ILP-based Resource Optimization Realized by Quantum Annealing for Optical Wide-area Communication Networks -- A Framework for Solving Combinatorial Problems of a Real-world Application by Quantum Annealing
Witt, Arthur, Kim, Jangho, Christopher Körber, Thomas Luu
Resource allocation of wide-area internet networks is inherently a combinatorial optimization problem that if solved quickly, could provide near real-time adaptive control of internet-protocol traffic ensuring increased network efficacy and robustness, while minimizing energy requirements coming from power-hungry transceivers. In recent works we demonstrated how such a problem could be cast as a quadratic unconstrained binary optimization (QUBO) problem that can be embedded onto the D-Wave AdvantageTM quantum annealer system, demonstrating proof of principle. Our initial studies left open the possibility for improvement of D-Wave solutions via judicious choices of system run parameters. Here we report on our investigations for optimizing these system parameters, and how we incorporate machine learning (ML) techniques to further improve on the quality of solutions. In particular, we use the Hamming distance to investigate correlations between various system-run parameters and solution vectors. We then apply a decision tree neural network (NN) to learn these correlations, with the goal of using the neural network to provide further guesses to solution vectors. We successfully implement this NN in a simple integer linear programming (ILP) example, demonstrating how the NN can fully map out the solution space that was not captured by D-Wave. We find, however, for the 3-node network problem the NN is not able to enhance the quality of space of solutions.
Resource allocation of wide-area internet networks is inherently a combinatorial optimization problem that if solved quickly, could provide near real-time adaptive control of internet-protocol traffic ensuring increased network efficacy and robustness, while minimizing energy requirements coming from power-hungry transceivers. In recent works we demonstrated how such a problem could be cast as a quadratic unconstrained binary optimization (QUBO) problem that can be embedded onto the D-Wave AdvantageTM quantum annealer system, demonstrating proof of principle. Our initial studies left open the possibility for improvement of D-Wave solutions via judicious choices of system run parameters. Here we report on our investigations for optimizing these system parameters, and how we incorporate machine learning (ML) techniques to further improve on the quality of solutions. In particular, we use the Hamming distance to investigate correlations between various system-run parameters and solution vectors. We then apply a decision tree neural network (NN) to learn these correlations, with the goal of using the neural network to provide further guesses to solution vectors. We successfully implement this NN in a simple integer linear programming (ILP) example, demonstrating how the NN can fully map out the solution space that was not captured by D-Wave. We find, however, for the 3-node network problem the NN is not able to enhance the quality of space of solutions.
Resource allocation of wide-area internet networks is inherently a combinatorial optimization problem that if solved quickly, could provide near real-time adaptive control of internet-protocol traffic ensuring increased network efficacy and robustness, while minimizing energy requirements coming from power-hungry transceivers. In recent works we demonstrated how such a problem could be cast as a quadratic unconstrained binary optimization (QUBO) problem that can be embedded onto the D-Wave Advantage™ quantum annealer system, demonstrating proof of principle. Our initial studies left open the possibility for improvement of D-Wave solutions via judicious choices of system run parameters. Here we report on our investigations for optimizing these system parameters, and how we incorporate machine learning (ML) techniques to further improve on the quality of solutions. In particular, we use the Hamming distance to investigate correlations between various system-run parameters and solution vectors. We then apply a decision tree neural network (NN) to learn these correlations, with the goal of using the neural network to provide further guesses to solution vectors. We successfully implement this NN in a simple integer linear programming (ILP) example, demonstrating how the NN can fully map out the solution space that was not captured by D-Wave. We find, however, for the 3-node network problem the NN is not able to enhance the quality of space of solutions.
