Implementing transferable annealing protocols for combinatorial optimization on neutral-atom quantum processors: A case study on smart charging of electric vehicles
Lucas Leclerc, Constantin Dalyac, Pascale Bendotti, Rodolphe Griset, Joseph Mikael, Loïc Henriet
In the quantum optimization paradigm, variational quantum algorithms face challenges with hardware-specific and instance-dependent parameter tuning, which can lead to computational inefficiencies. The promising potential of parameter transferability across problem instances with similar local structures has been demonstrated in the context of the quantum approximate optimization algorithm. In this paper we build on these advancements by extending the concept to annealing-based protocols, employing Bayesian optimization to design robust quasiadiabatic schedules. Our study reveals that, for maximum independent set problems on graph families with shared geometries, optimal parameters naturally concentrate, enabling efficient transferability between similar instances and from smaller to larger ones. Experimental results on the Orion Alpha platform validate the effectiveness of our approach, scaling to problems with up to 100 qubits. We apply this method to address a smart-charging optimization problem on a real dataset. These findings highlight a scalable, resource-efficient path for hybrid optimization strategies applicable in real-world scenarios.
In the quantum optimization paradigm, variational quantum algorithms face challenges with hardware-specific and instance-dependent parameter tuning, which can lead to computational inefficiencies. The promising potential of parameter transferability across problem instances with similar local structures has been demonstrated in the context of the quantum approximate optimization algorithm. In this paper we build on these advancements by extending the concept to annealing-based protocols, employing Bayesian optimization to design robust quasiadiabatic schedules. Our study reveals that, for maximum independent set problems on graph families with shared geometries, optimal parameters naturally concentrate, enabling efficient transferability between similar instances and from smaller to larger ones. Experimental results on the Orion Alpha platform validate the effectiveness of our approach, scaling to problems with up to 100 qubits. We apply this method to address a smart-charging optimization problem on a real dataset. These findings highlight a scalable, resource-efficient path for hybrid optimization strategies applicable in real-world scenarios.
We propose and analyze the use of Bayesian optimization techniques to design quantum annealing schedules with minimal user and resource requirements. We showcase our scheme with results for two paradigmatic spin models. We find that Bayesian optimization is able to identify schedules resulting in fidelities several orders of magnitude better than standard protocols for both quantum and reverse annealing, as applied to the p -spin model. We also show that our scheme can help improve the design of hybrid quantum algorithms for hard combinatorial optimization problems, such as the maximum independent set problem, and illustrate these results via experiments on a neutral-atom quantum processor available on Amazon Braket. Published by the American Physical Society 2024
Quantum computing has emerged as a promising computational paradigm with the potential to solve problems that are intractable for classical computers. This paper provides an overview of the current state of quantum computing, including its historical development, hardware advancements, applications, and challenges. Special attention is given to combinatorial optimization, which is considered one of the most promising application domains. The limitations of current quantum systems and future research directions are also discussed. This paper presents a comparative study between a conventional D-Wave-based simulated annealing approach and a proposed hybrid optimization model for solving largescale combinatorial optimization problems. The study focuses on benchmark problems, including AES, TSP gr24, and a real-world load balancing problem, all formulated as QUBO models. The D-Wave approach employs the dwave-neal simulated annealing engine with various parameter settings, while the proposed model introduces a decomposition-based framework combined with adaptive parameter control and iterative refinement. The experimental results demonstrate that the proposed model consistently outperforms the conventional approach in terms of solution quality, achieving significantly lower energy values across all problem instances. In particular, for the TSP gr24 problem, the proposed model achieves near-optimal solutions with substantially reduced computation time. For large-scale problems such as AES and load balancing, the proposed model maintains scalability and robustness, whereas the conventional approach suffers from increased computational cost and performance degradation. Although the proposed method introduces additional computational steps, its hybrid structure effectively mitigates limitations related to local minima, parameter sensitivity, and scalability. These findings indicate that integrating classical optimization techniques with quantum-inspired methods is essential for practical applications. The proposed model provides a promising framework for solving complex real-world optimization problems and highlights the importance of hybrid approaches in advancing quantum annealing technologies.
Solving combinatorial optimization problems (COPs) is a promising application of quantum computation, with the Quantum Approximate Optimization Algorithm (QAOA) being one of the most studied quantum algorithms for solving them. However, multiple factors make the parameter search of the QAOA a hard optimization problem. In this work, we study transfer learning (TL), a methodology to reuse pre-trained QAOA parameters of one problem instance into different COP instances. This methodology can be used to alleviate the necessity of classical optimization to find good parameters for individual problems. To this end, we select small cases of the traveling salesman problem (TSP), the bin packing problem (BPP), the knapsack problem (KP), the weighted maximum cut (MaxCut) problem, the maximal independent set (MIS) problem, and portfolio optimization (PO), and find optimal β and γ parameters for p layers. We compare how well the parameters found for one problem adapt to the others. Among the different problems, BPP is the one that produces the best transferable parameters, maintaining the probability of finding the optimal solution above a quadratic speedup over random guessing for problem sizes up to 42 qubits and p = 10 layers. Using the BPP parameters, we perform experiments on IonQ Harmony and Aria, Rigetti Aspen-M-3, and IBM Brisbane of MIS instances for up to 18 qubits. The results indicate that IonQ Aria yields the best overlap with the ideal probability distribution. Additionally, we show that cross-platform TL is possible using the D-Wave Advantage quantum annealer with the parameters found for BPP. We show an improvement in performance compared to the default protocols for MIS with up to 170 qubits. Our results suggest that there are QAOA parameters that generalize well for different COPs and annealing protocols.
