Alexander Cowtan, Silas Dilkes, Ross Duncan, Alexandre Krajenbrink, Will Simmons, Seyon Sivarajah
We introduce a new architecture-agnostic methodology for mapping abstract quantum circuits to realistic quantum computing devices with restricted qubit connectivity, as implemented by Cambridge Quantum Computing's tket compiler. We present empirical results showing the effectiveness of this method in terms of reducing two-qubit gate depth and two-qubit gate count, compared to other implementations.
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Despite rapid advances in quantum computing technologies, the qubit connectivity limitation remains to be a critical challenge. Both near-term NISQ quantum computers and relatively long-term scalable quantum architectures do not offer full connectivity. As a result, quantum circuits may not be directly executed on quantum hardware, and a quantum compiler needs to perform qubit routing to make the circuit compatible with the device layout. During the qubit routing step, the compiler inserts SWAP gates and performs circuit transformations. Given the connectivity topology of the target hardware, …
This paper addresses the problem of qubit routing in first-generation and other near-term quantum computers. In particular, it is asserted that the qubit routing problem can be formulated as a reinforcement learning (RL) problem, and that this is sufficient, in principle, to discover the optimal qubit routing policy for any given quantum computer architecture. In order to achieve this, it is necessary to alter the conventional RL framework to allow combinatorial action space, and this represents a second contribution of this paper, which is expected to find additional application, beyond the q…
"Qubit routing" refers to the task of modifying quantum circuits so that they satisfy the connectivity constraints of a target quantum computer. This involves inserting SWAP gates into the circuit so that the logical gates only ever occur between adjacent physical qubits. The goal is to minimise the circuit depth added by the SWAP gates. In this paper, we propose a qubit routing procedure that uses a modified version of the deep Q-learning paradigm. The system is able to outperform the qubit routing procedures from two of the most advanced quantum compilers currently available, on both random …
Routing Qubits on Noisy Networks
本文研究了在噪声网络中实现鲁棒量子路由的方法，通过模拟量子漫步者的位置来传输量子比特，并评估了不同噪声环境下路由协议的鲁棒性。
Algorithmic Theory of Qubit Routing
本文从理论计算机科学角度研究量子比特路由问题，证明其在LNN架构下是NP难的，并分别针对双量子比特门数量和每量子比特参与门数限制给出了固定参数算法和多项式时间算法。
Near-term quantum hardware can support two-qubit operations only on the qubits that can interact with each other. Therefore, to execute an arbitrary quantum circuit on the hardware, compilers have to first perform the task of qubit routing, i.e., to transform the quantum circuit either by inserting additional SWAP gates or by reversing existing CNOT gates to satisfy the connectivity constraints of the target topology. We propose a procedure for qubit routing that is architecture agnostic and that outperforms other available routing implementations on various circuit benchmarks. The depth of th…
beSnake: A routing algorithm for scalable spin-qubit architectures
本文提出 beSnake 路由算法，结合 SWAP 与 shuttle 操作及广度优先搜索，以噪声感知方式处理可扩展自旋量子比特架构中的并行路由，在多达 1000 量子比特时显著降低门、深度开销并提升路由速度。
Generating Compilers for Qubit Mapping and Routing
本文提出通过自动编译器生成量子比特映射和路由方案，以提高量子计算资源利用效率和减少计算错误概率。
We develop the work of Christandl et al. [M. Christandl, N. Datta, T. C. Dorlas, A. Ekert, A. Kay, and A. J. Landahl, Phys. Rev. A 71, 032312 (2005)], to show how a d-hypercube homogenous network can be dressed by additional links to perfectly route quantum information between any given input and output nodes in a duration which is independent of the routing chosen and, surprisingly, size of the network.
