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Register a new userLyapunov control-inspired strategies for quantum combinatorial optimization
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The prospect of using quantum computers to solve combinatorial optimization problems via the quantum approximate optimization algorithm (QAOA) has attracted considerable interest in recent years. However, a key limitation associated with QAOA is the need to classically optimize over a set of quantum circuit parameters. This classical optimization can have significant associated costs and challenges. Here, we provide an expanded description of Lyapunov control-inspired strategies for quantum optimization, as first presented in arXiv:2103.08619, that do not require any classical optimization effort. Instead, these strategies utilize feedback from qubit measurements to assign values to the quantum circuit parameters in a deterministic manner, such that the combinatorial optimization problem solution improves monotonically with the quantum circuit depth. Numerical analyses are presented that investigate the utility of these strategies towards MaxCut on weighted and unweighted 3-regular graphs, both in ideal implementations and also in the presence of measurement noise. We also discuss how how these strategies may be used to seed QAOA optimizations in order to improve performance for near-term applications, and explore connections to quantum annealing.
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Quantum hardware and quantum-inspired algorithms are becoming increasingly popular for combinatorial optimization. However, these algorithms may require careful hyperparameter tuning for each problem instance. We use a reinforcement learning agent in conjunction with a quantum-inspired algorithm to solve the Ising energy minimization problem, which is equivalent to the Maximum Cut problem. The agent controls the algorithm by tuning one of its parameters with the goal of improving recently seen solutions. We propose a new Rescaled Ranked Reward (R3) method that enables stable single-player version of self-play training that helps the agent to escape local optima. The training on any problem instance can be accelerated by applying transfer learning from an agent trained on randomly generated problems. Our approach allows sampling high-quality solutions to the Ising problem with high probability and outperforms both baseline heuristics and a black-box hyperparameter optimization approach.
As a hybrid of techniques from open-loop and feedback control, Lyapunov control has the advantage that it is free from the measurement-induced decoherence but it includes the systems instantaneous message in the control loop. Often, the Lyapunov control is confronted with time delay in the control fields and difficulty in practical implementations of the control. In this paper, we study the effect of time-delay on the Lyapunov control, and explore the possibility of replacing the control field with a pulse train or a bang-bang signal. The efficiency of the Lyapunov control is also presented through examining the convergence time of the controlled system. These results suggest that the Lyapunov control is robust gainst time delay, easy to realize and effective for high-dimensional quantum systems.
Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moores law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world datasets directly in the near future, leading to new challenges in utilizing these quantum processors for practical purposes. Hybrid quantum-classical algorithms that leverage both quantum and classical types of devices are considered as one of the main strategies to apply quantum computing to large-scale problems. In this paper, we advocate the use of multilevel frameworks for combinatorial optimization as a promising general paradigm for designing hybrid quantum-classical algorithms. In order to demonstrate this approach, we apply this method to two well-known combinatorial optimization problems, namely, the Graph Partitioning Problem, and the Community Detection Problem. We develop hybrid multilevel solvers with quantum local search on D-Waves quantum annealer and IBMs gate-model based quantum processor. We carry out experiments on graphs that are orders of magnitudes larger than the current quantum hardware size, and we observe results comparable to state-of-the-art solvers in terms of quality of the solution.
We develop a general method for incentive-based programming of hybrid quantum-classical computing systems using reinforcement learning, and apply this to solve combinatorial optimization problems on both simulated and real gate-based quantum computers. Relative to a set of randomly generated problem instances, agents trained through reinforcement learning techniques are capable of producing short quantum programs which generate high quality solutions on both types of quantum resources. We observe generalization to problems outside of the training set, as well as generalization from the simulated quantum resource to the physical quantum resource.
Quantum variational algorithms have garnered significant interest recently, due to their feasibility of being implemented and tested on noisy intermediate scale quantum (NISQ) devices. We examine the robustness of the quantum approximate optimization algorithm (QAOA), which can be used to solve certain quantum control problems, state preparation problems, and combinatorial optimization problems. We demonstrate that the error of QAOA simulation can be significantly reduced by robust control optimization techniques, specifically, by sequential convex programming (SCP), to ensure error suppression in situations where the source of the error is known but not necessarily its magnitude. We show that robust optimization improves both the objective landscape of QAOA as well as overall circuit fidelity in the presence of coherent errors and errors in initial state preparation.
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