The major advances in quantum computing over the last few decades have sparked great interest in applying it to solve the most challenging computational problems in a wide variety of areas. One of the most pronounced domains here are optimization problems and a number of algorithmic approaches have been proposed for their solution. For the current noisy intermediate-scale quantum (NISQ) computers the quantum approximate optimization algorithm (QAOA), the variational quantum eigensolver (VQE), and quantum annealing (QA) are the central algorithms for this problem class. The two former can be executed on digital gate-model quantum computers, whereas the latter requires a quantum annealer. Across all hardware architectures and manufactures, the quantum computers available today share the property of being too error-prone to reliably execute involved quantum circuits as they typically arise from quantum optimization algorithms. In order to characterize the limits of existing quantum computers, many component and system level benchmarks have been proposed. However, owing to the complex nature of the errors in quantum systems these benchmark fail to provide predictive power beyond simple quantum circuits and small examples. Application oriented benchmarks have been proposed to remedy this problem, but both, results from real quantum systems as well as use cases beyond constructed academic examples, remain very rare. This paper addresses precisely this gap by considering two industrial relevant use cases: one in the realm of optimizing charging schedules for electric vehicles, the other concerned with the optimization of truck routes. Our central contribution are systematic series of examples derived from these uses cases that we execute on different processors of the gate-based quantum computers of IBM as well as on the quantum annealer of D-Wave.
In order to qualify quantum algorithms for industrial NP-Hard problems, comparing them to available polynomial approximate classical algorithms and not only to exact ones -- exponential by nature -- , is necessary. This is a great challenge as, in many cases, bounds on the reachable approximation ratios exist according to some highly-trusted conjectures of Complexity Theory. An interesting setup for such qualification is thus to focus on particular instances of these problems known to be "less difficult" than the worst-case ones and for which the above bounds can be outperformed: quantum algorithms should perform at least as well as the conventional approximate ones on these instances, up to very large sizes. We present a case study of such a protocol for two industrial problems drawn from the strongly developing field of smart-charging of electric vehicles. Tailored implementations of the Quantum Approximate Optimization Algorithm (QAOA) have been developed for both problems, and tested numerically with classical resources either by emulation of Pasqal's Rydberg atom based quantum device or using Atos Quantum Learning Machine. In both cases, quantum algorithms exhibit the same approximation ratios than conventional approximation algorithms, or improve them. These are very encouraging results, although still for instances of limited size as allowed by studies on classical computing resources. The next step will be to confirm them on larger instances, on actual devices, and for more complex versions of the problems addressed.
Combinatorial optimization is one of the promising applications of quantum computation. Variational Quantum Algorithm (VQA) is a classical-quantum hybrid algorithm framework for noisy quantum devices. However, the quality of the solution is readily affected by statistical fluctuations and physical noise, making it challenging to maintain applicability for largescale problems. In contrast, sampling-based quantum algorithms have recently been successfully applied to large-scale quantum chemistry problems. In the sampling-based framework, the quantum device is used only for sampling, while the ground state and its energy are estimated on the classical device. In this study, we propose the Sampling-based Quantum Optimization Algorithm (SQOA) that leverages these advantages for combinatorial optimization. There are two challenges in constructing SQOA. The first challenge is that we need to encode the optimization problem in a non-diagonal Hamiltonian, even though many VQAs encode it into the Ising Hamiltonian, which is diagonal. The second challenge is that we need a method for efficient preparation of the input state to be sampled. To address the first challenge, we utilize the Quantum Relaxation (QR) method for encoding an optimization problem within a Hamiltonian. This method achieves a higher encoding density by mapping multiple variables to a single qubit, thus requiring fewer qubits for larger problems compared to the Ising Hamiltonian approach. Moreover, to address the second challenge, we investigate the parameter transferability within the Quantum Alternating Operator Ansatz for QR Hamiltonians. We show that restricting parameters to a linear form exhibits moderate transferability for 3-regular Max-Cut problems, similar to transferability observed in the Quantum Approximate Optimization Algorithm. Therefore, this property allows us to efficiently prepare the input state for a large problem instance using the parameters obtained from a small problem instance. We leveraged transferability to create input states and applied SQOA with QR to the Max-Cut instances. By transferring parameters from a 20-node problem, we demonstrate that SQOA with QR provides high-quality solutions for 40-node problems without variational parameter optimization.