Line-graph qubit routing: from kagome to heavy-hex and more
针对量子硬件耦合图与算法需求不匹配的问题，提出线图量子比特路由方法，可高效将多种晶格电路映射到重图结构硬件，性能优于现有通用方法，可用于晶格模型量子模拟。
The Swap gate is a ubiquitous tool for moving information on quantum hardware, yet it can be considered a classical operation because it does not entangle product states. Genuinely quantum operations could outperform Swap for the task of permuting qubits within an architecture, which we call routing. We consider quantum routing in two models: (1) allowing arbitrary two-qubit unitaries, or (2) allowing Hamiltonians with norm-bounded interactions. We lower bound the circuit depth or time of quantum routing in terms of spectral properties of graphs representing the architecture interaction constr…
The cost of enabling connectivity in Noisy-Intermediate-Scale-Quantum devices is an important factor in determining computational power. We have created a qubit routing algorithm which enables efficient global connectivity in a previously proposed trapped ion quantum computing architecture. The routing algorithm was characterized by comparison against both a strict lower bound, and a positional swap based routing algorithm. We propose an error model which can be used to estimate the achievable circuit depth and quantum volume of the device as a function of experimental parameters. We use a new…
Spatio-Temporal Characterization of Qubit Routing in Connectivity-Constrained Quantum Processors
针对连接受限量子处理器的量子比特路由通信开销问题，本研究从时空维度表征量子比特移动特性，对比三种拓扑结构，发现方格布局更适合规模化量子计算架构。
Dynamic Qubit Routing with CNOT Circuit Synthesis for Quantum Compilation
本文提出PermRowCol算法，在量子编译中动态重映射逻辑量子比特以路由CNOT门，相比Steiner-Gauss和RowCol减少输出CNOT数量，并可推广至Clifford+T电路及相位多项式综合。
Quantum computer architectures impose restrictions on qubit interactions. We propose efficient circuit transformations that modify a given quantum circuit to fit an architecture, allowing for any initial and final mapping of circuit qubits to architecture qubits. To achieve this, we first consider the qubit movement subproblem and use the routing via matchings framework to prove tighter bounds on parallel routing. In practice, we only need to perform partial permutations, so we generalize routing via matchings to that setting. We give new routing procedures for common architecture graphs and f…
We present methods for implementing arbitrary permutations of qubits under interaction constraints. Our protocols make use of previous methods for rapidly reversing the order of qubits along a path. Given nearest-neighbor interactions on a path of length $n$, we show that there exists a constant $ε\approx 0.034$ such that the quantum routing time is at most $(1-ε)n$, whereas any swap-based protocol needs at least time $n-1$. This represents the first known quantum advantage over swap-based routing methods and also gives improved quantum routing times for realistic architectures such as grids. …
Adaptive Parallelism-Aware Qubit Routing for Ion Trap QCCD Architectures
本文提出一种自适应并行意识量子比特路由策略，通过可配置多参数评分机制优化离子运输效率，提升量子处理器的执行保真度。
Qubit efficient quantum algorithms for the vehicle routing problem on NISQ processors
本文提出一种量子比特高效编码方案，将大规模VRPTW问题压缩到更少量子比特上，并在多种NISQ硬件上验证其近似求解效果与完整编码相当，为行业优化问题提供了可行路径。
Divide-et-impera Heuristic-based Randomized Search for the Qubit Routing Problem
针对量子比特路由问题，提出DIRSH算法，采用分治启发式随机搜索策略，结合块分解、老虎机参数自适应调整及局部剪枝，在IBMQ Tokyo拓扑的RevLib基准测试中优于LightSABRE变体，提升量子电路路由性能。
