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Leveraging Artificial Intelligence to Advance Problem-Solving with Quantum Annealers

Ramin Ayanzadeh

Published Jan 20, 2020• 6 citations
Publisher

Abstract

We show how to advance quantum information processing, specifically problem-solving with quantum annealers, in the realm of artificial intelligence. We introduce SAT++, as a novel quantum programming paradigm, that can compile classical algorithms (implemented in classical programming languages) and execute them on quantum annealers. Moreover, we introduce a post-quantum error correction method that can find samples with significantly lower energy values, compared to the state-of-the-art techniques in quantum annealing. We also demonstrate that performing post-quantum error correction methods can make results of quantum annealers reproducible?i.e., more robust behavior of quantum annealers, compared to recent software and hardware advancements in quantum annealing. In addition, we offer to conjugate both optimization and sampling aspects of the quantum annealers and introduce two AI hybrid approaches. In reinforcement quantum annealing (RQA) scheme, an intelligent agent interacts with a quantum annealer that plays the stochastic environment role of learning automata and searches in the space of Hamiltonians, rather than exploring the Hilbert space of a given Ising model. In the same manner, greedy quantum annealing (GQA) is a novel model that utilizes quantum annealers to better select candidates in greedy algorithms. We experimentally demonstrate that our proposed AI hybrid approaches outperform the best-known techniques in quantum annealing, specifically when problems require longer chains for forming virtual qubits with higher connectivity. Furthermore, we introduce the theory of ensemble quantum annealing (EQA) that generates multiple (distinct) Ising Hamiltonians whose ground states are all identical to a solution to the problem of interest. Our experimental results reveal that applying EQA can significantly boost the performance of the quantum annealers. After benchmarking the D-Wave 2000Q quantum processors, as a proof-of-concept, we apply our proposed models on two real-world problems. As our first study case, we use SAT++ for factoring pseudo-prime numbers on a D-Wave quantum processor that can jeopardize the security of modern public-key cryptography systems. As our second case of study, we address the NP-hard problem of compressive sensing (i.e., the $\ell_0$-norm problem of sparse recovery) through reducing the original problem of compressive sensing to Weighted-MAX-SAT instances, casting the $\ell_0$-norm problem of binary compressive sensing to quadratic unconstrained binary optimization (QUBO), and proposing to solve the original problems of binary compressive sensing and binary compressive sensing with matrix uncertainty on quantum annealers.

