Daniel Jaroszewski, Fabian Klos, Benedikt Sturm
We formulate binary optimization functions for single-vehicle routing, travelling salesperson and collision-free multi-vehicle routing with significant improvements in the number of variables over existing formulations. The provided functions are readily implemented on gate-based quantum computers using variational algorithms and on adiabatic quantum hardware.
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It is imperative to compile quantum circuits for Noisy Intermediate-Scale Quantum (NISQ) devices because of the limited connectivity of physical qubits and the high error rates of gate operations. One of the most critical steps in quantum circuit compilation is qubit routing, an NP-Hard problem that involves placing and moving logical qubits to minimize compilation overhead. In this study, we propose ISing mAchine Assisted Quantum compiler (ISAAQ) to perform qubit routing with Ising machines, which can efficiently solve Quadratic Unconstrained Binary Optimization (QUBO) problems. ISAAQ accurat…
In this paper, we describe the usage of the Quantum Approximate Optimization Algorithm (QAOA), which is a quantum-classical heuristic, to solve a combinatorial optimization and integer programming task known as Vehicle Routing Problem (VRP). We outline the Ising formulation for VRP and present a detailed procedure to solve VRP by minimizing its simulated Ising Hamiltonian using the IBM Qiskit platform. Here, we attempt to find solutions for the VRP problems: (4,2), (5,2), and (5,3), where each (n, k) represents a VRP problem with n locations and k vehicles. We find that the performance of QAOA…
Multi-Objective Routing Optimization Using Coherent Ising Machine in Wireless Multihop Networks
本文提出将相干伊辛机（CIM）应用于无线多跳网络的多目标路由优化，通过将问题建模为QUBO并映射到伊辛模型求解，在数百节点规模网络中实现可行且近优的解，并展现出优于QAOA和VQE的可扩展性。
Recently, the coherent Ising machine (CIM) as a degenerate optical parametric oscillator (DOPO) network has been researched to solve Ising combinatorial optimization problems. We formulate a theoretical model for the CIM with discrete-time measurement feedback processes, and perform numerical simulations for the simplest network, composed of two degenerate optical parametric oscillator pulses with the anti-ferromagnetic mutual coupling. We evaluate the extent to which quantum coherence exists during the optimization process.
Quantum annealing is a heuristic algorithm for searching the ground state of an Ising model. Heuristic algorithms aim to obtain near-optimal solutions with a reasonable computation time. Accordingly, many algorithms have so far been proposed. In general, the performance of heuristic algorithms strongly depends on the instance of the combinatorial optimization problem to be solved because they escape the local minima in different ways. Therefore, combining several algorithms to exploit their complementary strength is effective for obtaining highly accurate solutions for a wide range of combinat…
Quadratic Formulation of Mutual Information for Sensor Placement Optimization using Ising and Quantum Annealing Machines
针对传感器放置组合优化问题，提出将多元正态分布假设下选定与其余传感器位置间的互信息形式化为QUBO问题，并利用量子退火机求解验证，为大规模传感器优化提供了新方法。
Ising model formulation for highly accurate topological color codes decoding
针对拓扑颜色码解码难度大的问题，提出将解码转化为Ising哈密顿量能量最小化问题并通过模拟退火求解的方法，在多种噪声模型下实现了更高的错误阈值和接近最优的逻辑错误率。
Formulation of the Electric Vehicle Charging and Routing Problem for a Hybrid Quantum-Classical Search Space Reduction Heuristic
本文提出一种利用qudit的混合经典-量子启发式策略，通过缩减搜索空间求解受约束组合优化问题，并以EVCRP为例验证了方法有效性。
We provide Ising formulations for many NP-complete and NP-hard problems, including all of Karp's 21 NP-complete problems. This collects and extends mappings to the Ising model from partitioning, covering and satisfiability. In each case, the required number of spins is at most cubic in the size of the problem. This work may be useful in designing adiabatic quantum optimization algorithms.
Energy Internet Routing using Quantum Optimization Algorithms
针对能源互联网高效路径选择的NP难问题，提出QUBO与伊辛哈密顿量公式化方法，通过9节点和30节点网络案例验证，仿真结果与精确解一致，经典方法运行时短于量子方法，其中量子方法里Simulated Annealing采样器最快。
Floquet-engineered system-reservoir interaction in the transverse field Ising model
本研究提出Floquet工程化的横场Ising模型，利用高频驱动下的参数共振调控自旋相互作用，实现自旋波传播控制与量子开关，可应用于电路QED及量子网络路由。
Quantum Computing, Ising Formulation, and the Traveling Salesman Problem
本文探讨了ising模型与旅行商问题的关系，分析了量子计算方法在解决np难问题中的应用，包括vqe和discrete量子穷举搜索方法，并讨论了其在量子计算中的扩展性。
As a means to solve optimization problems using quantum computers, the problem is typically recast into a Ising spin model whose ground-state is the solution of the optimization problem. An alternative to the Ising formulation is the Lechner-Hauke-Zoller model, which has the form of a lattice gauge model with nearest neighbor 4-body constraints. Here we introduce a method to find the minimal strength of the constraints which are required to conserve the correct ground-state. Based on this, we derive upper and lower bounds for the minimal constraints strengths. We find that depending on the pro…
