Exploring Affine Abstractions for Qubit Mapping

One of the key compilation steps in Quantum Computing (QC) is to determine an initial logical to physical mapping of the qubits used in a quantum circuit. The impact of the starting qubit layout can vastly affect later scheduling and placement decisions of QASM operations, yielding higher values on critical performance metrics (gate count and circuit depth) as a result of a quantum compilers introducing communication operations to meet the underlying physical neighboring and connectivity constraints of the quantum device.We present our ongoing work on qubit mapping with affine abstractions, which aims to compute effective initial qubit layouts. The key assumption is that the quantum program is represented in an affine representation, a property which permits us to apply aggressive program analyses to determine the potential of sharing qubit accesses among groups of quantum operations prescribed by linear and affine relations. We present preliminary results demonstrating the effectiveness of our novel approach on 69 quantum circuits, while using the QISKIT compiler on IBM Tokyo and Google Sycamore, obtaining between 16% and 21% average improvement on circuit depth and 24%–47% improvement on the number of added gates.