In the era of noisy intermediate-scale quantum (NISQ) computing, the limited connectivity between qubits is one of the common physical limitations faced by current quantum computing devices. Quantum circuit mapping methods transform quantum circuits into equivalent circuits that satisfy physical connectivity constraints by remapping logical qubits, making them executable. The optimization problem of quantum circuit mapping has NP-hard computational complexity, and existing heuristic mapping algorithms still have significant potential for optimization in terms of the number of quantum gates generated. To reduce the number of SWAP gates inserted during mapping, the solution space of the mapping problem is represented as a tree structure, and the mapping process is equivalent to traversing this tree structure. To effectively and efficiently complete the search process, a beam search framework (BSF) is proposed for solving quantum circuit mapping. By iteratively selecting, expanding, and making decisions, high-quality target circuits are generated. Experimental results show that this method can significantly reduce the number of inserted SWAP gates on medium to large circuits, achieving an average reduction of 44% compared to baseline methods, and is applicable to circuits of various sizes and complexities.
In the era of noisy intermediate-scale quantum (NISQ) computing, the limited connectivity between qubits is one of the common physical limitations faced by current quantum computing devices. Quantum circuit mapping methods transform quantum circuits into equivalent circuits that satisfy physical connectivity constraints by remapping logical qubits, making them executable. The optimization problem of quantum circuit mapping has NP-hard computational complexity, and existing heuristic mapping algorithms still have significant potential for optimization in terms of the number of quantum gates generated. To reduce the number of SWAP gates inserted during mapping, the solution space of the mapping problem is represented as a tree structure, and the mapping process is equivalent to traversing this tree structure. To effectively and efficiently complete the search process, a beam search framework (BSF) is proposed for solving quantum circuit mapping. By iteratively selecting, expanding, and making decisions, high-quality target circuits are generated. Experimental results show that this method can significantly reduce the number of inserted SWAP gates on medium to large circuits, achieving an average reduction of 44% compared to baseline methods, and is applicable to circuits of various sizes and complexities.
The qubit mapping approach serves to transform a quantum logical circuit (LC) into a physical one that satisfies the connectivity constraints imposed by the noisy intermediate-scale quantum (NISQ) devices. The quality of the physical circuit generated by a mapping approach depends largely on the initial mapping, which specifies the correspondence between the qubits in the LC and the qubits on the NISQ device. There are a total ofn!different initial mappings for a qubit mapping problem withnqubits, and among them, there is at least one initial mapping corresponding to the smallest physical circuit that this mapping approach can output. Finding such an initial mapping is very important for reliable computations on the NISQ device. To this end, we propose an iterated local search framework as well as a heuristic circuit mapper. In this framework, we perform multiple local searches on the space of initial mappings, and during each local search, several promising neighborhoods of the current initial mapping are generated and evaluated by invoking the circuit mapper in a forward or a backward manner. This framework provides a way for the qubit mapping approach to find the best physical circuit that it can produce, allowing it to trade time for circuit quality, which is necessary in the NISQ era. The experimental results demonstrate the stability, scalability, and effectiveness of this approach in reducing the number of additional gates. Moreover, although this approach is a multipass circuit mapping process, it can generate a good-quality physical circuit within half an hour, even for the circuit with more than 10 000 gates.
In Noisy Intermediate-Scale Quantum (NISQ) era, quantum processing units (QPUs) suffer from, among others, highly limited connectivity between physical qubits. To make a quantum circuit executable, a circuit transformation process is necessary to transform it into a functionally equivalent one so that the connectivity constraints imposed by the QPU are satisfied. Due to the high branching factor and vast search space, almost all existing algorithms search very shallowly and thus, very often, can reach (at most) locally optimal solutions. We propose a Monte Carlo Tree Search framework to tackle this problem, which enables the search process to go deeper. In particular, we design, by taking both short- and long-term rewards into consideration, a scoring mechanism, and propose to use a fast random strategy for simulation. The thus designed search algorithm is polynomial in all relevant parameters and empirical results on extensive realistic circuits show that it can reduce, in average, the size of the output circuits by at least 30% when compared with the state-of-the-art algorithms on IBM Q20.
