Quantum-enhanced greedy combinatorial optimization solver

Dupont, Maxime; Evert, Bram; Hodson, Mark J.; Sundar, Bhuvanesh; Jeffrey, Stephen; Yamaguchi, Yuki; Feng, Dennis; Maciejewski, Filip B.; Hadfield, Stuart; Alam, M. Sohaib; Wang, Zhihui; Grabbe, Shon; Lott, P. Aaron; Rieffel, Eleanor G.; Venturelli, Davide; Reagor, Matthew J.

doi:10.1126/sciadv.adi0487

Cited by 12 publications

(3 citation statements)

References 60 publications

(89 reference statements)

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“…Several pre-prints on iterative/recursive quantum optimization algorithms generalizing RQAOA have appeared since the submission of this work on arXiv. Parallel works such as [ 28 – 30 ] widen the selection and variable elimination schemes within the framework of recursive quantum optimization in application to constrained problems such as Maximum Independent Set (MIS) and Max-2-SAT. Moreover, [ 28 ] show theoretical justifications of why depth-1 QAOA might not be a suitable candidate for quantum advantage and consequently urge the community to explore higher depth alternatives.…”

Section: Related Workmentioning

confidence: 99%

Reinforcement learning assisted recursive QAOA

Patel,

Jerbi,

Bäck

et al. 2024

EPJ Quantum Technol.

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In recent years, variational quantum algorithms such as the Quantum Approximation Optimization Algorithm (QAOA) have gained popularity as they provide the hope of using NISQ devices to tackle hard combinatorial optimization problems. It is, however, known that at low depth, certain locality constraints of QAOA limit its performance. To go beyond these limitations, a non-local variant of QAOA, namely recursive QAOA (RQAOA), was proposed to improve the quality of approximate solutions. The RQAOA has been studied comparatively less than QAOA, and it is less understood, for instance, for what family of instances it may fail to provide high-quality solutions. However, as we are tackling -hard problems (specifically, the Ising spin model), it is expected that RQAOA does fail, raising the question of designing even better quantum algorithms for combinatorial optimization. In this spirit, we identify and analyze cases where (depth-1) RQAOA fails and, based on this, propose a reinforcement learning enhanced RQAOA variant (RL-RQAOA) that improves upon RQAOA. We show that the performance of RL-RQAOA improves over RQAOA: RL-RQAOA is strictly better on these identified instances where RQAOA underperforms and is similarly performing on instances where RQAOA is near-optimal. Our work exemplifies the potentially beneficial synergy between reinforcement learning and quantum (inspired) optimization in the design of new, even better heuristics for complex problems.

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Section: Related Workmentioning

confidence: 99%

Reinforcement learning assisted recursive QAOA

Patel,

Jerbi,

Bäck

et al. 2024

EPJ Quantum Technol.

View full text Add to dashboard Cite

show abstract

“…spins). Demonstrations of QAOA range from 40-qubits on 3-regular graphs [76], over 72 qubits in a Sherrington-Kirkpatrick model [77], to up to 434 qubits on hardware-native graphs [78,79] on superconducting devices.…”

Section: Demonstrationsmentioning

confidence: 99%

“…The derivatives of f can then be computed by means of the chain rule and correctly chaining the Jacobians of the nodes in the graph. By traversing the computational graph and employing the chain rule on each node, the derivative νk of each node is computed as νk = j ∈pred(k) ∂ν k ∂ν j νj , (C. 77) where ∂ν k /∂ν j denotes the Jacobian of node ν k with respect to the input node ν j . If node ν k has n k inputs and m k outputs, the Jacobian is a map from R n k → R m k , which depends on the values of the input nodes.…”

Section: Approximation Of the Fubini-study Metricmentioning

confidence: 99%

Variational quantum algorithm for unconstrained black box binary optimization: Application to feature selection

Zoufal

Mishmash

Sharma

et al. 2023

Quantum

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We introduce a variational quantum algorithm to solve unconstrained black box binary optimization problems, i.e., problems in which the objective function is given as black box. This is in contrast to the typical setting of quantum algorithms for optimization where a classical objective function is provided as a given Quadratic Unconstrained Binary Optimization problem and mapped to a sum of Pauli operators. Furthermore, we provide theoretical justification for our method based on convergence guarantees of quantum imaginary time evolution.To investigate the performance of our algorithm and its potential advantages, we tackle a challenging real-world optimization problem: feature selection. This refers to the problem of selecting a subset of relevant features to use for constructing a predictive model such as fraud detection. Optimal feature selection---when formulated in terms of a generic loss function---offers little structure on which to build classical heuristics, thus resulting primarily in ‘greedy methods’. This leaves room for (near-term) quantum algorithms to be competitive to classical state-of-the-art approaches. We apply our quantum-optimization-based feature selection algorithm, termed VarQFS, to build a predictive model for a credit risk data set with 20 and 59 input features (qubits) and train the model using quantum hardware and tensor-network-based numerical simulations, respectively. We show that the quantum method produces competitive and in certain aspects even better performance compared to traditional feature selection techniques used in today's industry.

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Approximating Maximum Independent Set on Rydberg Atom Arrays Using Local Detunings

Yeo,

Kim,

Jeong

2024

Adv Quantum Tech

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Rydberg atom arrays operated by a quantum adiabatic principle are among the most promising quantum simulating platforms due to their scalability and long coherence time. From the perspective of combinatorial optimization, they offer an efficient solution for an intrinsic maximum independent set problem because of the resemblance between the Rydberg Hamiltonian and the cost function of the maximum independent set problem. In this study, a strategy is suggested to approximate maximum independent sets by adjusting local detunings on the Rydberg Hamiltonian according to each vertex's vertex support, which is a quantity that represents connectivity between vertices. By doing so, the strategy successfully reduces the error rate three times for the checkerboard graphs with defects when the adiabaticity is sufficient. In addition, the strategy decreases the error rate for random graphs even when the adiabaticity is relatively insufficient. Moreover, it is shown that the strategy helps to prepare a quantum many‐body ground state by raising the fidelity between the evolved quantum state and a 2D cat state on a square lattice. Finally, the strategy is combined with the non‐abelian adiabatic mixing and this approach is highly successful in finding maximum independent sets compared to the conventional adiabatic evolution with local detunings.

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Quantum-enhanced greedy combinatorial optimization solver

Cited by 12 publications

References 60 publications

Reinforcement learning assisted recursive QAOA

Reinforcement learning assisted recursive QAOA

Variational quantum algorithm for unconstrained black box binary optimization: Application to feature selection

Approximating Maximum Independent Set on Rydberg Atom Arrays Using Local Detunings

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