Hybrid quantum-classical algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications. Such algorithms are usually implemented in a variational form, combining a classical optimization method with a quantum machine to find good solutions to an optimization problem. The solution quality of QAOA depends to a high degree on the parameters chosen by the classical optimizer at each iteration. However, the solution landscape of those parameters is highly multi-dimensional and contains many low-quality local optima. In this study we apply a Cross-Entropy method to shape this landscape, which allows the classical optimizer to find better parameter more easily and hence results in an improved performance. We empirically demonstrate that this approach can reach a significant better solution quality for the Knapsack Problem.
We develop a global variable substitution method that reduces $n$-variable monomials in combinatorial optimization problems to equivalent instances with monomials in fewer variables. We apply this technique to $3$-SAT and analyze the optimal quantum circuit depth needed to solve the reduced problem using the quantum approximate optimization algorithm. For benchmark $3$-SAT problems, we find that the upper bound of the circuit depth is smaller when the problem is formulated as a product and uses the substitution method to decompose gates than when the problem is written in the linear formulatio…
Constrained Quantum Optimization at Utility Scale: Application to the Knapsack Problem
E.ON Digital Technology GmbH（E.ON数字技术有限公司）；University of Calgary（卡尔加里大学）；Université de Sherbrooke（舍布鲁克大学）；IBM Quantum, Thomas J. Watson Research Center（IBM量子，托马斯·J·沃森研究中心）
Quantum Approximate Optimization Algorithm (QAOA) is a hybrid algorithm whose control parameters are classically optimized. In addition to the variational parameters, the right choice of hyperparameter is crucial for improving the performance of any optimization model. Control depth, or the number of variational parameters, is considered as the most important hyperparameter for QAOA. In this paper we investigate the control depth selection with an automatic algorithm based on proximal gradient descent. The performances of the automatic algorithm are demonstrated on 7-node and 10-node Max-Cut p…
Scaling QAOA: transferring optimal adiabatic schedules from small-scale to large-scale variational circuits
Aix-Marseille Université, Université de Toulon（艾克斯-马赛大学、土伦大学）；ENSTA, Institut Polytechnique de Paris（巴黎理工学院）；Conservatoire National des Arts et Métiers（国立工艺博物馆）；Université Paris Cité（巴黎西岱大学）
REGRID-QAOA: A Resource-Efficient Hybrid QAOA Framework for Physics-Constrained Power System Islanding
Pennsylvania State University（宾夕法尼亚州立大学）；Kent State University（肯特州立大学）；Rensselaer Polytechnic Institute（伦斯勒理工学院）；Clemson University（克莱姆森大学）；University of Pretoria（比勒陀利亚大学）
We implement two Quantum Approximate Optimisation Algorithm (QAOA) variants for a battery revenue optimisation problem, equivalent to the weakly NP-hard Knapsack Problem. Both approaches investigate how to tackle constrained problems with QAOA. A first 'constrained' approach introduces a quadratic penalty to enforce the constraint to be respected strictly and reformulates the problem into an Ising Problem. However, simulations on IBM's simulator highlight non-convergent results for intermediate depth ($ p\leq 50$). A second 'relaxed' approach applies the QAOA with a non-Ising target function t…
Constrained Portfolio Optimization via Quantum Approximate Optimization Algorithm (QAOA) with XY-Mixers and Trotterized Initialization: A Hybrid Approach for Direct Indexing
SquareOne Capital（SquareOne资本）；School of Physics, Faculty of Sciences, Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学理学院物理系）
Learned-projector QAOA for hierarchical optimization
Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）；Qiuzhen College, Tsinghua University（清华大学求真学院）；Beijing International Center for Mathematical Research, Peking University（北京大学北京国际数学研究中心）；Institute for Applied Mathematics, Tsinghua University（清华大学应用数学中心）；Beijing Institute of Mathematical Sciences and Applications（北京数学与应用科学研究所以）
PACE-QAOA: Physics-Constrained Quantum Optimization for Qubit-Efficient Power System Islanding
Pennsylvania State University（宾夕法尼亚州立大学）；Rensselaer Polytechnic Institute（伦斯勒理工学院）；Kent State University（肯特州立大学）；Clemson University（克莱姆森大学）；University of Pretoria（比勒陀利亚大学）
We develop a framework for analyzing layered quantum algorithms such as quantum alternating operator ansätze. Our framework relates quantum cost gradient operators, derived from the cost and mixing Hamiltonians, to classical cost difference functions that reflect cost function neighborhood structure. By considering QAOA circuits from the Heisenberg picture, we derive exact general expressions for expectation values as series expansions in the algorithm parameters, cost gradient operators, and cost difference functions. This enables novel interpretability and insight into QAOA behavior in vario…
We present a general framework for modifying quantum approximate optimization algorithms (QAOA) to solve constrained network flow problems. By exploiting an analogy between flow constraints and Gauss's law for electromagnetism, we design lattice quantum electrodynamics (QED) inspired mixing Hamiltonians that preserve flow constraints throughout the QAOA process. This results in an exponential reduction in the size of the configuration space that needs to be explored, which we show through numerical simulations, yields higher quality approximate solutions compared to the original QAOA routine. …
Realizing the potential of near-term quantum computers to solve industry-relevant constrained-optimization problems is a promising path to quantum advantage. In this work, we consider the extractive summarization constrained-optimization problem and demonstrate the largest-to-date execution of a quantum optimization algorithm that natively preserves constraints on quantum hardware. We report results with the Quantum Alternating Operator Ansatz algorithm with a Hamming-weight-preserving XY mixer (XY-QAOA) on trapped-ion quantum computer. We successfully execute XY-QAOA circuits that restrict th…
We introduce multiple parametrized circuit ansätze and present the results of a numerical study comparing their performance with a standard Quantum Alternating Operator Ansatz approach. The ansätze are inspired by mixing and phase separation in the QAOA, and also motivated by compilation considerations with the aim of running on near-term superconducting quantum processors. The methods are tested on random instances of a weighted quadratic binary constrained optimization problem that is fully connected for which the space of feasible solutions has constant Hamming weight. For the parameter set…
A Hybrid Classical-Quantum Approach for Multi-Constrained Location Optimization Problem
The Catholic University of America（美国天主教大学）；Institute for Advanced Simulation（先进模拟研究所）；Jülich Supercomputing Centre（于利希超级计算中心）；T.J. Watson Research Center（T.J.沃森研究中心）；IBM
Constraint-Aware Quantum Optimization via Hamming Weight Operators
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学基础与前沿科学学院）；Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China（电子科技大学量子物理与光子量子信息教育部重点实验室）；Center on Frontiers of Computing Studies, Peking University（北京大学前沿计算研究中心）；School of Computer Science, Peking University（北京大学计算机学院）
Quantum Approaches to Urban Logistics: From Core QAOA to Clustered Scalability
Politecnico di Milano（米兰理工大学）；International Foundation Big Data And Artificial Intelligence For Human Development Via Galliera n. 32 – Bologna（大数据与人工智能促进人类发展的国际基金会，via Galliera n. 32 – 玻利维亚）
