QUBO, we describe preliminary results from running an early quantum annealer on a parametrized family of hard planning problems. The results show that different mappings can substantially affect performance, even when many features of the resulting instances are similar. We conclude with insights gained from this early study that suggest directions for future work.
Abstract One approach to solving planning problems is to compile them to other problems 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 of quadratic unconstrained binary optimization (QUBO) problem. Early quantum annealers are now available, though their constraints restrict the types of QUBOs they can take as input. Here, we introduce the planning community to the key steps in compiling planning problems to QA hardware: a hardware-independent step, mapping, and a hardware-dependent step, embedding. After describing two approaches to mapping general planning problems to QUBO, we describe preliminary results from running an early quantum annealer on a parametrized family of hard planning problems. The results show that different mappings can substantially affect performance, even when many features of the resulting instances are similar. We conclude with insights gained from this early study that suggest directions for future work.
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.
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.
Given a query plan, the goal of multiobjective query optimization [1] is to optimally map each operator in a plan to an implementation. Operator implementations differ by quality metrics such as cost and latency. In this context, query optimization becomes a multiobjective optimization problem. The optimal solution depends on user preferences and minimizes, for instance, a weighted sum over different cost metrics. We show how to transform instances of multiobjective query optimization, an NP-hard problem [1], into equivalent Quadratic Unconstrained Binary Optimization (QUBO) formulas that can be solved efficiently on quantum annealers.
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.
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.
Quantum annealing is a metaheuristic method aimed at finding the global minimum of a pseudo-Boolean quadratic function. To solve a problem by a quantum annealer, it must be restated as a QUBO (quadratic unconstrained binary optimization) problem, the standard format acceptable to an annealer. However, there are many natural problems that turn out be of cubic or higher order, yet promising solutions can be obtained for many instances using quantum annealers, after converting to the QUBO format, using order reduction criteria. Accordingly, quadratization becomes a crucial preprocessing step in order to make use of present-day quantum annealing hardware that relies on coupling technology, which can only process interactions of at most degree two. A critical challenge is that quadratization methods often require many additional variables, degrading the performance of the annealers. A number of algorithmic and heuristic quadratization techniques have been proposed and used for annealing in the literature, affecting the performance of the annealers differently. We examine a number of such quadratization techniques, focusing on their efficiency, compactness, and applicability. We analyze the approaches motivated by diverse goals and highlight the transition from foundational approaches to more recent compact approaches. An evaluation of the current usage of different quadratization methods in the literature is carried out at the end of the survey. Further, we comment on the limitations on usage and show possible opportunities to enhance the performance of annealers.