Due to the short decohorence time of qubits available in the NISQ-era, it is essential to pack (minimize the size and or the depth of) a logical quantum circuit as efficiently as possible given a sparsely coupled physical architecture. In this work we introduce a locality-aware qubit routing algorithm based on a graph theoretic framework. Our algorithm is designed for the grid and certain "grid-like" architectures. We experimentally show the competitiveness of algorithm by comparing it against the approximate token swapping algorithm, which is used as a primitive in many state-of-the-art quant…
Qubit Routing for (Almost) Free
本文证明了合成n个量子比特相位多项式所需CNOT门数的下界和上界，并探讨了在受限硬件下通过量子比特路由减少CNOT门数的方法，提出无需路由时的路由开销为常数。
Gate teleportation-assisted routing for quantum algorithms
针对 SWAP 路由导致电路深度增加的问题，本文提出利用空闲辅助量子比特构建门隐形传态路径，并设计连接选择算法，在重六边形等基准上实现 10–25% 的深度降低。
Improving Qubit Routing by Using Entanglement Mediated Remote Gates
本研究提出利用EPR介导的远程门优化量子比特路由，通过高效编译器减少编译电路的门数和深度。
Routing Techniques for Error-Corrected Silicon Spin Qubit Quantum Architectures
研究硅自旋量子比特编译难题，基于平面上的蛇模型引入编译框架，提出最短路径和基于旋转的算法等，评估显示最短路径方法在稀疏场景优，基于旋转的方法在高密度环境好，实现开源。
Unifying Qubit Routing Across Diverse Quantum ISAs via Canonical Representation
本文提出Canopus框架，通过规范表示和单调多面体理论，统一不同量子指令集架构中的量子路由，减少路由开销15%-35%。
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。
Scaling Qubit Mapping and Routing With Position Graph Abstraction and Memoization
本文提出基于位置图抽象与记忆化的量子比特映射与路由方法，通过缓存启发式移动评估和记忆化拥堵解决，提升TI-QCCD架构的可扩展性。
Improved Qubit Routing for QAOA Circuits
我们提出一种两步式量子比特路由算法，基于Vizing定理和贪婪SWAP门应用，平衡电路深度与SWAP门数量，在QAOA电路上优于现有最先进方法。
Parallel Token Swapping for Qubit Routing
本文提出了一种常数因子近似算法，用于解决量子比特路由中的并行令牌交换问题，并研究了其下界及着色版本。
We show a perfect state transfer of an arbitrary unknown two-qubit state can be achieved via a discrete-time quantum walk with various settings of coin flippings, and extend this method to distribution of an arbitrary unknown multi-qubit entangled state between every pair of sites in the multi-dimensional network. Furthermore, we study the routing of quantum information on this network in a quantum walk architecture, which can be used as quantum information processors to communicate between separated qubits.
SWAP-Network Routing and Spectral Qubit Ordering for MPS Imaginary-Time Optimization
提出一种受量子启发的MPS虚拟时间演化求解器，通过结构化SWAP网络与谱量子比特映射引入非局部耦合，在MaxCut与180量子比特投资组合优化中显著降低误差并增强纠缠。
We consider the problem of mapping a logical quantum circuit onto a given hardware with limited two-qubit connectivity. We model this problem as an integer linear program, using a network flow formulation with binary variables that includes the initial allocation of qubits and their routing. We consider several cost functions: an approximation of the fidelity of the circuit, its total depth, and a measure of cross-talk, all of which can be incorporated in the model. Numerical experiments on synthetic data and different hardware topologies indicate that the error rate and depth can be optimized…
Constraint programming models for depth-optimal qubit assignment and SWAP-based routing
针对量子比特分配与路由问题，提出约束规划（CP）模型，经随机实例验证，在线性和二维网格拓扑下的电路深度最小化任务中，其求解质量与运行时间均优于现有整数线性规划（ILP）模型。
Controlling and swapping quantum information in a quantum coherent way between the microwave and optical regimes is essential for building long-range superconducting quantum networks but extremely challenging. We propose a hybrid quantum interface between the microwave and optical domains where the propagation of a single-photon pulse along a nanowaveguide is controlled in a coherent way by tuning electromagnetically induced transparency window with the quantum state of a flux qubit. The qubit can route a single-photon pulse with a single spin in nanodiamond into a quantum superposition of pat…