Agile networks with fast adaptation and reconfiguration capabilities are required for on-demand provisioning of various network services. We propose a new methodical framework for short-time network optimization based on quantum computing (QC) and integer linear program (ILP) models, which has the potential of realizing a real-time network automation. We define methods to map a nearly real-world ILP model for resource provisioning to a quadratic unconstrained binary optimization (QUBO) problem, which is solvable on quantum annealer (QA). We concentrate on the three-node network to evaluate our approach and its obtainable quality of solution using the state-of-the-art quantum annealer D-Wave Advantage™ 5.2/5.3. By studying the annealing process, we find annealing configuration parameters that obtain feasible solutions close to the reference solution generated by the classical ILP-solver CPLEX. Further, we studied the scaling of the network problem and provide estimations on quantum annealer's hardware requirements to enable a proper QUBO problem embedding of larger networks. We achieved the QUBO embedding of networks with up to 6 nodes on the D-Wave Advantage™. According to our estimates a real-sized network with 12 to 16 nodes require a QA hardware with at least 50000 qubits or more.
Quantum networks attract increasing attention due to their unique advantages over classical networks. However, the challenge of efficiently and economically constructing reliable wide-area quantum networks remains unresolved. This problem, termed network planning, is typically modeled as an Integer Linear Programming (ILP) problem. Existing solver-based solutions for classical networks face scalability issues, while heuristic approaches that sacrifice optimality for scalability heavily rely on human expertise and lack generalizability. Recently, deep reinforcement learning (DRL) has demonstrated potential in adaptive decision-making for classical network planning. However, quantum networks introduce unique constraints due to their end-to-end entanglement distribution requirements. To address this, we propose a two-stage quantum network resource allocation framework, QPLAN, that combines multi-agent DRL with traditional optimization solvers. Our approach uses a novel multi-agent reinforcement learning strategy using graph neural networks (GNNs) and transformers for traffic flow and corresponding hardware resource allocation to minimize hardware cost while cooperatively satisfying problem constraints as much as possible. The output of the DRL algorithm is then used as an initial input to prune the solution space, "warm-starting" the ILP solver and further improving the solution. This hybrid approach effectively reduces manual effort and enhances scalability. Experimental results show that our method yields near-optimal solutions with better scalability than only using ILP solvers.
Quantum annealers, such as the device built by D-Wave Systems, Inc., offer a way to compute solutions of NP-hard problems that can be expressed in Ising or quadratic unconstrained binary optimization (QUBO) form. Although such solutions are typically of very high quality, problem instances are usually not solved to optimality due to imperfections of the current generations quantum annealers. In this contribution, we aim to understand some of the factors contributing to the hardness of a problem instance, and to use machine learning models to predict the accuracy of the D-Wave 2000Q annealer for solving specific problems. We focus on the maximum clique problem, a classic NP-hard problem with important applications in network analysis, bioinformatics, and computational chemistry. By training a machine learning classification model on basic problem characteristics such as the number of edges in the graph, or annealing parameters, such as the D-Wave’s chain strength, we are able to rank certain features in the order of their contribution to the solution hardness, and present a simple decision tree which allows to predict whether a problem will be solvable to optimality with the D-Wave 2000Q. We extend these results by training a machine learning regression model that predicts the clique size found by D-Wave.
The focus of this work is to explore the use of quantum annealing solvers for the problem of phase unwrapping of synthetic aperture radar (SAR) images. Although solutions to this problem exist based on network programming, these techniques do not scale well to larger-sized images. Our approach involves formulating the problem as a quadratic unconstrained binary optimization (QUBO) problem, which can be solved using a quantum annealer. Given that present embodiments of quantum annealers remain limited in the number of qubits they possess, we decompose the problem into a set of subproblems that can be solved individually. These individual solutions are close to optimal up to an integer constant, with one constant per sub-image. In a second phase, these integer constants are determined as a solution to yet another QUBO problem. We test our approach with a variety of software-based QUBO solvers and on a variety of images, both synthetic and real. Additionally, we experiment using D-Wave Systems's quantum annealer, the D-Wave 2000Q. The software-based solvers obtain high-quality solutions comparable to state-of-the-art phase-unwrapping solvers. We are currently working on optimally mapping the problem onto the restricted topology of the quantum annealer to improve the quality of the solution.
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.