From Cables to Qubits: A Decomposed Variational Quantum Optimization Pipeline
本文提出一种分解的变分量子优化流程，用于解决电缆路由优化问题，通过将多商品流问题分解为单商品子问题，提升计算效率并实现更灵活的优化方案。
Applying quantum approximate optimization to the heterogeneous vehicle routing problem
研究使用QAOA算法求解异构车辆路径问题，将其映射至Ising哈密顿量并在多达21个量子比特上模拟，发现所需量子比特数随客户数二次增长，且经典优化器在性能与运行时间间存在权衡。
Hierarchical QAOA for the Vehicle Routing Problem via Clustered Decomposition and Local Feasibility Repair
本文提出了一种分层量子近似优化框架，通过聚类分解和局部修复提升大规模车辆路径问题求解效率，使用QAOA算法在12个逻辑量子位上实现高精度解决方案。
Quantum algorithmic solutions to the shortest vector problem on simulated coherent Ising machines
本文利用二次无约束二元优化将最短向量问题映射为量子伊辛模型，在模拟相干伊辛机上求解，展示了三种算法变体的进展。
We propose a new Quadratic Unconstrained Binary Optimization (QUBO) formulation of the Travelling Salesman Problem (TSP), with which we overcame the best formulation of the Vehicle Routing Problem (VRP) in terms of the minimum number of necessary variables. After, we present a detailed study of the constraints subject to the new TSP model and benchmark it with MTZ and native formulations. Finally, we tested whether the correctness of the formulation by entering it into a QUBO problem solver. The solver chosen is a D-Wave\_2000Q6 quantum computer simulator due to the connection between Quantum …
Emergence of Strategic Equilibria from Transverse Field Ising Hamiltonian Dynamics
该研究基于横向场伊辛哈密顿量动力学，提出算子形式的量子博弈研究方法，通过可调纠缠算子解决博弈困境，获得优于经典结果的量子优势，为量子博弈设计提供硬件相关视角。
A promising approach to achieve computational supremacy over the classical von Neumann architecture explores classical and quantum hardware as Ising machines. The minimisation of the Ising Hamiltonian is known to be NP-hard problem for certain interaction matrix classes, yet not all problem instances are equivalently hard to optimise. We propose to identify computationally simple instances with an `optimisation simplicity criterion'. Such optimisation simplicity can be found for a wide range of models from spin glasses to k-regular maximum cut problems. Many optical, photonic, and electronic s…
A reduction scheme for general-order Ising-like Hamiltonians in quantum heuristic solvers
针对伊辛模型求解难问题，将不可分离组概念推广到任意阶伊辛类模型，开发哈密顿量约化框架，通过迭代检测合并受约束自旋组为单变量，在合成超图等数据集上测试并评估其与下游流程集成，为高阶伊辛类优化问题约化奠定基础。
We propose a brand-new formulation of capacitated vehicle routing problem (CVRP) as quadratic unconstrained binary optimization (QUBO). The formulated CVRP is equipped with time-table which describes time-evolution of each vehicle. Therefore, various constraints associated with time are successfully realized. With a similar method, constraints of capacities are also introduced, where capacitated quantities are allowed to increase and decrease according to the cities which vehicles arrive. As a bonus of capacity-qubits, one also obtains a description of state, which allows us to set a variety o…
Quantum-Assisted Vehicle Routing: Realizing QAOA-based Approach on Gate-Based Quantum Computer
本研究提出在基于门的量子计算机上实现QAOA方法解决车辆路径问题，通过量子辅助框架优化路径规划并探讨量子优化在物流中的应用。
On Utility-optimal Entanglement Routing in Quantum Networks
本文提出了一种基于混合整数凸规划的量子网络纠缠路由方法，通过优化路由策略以实现最大网络效用。
Encoding Matters: A Qubit-Efficient Reformulation for Quantum Resilient Routing
该研究针对双链路故障下的延迟弹性路由基准问题，提出感知结构的编码缩减方法，在保留优化任务的同时降低量子比特数量与电路复杂度，使离子阱量子计算机的成功概率提升100倍。
The compression of geometry data is an important aspect of bandwidth-efficient data transfer for distributed 3d computer vision applications. We propose a quantum-enabled lossy 3d point cloud compression pipeline based on the constructive solid geometry (CSG) model representation. Key parts of the pipeline are mapped to NP-complete problems for which an efficient Ising formulation suitable for the execution on a Quantum Annealer exists. We describe existing Ising formulations for the maximum clique search problem and the smallest exact cover problem, both of which are important building blocks…
Cooperative Platoon Routing and Dispatching via Edge-Assisted Hybrid Quantum Optimization
该研究针对网联自动驾驶车辆协同车队路由难题，开发边缘辅助闭环流水线，将问题转化为QUBO模型，经仿真和量子硬件测试，实现18.5%的车队能耗降低，为闭环调度提供可行方案。
Many emerging commercial services are based on the sharing or pooling of resources for common use with the aim of reducing costs. Businesses such as delivery-, mobility-, or transport-as-a-service have become standard in many parts of the world, fulfilling on-demand requests for customers in live settings. However, it is known that many of these problems are NP-hard, and therefore both modeling and solving them accurately is a challenge. Here we focus on one such routing problem, the Ride Pooling Problem (RPP), where multiple customers can request on-demand pickups and drop-offs from shared ve…
An iterative Ising decoder for quantum error correction codes
提出迭代低阶解码(ILOD)算法，通过交替求解X和Z子哈密顿量并利用贝叶斯先验近似交叉关联，将相互作用项的最大体数减半，加速求解器并降低自旋开销，在容错阈值和收敛性上接近或优于联合公式。
Geometric Characteristics of Subproblems in Ising-Machine-Assisted Large Neighborhood Search
研究受限组合优化问题的大规模二次无约束二元优化，通过比较基于当前解车辆路线的LNS-K和基于QUBO变量及约束关系的LNS-Q构建方式，发现子问题设计应考虑多种因素。
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