Optimal Quantum Circuit Mapping

Toshinari Itoko, Rudy Raymond, Takashi Imamichi +1 more

賢太 海老澤, 1477, Kenta Ebisawa

Lalengmawia Chhangte, Alok Chakrabarty

Tom Peham, Lukas Burgholzer, Robert Wille

Compiling a high-level quantum circuit down to a low-level description that can be executed on state-of-the-art quantum computers is a crucial part of the software stack for quantum computing. One step in compiling a quantum circuit to some device is quantum circuit mapping, where the circuit is transformed such that it complies with the architecture’s limited qubit connectivity. Because the search space in quantum circuit mapping grows exponentially in the number of qubits, it is desirable to consider as few of the device’s physical qubits as possible in the process. Previous work conjectured that it suffices to consider only subarchitectures of a quantum computer composed of as many qubits as used in the circuit. In this work, we refute this conjecture and establish criteria for judging whether considering larger parts of the architecture might yield better solutions to the mapping problem. We show that determining subarchitectures that are of minimal size, i.e., from which no physical qubit can be removed without losing the optimal mapping solution for some quantum circuit, is a very hard problem. Based on a relaxation of the criteria for optimality, we introduce a relaxed consideration that still maintains optimality for practically relevant quantum circuits. Eventually, this results in two methods for computing near-optimal sets of subarchitectures—providing the basis for efficient quantum circuit mapping solutions. We demonstrate the benefits of this novel method for state-of-the-art quantum computers by IBM, Google, and Rigetti.

Omid Daei, Keivan Navi, Mariam Zomorodi Moghadam

Cheng Qiu, Pengcheng Zhu, Lihua Wei

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.