DOI
10.13016/m28hdb-uoun

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We show how to advance quantum information processing, specifically problem-solving with quantum annealers, in the realm of artificial intelligence. We introduce SAT++, as a novel quantum programming paradigm, that can compile classical algorithms (implemented in classical programming languages) and execute them on quantum annealers. Moreover, we introduce a post-quantum error correction method that can find samples with significantly lower energy values, compared to the state-of-the-art techniques in quantum annealing. We also demonstrate that performing post-quantum error correction methods can make results of quantum annealers reproducible?i.e., more robust behavior of quantum annealers, compared to recent software and hardware advancements in quantum annealing. In addition, we offer to conjugate both optimization and sampling aspects of the quantum annealers and introduce two AI hybrid approaches. In reinforcement quantum annealing (RQA) scheme, an intelligent agent interacts with a quantum annealer that plays the stochastic environment role of learning automata and searches in the space of Hamiltonians, rather than exploring the Hilbert space of a given Ising model. In the same manner, greedy quantum annealing (GQA) is a novel model that utilizes quantum annealers to better select candidates in greedy algorithms. We experimentally demonstrate that our proposed AI hybrid approaches outperform the best-known techniques in quantum annealing, specifically when problems require longer chains for forming virtual qubits with higher connectivity. Furthermore, we introduce the theory of ensemble quantum annealing (EQA) that generates multiple (distinct) Ising Hamiltonians whose ground states are all identical to a solution to the problem of interest. Our experimental results reveal that applying EQA can significantly boost the performance of the quantum annealers. After benchmarking the D-Wave 2000Q quantum processors, as a proof-of-concept, we apply our proposed models on two real-world problems. As our first study case, we use SAT++ for factoring pseudo-prime numbers on a D-Wave quantum processor that can jeopardize the security of modern public-key cryptography systems. As our second case of study, we address the NP-hard problem of compressive sensing (i.e., the ℓ0\ell_0ℓ0​-norm problem of sparse recovery) through reducing the original problem of compressive sensing to Weighted-MAX-SAT instances, casting the ℓ0\ell_0ℓ0​-norm problem of binary compressive sensing to quadratic unconstrained binary optimization (QUBO), and proposing to solve the original problems of binary compressive sensing and binary compressive sensing with matrix uncertainty on quantum annealers.
We introduce the notion of reinforcement quantum annealing (RQA) scheme in which an intelligent agent searches in the space of Hamiltonians and interacts with a quantum annealer that plays the stochastic environment role of learning automata. At each iteration of RQA, after analyzing results (samples) from the previous iteration, the agent adjusts the penalty of unsatisfied constraints and re-casts the given problem to a new Ising Hamiltonian. As a proof-of-concept, we propose a novel approach for casting the problem of Boolean satisfiability (SAT) to Ising Hamiltonians and show how to apply the RQA for increasing the probability of finding the global optimum. Our experimental results on two different benchmark SAT problems (namely factoring pseudo-prime numbers and random SAT with phase transitions), using a D-Wave 2000Q quantum processor, demonstrated that RQA finds notably better solutions with fewer samples, compared to the best-known techniques in the realm of quantum annealing.
We introduce the reinforcement quantum annealing (RQA) scheme in which an intelligent agent interacts with a quantum annealer that plays the stochastic environment role of learning automata and tries to iteratively find better Ising Hamiltonians for the given problem of interest. As a proof-of-concept, we propose a novel approach for reducing the NP-complete problem of Boolean satisfiability (SAT) to minimizing Ising Hamiltonians and show how to apply the RQA for increasing the probability of finding the global optimum. Our experimental results on two different benchmark SAT problems (namely factoring pseudo-prime numbers and random SAT with phase transitions), using a D-Wave 2000Q quantum processor, demonstrated that RQA finds notably better solutions with fewer samples, compared to state-of-the-art techniques in the realm of quantum annealing.
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.
Natural Language Processing and Semantic Web include several NP complete/hard problems that are intractable for classical computing machines. Even though distributed computing has provided remarkable advances (more precisely in dealing with big data), non-decomposable NP problems are still intractable in many real-world applications. And, from quantum computing perspective, solving complex problems with universal quantum gates requires developing of quantum algorithms. Considering commercializing quantum annealing machines by D-Wave, achieving global optimum for discrete optimization problems has been realized. In this study, a novel approach has been introduced to convert symbolic AI problems into quadratic unconstrained binary optimization (QUBO) form. More narrowly, this method represents classification of text documents (fragments) as optimizing a QUBO function. After embedding the train corpus into a QUBO function, D-Wave quantum annealer is used to classify new observations with finding the minimum energy level of the system.
We leverage the idea of a statistical ensemble to improve the quality of quantum annealing based binary compressive sensing. Since executing quantum machine instructions on a quantum annealer can result in an excited state, rather than the ground state of the given Hamiltonian, we use different penalty parameters to generate multiple distinct quadratic unconstrained binary optimization (QUBO) functions whose ground state(s) represent a potential solution of the original problem. We then employ the attained samples from minimizing all corresponding (different) QUBOs to estimate the solution of the problem of binary compressive sensing. Our experiments, on a D-Wave 2000Q quantum processor, demonstrated that the proposed ensemble scheme is notably less sensitive to the calibration of the penalty parameter that controls the trade-off between the feasibility and sparsity of recoveries.
Quantum computing, leveraging quantum mechanics, promises to enhance optimization processes in artificial intelligence (AI) by addressing challenges faced by classical computing in solving complex problems. This study investigates the role of quantum computing in optimizing AI tasks, focusing on algorithms such as Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing (QA) for improved efficiency in optimization. A hybrid quantum-classical approach was used to evaluate the performance of quantum algorithms in optimization tasks, including combinatorial optimization and machine learning model tuning. QAOA and QA were applied to benchmark problems, such as Max-Cut and Traveling Salesman Problem (TSP). The study involved a comparative analysis between quantum algorithms and classical optimization techniques using performance metrics like solution quality, computational time, and scalability. Data were gathered through simulation on a quantum computing platform, and results were analyzed using statistical methods to assess improvements. The results showed that quantum computing significantly outperformed classical methods in solving large-scale optimization problems. QAOA demonstrated a 30% improvement in solution quality for Max-Cut problems, and QA showed a 25% faster convergence in TSP compared to classical algorithms. Quantum algorithms demonstrated scalability advantages as the problem size increased, with quantum methods achieving up to a 40% reduction in computational time for large instances. Furthermore, 70% of the tested cases showed significant improvements in solution accuracy, confirming the potential of quantum computing in real-world AI applications. Quantum computing, through QAOA and QA, offers substantial improvements in solving complex optimization problems in AI, presenting a transformative opportunity for the future of optimization algorithms.