Quantum computing is currently in the era of Noisy-Intermediate-Scale Quantum (NISQ), where superconducting quantum chips can only support two-qubit gates between adjacent physical qubits. This constraint necessitates the insertion of SWAP gates during circuit mapping to ensure that the nearest neighbor requirements are met on actual quantum computing devices. In this work, based on the circuit partitioning and unitary matrix decomposition mechanism, an equivalent transformation form of quantum circuit is given to reduce the number of two-qubit gates in the target quantum circuit. Experimental results demonstrate that the decomposed equivalent circuits have a shorter depth, with an average optimization rate of 18.41%. Our proposed optimization method effectively reduces the number of two-qubit gates in quantum circuits, enhancing the efficiency of mapping on NISQ devices.
In Noisy Intermediate-Scale Quantum (NISQ) era, quantum processing units (QPUs) suffer from, among others, highly limited connectivity between physical qubits. To make a quantum circuit effectively executable, a circuit transformation process is necessary to transform it, with overhead cost the smaller the better, into a functionally equivalent one so that the connectivity constraints imposed by the QPU are satisfied. While several algorithms have been proposed for this goal, the overhead costs are often very high, which degenerates the fidelity of the obtained circuits sharply. One major reason for this lies in that, due to the high branching factor and vast search space, almost all these algorithms only search very shallowly and thus, very often, only (at most) locally optimal solutions can be reached. In this paper, we propose a Monte Carlo Tree Search (MCTS) framework to tackle the circuit transformation problem, which enables the search process to go much deeper. The general framework supports implementations aiming to reduce either the size or depth of the output circuit through introducing SWAP or remote CNOT gates. The algorithms, called MCTS-Size and MCTS-Depth, are polynomial in all relevant parameters. Empirical results on extensive realistic circuits and IBM Q Tokyo show that the MCTS-based algorithms can reduce the size (depth, resp.) overhead by, on average, 66% (84%, resp.) when compared with tket, an industrial level compiler.
In recent years, the emergence of the Noisy Intermediate-Scale Quantum (NISQ) era has led to the development of a wide variety of quantum devices, marking a dynamic phase in the field of quantum computing. Despite these advancements, practical applications of quantum computers still face significant challenges, one of the most prominent being the limited connectivity between physical quantum bits (qubits). This limitation requires quantum circuits to be recompiled through layout synthesis before they can be executed on quantum devices. Layout synthesis determines the specific placement of quantum gates within the circuit on the physical hardware. When gates do not align with the connectivity constraints of the device, additional quantum gates must be inserted to remap the qubits, which can negatively affect the circuit’s efficiency and performance. To address this issue, the primary goal of this paper is to enhance the mapping process within layout synthesis, aiming to optimize both the layout and the circuit depth. Experimental results demonstrate that the proposed method effectively reduces the quantum circuit depth, outperforming other existing approaches in terms of efficiency.
Quantum algorithm design usually assumes access to a perfect quantum computer with ideal properties like full connectivity, noise-freedom, and arbitrarily long coherence time. In noisy intermediate-scale quantum (NISQ) devices, however, the number of qubits is highly limited and quantum operation error and qubit coherence are not negligible. Besides, the connectivity of physical qubits in a quantum processing unit (QPU) is also strictly constrained. Thereby, additional operations like SWAP gates have to be inserted to satisfy this constraint while preserving the functionality of the original circuit. This process is known as quantum circuit transformation. Adding additional gates will increase both the size and depth of a quantum circuit and, therefore, cause further decay of the performance of a quantum circuit. Thus, it is crucial to minimize the number of added gates. In this article, we propose an efficient method to solve this problem. We first choose by using simulated annealing an initial mapping which fits well with the input circuit and then, with the help of a heuristic cost function, stepwise apply the best-selected SWAP gates until all quantum gates in the circuit can be executed. Our algorithm runs in time polynomial in all parameters, including the size and the qubit number of the input circuit, and the qubit number in the QPU. Its space complexity is quadratic to the number of edges in the QPU. The experimental results on extensive realistic circuits confirm that the proposed method is efficient and the number of added gates of our algorithm is, on average, only 57% of that of state-of-the-art algorithms on IBM Q20 (Tokyo), the most recent IBM quantum device.