We demonstrate experimentally the creation and measurement of an entangled state between a microscopic two level system and a macroscopic superconducting resonator where their indirect interaction is mediated by an artificial atom, a superconducting persistent current qubit (PCQB). We show that the microscopic two level system, formed by a defect in an oxide layer, exhibits an order of magnitude longer dephasing time than the PCQB, while the dephasing time of the entangled states between the microscopic two level system and macroscopic superconducting resonator is significantly longer than the…
Optimal, Qubit-Efficient Quantum Vehicle Routing via Colored-Permutations
本文提出一种全局位置彩色排列编码，用于解决具有容量限制的车辆路径问题，通过K辆车辆选择不相交的排列，形成完整的n×n排列矩阵，以高效利用量子资源，减少逻辑量子比特成本。
Near-term quantum computers will operate in a noisy environment, without error correction. A critical problem for near-term quantum computing is laying out a logical circuit onto a physical device with limited connectivity between qubits. This is known as the qubit mapping and routing (QMR) problem, an intractable combinatorial problem. It is important to solve QMR as optimally as possible to reduce the amount of added noise, which may render a quantum computation useless. In this paper, we present a novel approach for optimally solving the QMR problem via a reduction to maximum satisfiability…
We propose a hypercube switching architecture for the perfect state transfer (PST) where we prove that it is always possible to find an induced hypercube in any given hypercube of any dimension such that PST can be performed between any two given vertices of the original hypercube. We then generalise this switching scheme over arbitrary number of qubits where also this routing feature of PST between any two vertices is possible. It is shown that this is optimal and scalable architecture for quantum computing with the feature of routing. This allows for a scalable and growing network of qubits.…
DPRQ: A Dynamic Programming-based Qubit Routing Algorithm for Collective Communication in Distributed Quantum Computing
针对分布式量子计算节点间通信的瓶颈问题，提出基于动态规划的DPRQ量子比特路由算法，经实验验证其相较QuComm可显著减少节点间通信量。
Low-depth fermion routing without ancillas
针对Jordan-Wigner编码下费米子模拟的路由开销问题，提出无辅助量子比特的O(log²N)深度费米子路由方案，并推广至所有保乘积三元树费米子编码，同时给出受限连接设备的路由上界。
QAP-Router: Tackling Qubit Routing as Dynamic Quadratic Assignment with Reinforcement Learning
本文提出QAP-Router，将量子比特路由建模为动态二次分配问题，利用强化学习解决路由决策，通过Transformer架构和前瞻机制优化交互距离耦合，实验表明其显著降低CNOT门数量。
Improving Quantum Computation by Optimized Qubit Routing
本研究提出一种将量子比特路由分解为分配子问题和令牌交换问题的优化方法，通过二进制规划与分支定界算法，显著减少门数量和电路深度，提升量子算法在真实硬件上的解质量。
Preparing problems for execution on quantum computers can require many compilation steps. Automated compilation software is useful not only for easier and faster problem execution, but also for facilitating the comparison between different algorithmic choices. Here we describe mat2qubit, a Python package for encoding several classes of classical and quantum problems into qubit representations. It is intended for use especially on Hamiltonians and functions defined over variables (e.g. particles) with cardinality larger than 2. More specifically, mat2qubit may be used to compile bosonic, phonon…
Optimized Qubit Routing for Commuting Gates via Integer Programming
针对交换门的量子比特路由问题，提出基于整数规划的两步分解方法，保证最优解并优于现有启发式和精确方法。
Routing quantum information among different nodes in a network is a fundamental prerequisite for a quantum internet. While single-qubit routing has been largely addressed, many-qubit routing protocols have not been intensively investigated so far. Building on the many-excitation transfer protocol in arXiv:1911.12211, we apply the perturbative transfer scheme to a two-excitation routing protocol on a network where multiple two-receivers block are coupled to a linear chain. We address both the case of switchable and permanent couplings between the receivers and the chain. We find that the protoc…
