Compression of Qubit Circuits: Mapping to Mixed-Dimensional Quantum Systems

Quantum computers are becoming a reality thanks to the accomplishments made in recent years. The quantum computers available today offer hundreds of qubits but are still limited in the number of operations they can perform before errors accumulate and the quantum state decays. In regard to the error accumulation, non-local operations such as CX or CZ are main contributors. One promising solution to reduce the number of required non-local operations is to make a more efficient use of the quantum hardware by exploiting the inherent high-dimensional capabilities of quantum systems. In a process called circuit compression, non-local operations between qubits are mapped to local operations in qudits, i.e., higher-dimensional systems. In this work, we present a strategy for enabling quantum circuit compression with the aim of mapping clusters of qubits in a given circuit to the mixed-dimensional qudits of the target hardware. Further, we discuss the principles of circuit compression as well as the physical structure of qubits and qudits, before introducing a new representation that captures the essence of quantum operations, affecting the different logical levels in the quantum states in nodes and edges of a graph. Based on this, we propose an automated approach for mapping qubit circuits of arbitrary gate sets to mixed-dimensional quantum systems, lowering the number of non-local operations. Empirical evaluations confirm the effectiveness of the proposed approach reducing the number of non-local operations by up to 50% for almost half of the cases. Finally, the corresponding source code is available freely at github.com/cda-tdum/qudit-compression.