We present an approach to solve the NP-hard database index selection problem on a D-Wave 2X adiabatic quantum annealer with over 1000 qubits. One of our main contributions is an efficient algorithm that maps instances of the index selection problem onto the qubits of the quantum annealer. Our mapping algorithm introduces several novel techniques that have not been used in the context of quantum annealing so far. Compared to prior approaches, we exploit qubits more efficiently which increases the size of the problem instances that can be represented with the given number of qubits by orders of magnitude. Furthermore, our algorithm decreases mapping time by many orders of magnitude compared to prior methods. The fundamental ideas that we present in this paper are applicable to similar optimization problems (e.g., other database related tuning problems). We analyze our algorithm formally and present experimental results on a real quantum annealer located at NASA Ames Research Center in California.
We present an approach to solve the NP-hard database index selection problem on a D-Wave 2X adiabatic quantum annealer with over 1000 qubits. One of our main contributions is an efficient algorithm that maps instances of the index selection problem onto the qubits of the quantum annealer. Our mapping algorithm introduces several novel techniques that have not been used in the context of quantum annealing so far. Compared to prior approaches, we exploit qubits more efficiently which increases the size of the problem instances that can be represented with the given number of qubits by orders of magnitude. Furthermore, our algorithm decreases mapping time by many orders of magnitude compared to prior methods. The fundamental ideas that we present in this paper are applicable to similar optimization problems (e.g., other database related tuning problems). We analyze our algorithm formally and present experimental results on a real quantum annealer located at NASA Ames Research Center in California.
The D-Wave adiabatic quantum annealer solves hard combinatorial optimization problems leveraging quantum physics. The newest version features over 1000 qubits and was released in August 2015. We were given access to such a machine, currently hosted at NASA Ames Research Center in California, to explore the potential for hard optimization problems that arise in the context of databases. In this paper, we tackle the problem of multiple query optimization (MQO). We show how an MQO problem instance can be transformed into a mathematical formula that complies with the restrictive input format accepted by the quantum annealer. This formula is translated into weights on and between qubits such that the configuration minimizing the input formula can be found via a process called adiabatic quantum annealing. We analyze the asymptotic growth rate of the number of required qubits in the MQO problem dimensions as the number of qubits is currently the main factor restricting applicability. We experimentally compare the performance of the quantum annealer against other MQO algorithms executed on a traditional computer. While the problem sizes that can be treated are currently limited, we already find a class of problem instances where the quantum annealer is three orders of magnitude faster than other approaches.
The D-Wave adiabatic quantum annealer solves hard combinatorial optimization problems leveraging quantum physics. The newest version features over 1000 qubits and was released in August 2015. We were given access to such a machine, currently hosted at NASA Ames Research Center in California, to explore the potential for hard optimization problems that arise in the context of databases. In this paper, we tackle the problem of multiple query optimization (MQO). We show how an MQO problem instance can be transformed into a mathematical formula that complies with the restrictive input format accepted by the quantum annealer. This formula is translated into weights on and between qubits such that the configuration minimizing the input formula can be found via a process called adiabatic quantum annealing. We analyze the asymptotic growth rate of the number of required qubits in the MQO problem dimensions as the number of qubits is currently the main factor restricting applicability. We experimentally compare the performance of the quantum annealer against other MQO algorithms executed on a traditional computer. While the problem sizes that can be treated are currently limited, we already find a class of problem instances where the quantum annealer is three orders of magnitude faster than other approaches.
The recent availability of the first commercial quantum computers has provided a promising tool to tackle NP hard problems which can only be solved heuristically with present techniques. However, it is unclear if the current state of quantum computing already provides a quantum advantage over the current state of the art in classical computing. This article assesses the performance of the D-Wave 2X quantum annealer on two NP hard graph problems, in particular clique finding and graph partitioning. For this, we provide formulations as Qubo and Ising Hamiltonians suitable for the quantum annealer and compare a variety of quantum solvers (Sapi, QBSolv, QSage provided by D-Wave Sys, Inc.) to current classical algorithms (METIS, Simulated Annealing, third-party clique finding and graph splitting heuristics) on certain test sets of graphs. We demonstrate that for small graph instances, classical methods still outperform the quantum annealer in terms of computing time, even though the quality of the best solutions obtained is comparable. Nevertheless, due to the limited problem size which can be embedded on the D-Wave 2X chip, the aforementioned finding applies to most of problems of general nature solvable on the quantum annealer. For instances specifically designed to fit the D-Wave 2X architecture, we observe substantial speed-ups in computing time over classical approaches.
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.
Quantum annealers offer a promising sampling-based computing paradigm for large-scale combinatorial optimization. However, directly using them to solve database optimization problems in real-time scenarios remains challenging due to strict hardware constraints and the opacity of commercial hybrid solvers. To address these challenges, we present QDBO , a white-box quantum-augmented database optimizer that directly leverages low-level quantum sampling on a quantum annealer. It first performs an initial reduction to produce embeddable QUBO instances via multiple mapping strategies that trade off efficiency and quality. It then applies an online iterative relaxation correction procedure that uses sampling feedback to correct the reduced QUBO across iterations, enabling controllable quality improvements under varying time budgets. We integrate QDBO with the PostgreSQL query optimizer to construct Q 2 O-QDBO for join order optimization. Evaluations on the Join Order Benchmark (JOB) and the Cardinality Estimation Benchmark (CEB) show that Q 2 O-QDBO improves 62 out of 113 JOB queries, and achieves up to 49.36× execution-time speedup and 36.88× end-to-end speedup on the CEB workload. Evaluations on synthetic queries with up to 50 relations show that Q 2 O-QDBO achieves significantly less end-to-end latency while maintaining similar solution quality compared with black-box quantum solvers. To demonstrate generality, we further integrate QDBO with PostgreSQL for index selection on TPC-H, where QDBO achieves up to 2.64× workload speedup over the empty-index baseline and outperforms classical and black-box solver baselines. These results demonstrate that using QDBO to solve large-scale database optimization problems in real-time settings is promising.
Quantum annealers of D-Wave Systems, Inc., offer an efficient way to compute high quality solutions of NP-hard problems. This is done by mapping a problem onto the physical qubits of the quantum chip, from which a solution is obtained after quantum annealing. However, since the connectivity of the physical qubits on the chip is limited, a minor embedding of the problem structure onto the chip is required. In this process, and especially for smaller problems, many qubits will stay unused. We propose a novel method, called parallel quantum annealing, to make better use of available qubits, wherein either the same or several independent problems are solved in the same annealing cycle of a quantum annealer, assuming enough physical qubits are available to embed more than one problem. Although the individual solution quality may be slightly decreased when solving several problems in parallel (as opposed to solving each problem separately), we demonstrate that our method may give dramatic speed-ups in terms of the Time-To-Solution (TTS) metric for solving instances of the Maximum Clique problem when compared to solving each problem sequentially on the quantum annealer. Additionally, we show that solving a single Maximum Clique problem using parallel quantum annealing reduces the TTS significantly.