Implementation of a quantum addressable router using superconducting qubits
本研究利用固定频率transmon量子比特，基于两个原生c-iSWAP门和强ZZ相互作用实现了兼具量子信号路由与寻址功能的Q2-router，测得平均路由保真度95.3%，并完成了全面校准表征，为量子网络和量子随机存取存储器构建提供了关键支撑。
Improving and benchmarking NISQ qubit routers
本文针对NISQ量子计算机中量子比特路由问题，提出基于SABRE算法的新路由方法，并在不同连通性下进行基准测试，实现大型器件平均电路保真度最高84%的提升。
A quantum network promises to enable long distance quantum communication, and assemble small quantum devices into a large quantum computing cluster. Each network node can thereby be seen as a small few qubit quantum computer. Qubits can be sent over direct physical links connecting nearby quantum nodes, or by means of teleportation over pre-established entanglement amongst distant network nodes. Such pre-shared entanglement effectively forms a shortcut - a virtual quantum link - which can be used exactly once. Here, we present an abstraction of a quantum network that allows ideas from computer…
Co-Designed Superconducting Architecture for Lattice Surgery of Surface Codes with Quantum Interface Routing Card
本文提出超导量子接口路由卡 QuIRC，通过多芯片分布式架构优化表面码格点手术中的芯片间门、网络冲突和路由硬件成本，显著减小辅助量子比特补丁和层转译尺寸。
Non-Hermitian unidirectional routing of photonic qubits
该研究利用多能级中性冷原子同时介导相干与耗散耦合，通过场螺旋度调控实现兼具光子量子比特单向路由和自旋波二极管功能的非厄米系统，并获得高保真、高隔离、低损耗的实验结果。
Quantum Compiler Design for Qubit Mapping and Routing: A Cross-Architectural Survey of Superconducting, Trapped-Ion, and Neutral Atom Systems
本综述系统分类了超导、离子阱和中性原子平台上的量子比特映射与路由方法，分析硬件感知编译器的优化目标，并总结挑战与未来研究方向。
A simple universal routing strategy for reducing the connectivity requirements of quantum LDPC codes
针对量子 LDPC 码硬件实现所需的密集长程连接问题，提出利用辅助量子比特短回路路由数据信息的通用策略，以约一倍电路深度换取最高 50% 长程连接削减且基本保持电路级距离。
Solving Large-Scale Vehicle Routing Problems with Hybrid Quantum-Classical Decomposition
该研究提出两级分解策略，通过问题级分解将大规模VRP划分为小TSP实例，再经电路级分解适配近量子设备，大幅减少量子资源需求，验证了在标准与新型编码上的可行性，为量子解决复杂VRP提供早期证据。
Quantum router is an essential ingredient in a quantum network. Here, we propose a new quantum circuit for designing quantum router by using IBM's five-qubit quantum computer. We design an equivalent quantum circuit, by the means of single-qubit and two-qubit quantum gates, which can perform the operation of a quantum router. Here, we show the routing of signal information in two different paths (two signal qubits) which is directed by a control qubit. According to the process of routing, the signal information is found to be in a coherent superposition of two paths. We demonstrate the quantum…
A doubly stochastic matrices-based approach to optimal qubit routing
本文提出基于双随机矩阵的平滑约束优化方法解决量子比特路由问题，将离散SWAP门放置转化为Birkhoff多面体上的连续优化，实验表明相比SABRE算法可显著降低电路深度。
Graph Reinforcement Learning for Calibration-Aware Quantum Circuit Routing
提出一种利用图强化学习进行校准感知的量子电路路由方法，通过IBM Heron r2校准数据选择SWAP操作，在MQT Bench电路上平均保真度达0.727，优于SABRE-best20的0.440。
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。
XGSwap: eXtreme Gradient boosting Swap for Routing in NISQ Devices
针对 NISQ 设备有限连接性导致的长程纠缠保真度低的问题，提出基于梯度提升的机器学习模型预测替代路由路径保真度，在 127 量子比特硬件上约 23% 的测试中成功识别出更高保真度的路径。
Robust Qubit Mapping Algorithm via Double-Source Optimal Routing on Large Quantum Circuits
提出Duostra算法，通过双源最优路由和启发式调度，在大规模量子电路上实现高效量子比特映射，平均降低映射成本21.75%，优于现有方法。
Full Characterization of the Depth Overhead for Quantum Circuit Compilation with Arbitrary Qubit Connectivity Constraint
本文用约束图的路由数完整刻画了量子电路编译中由量子比特连通性约束引起的深度开销，并通过图间归约算法为常见连通性图给出了渐近最优编译。
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