String 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 quantum
compilers introducing SWAP operations to meet the underlying physical
neighboring and connectivity constraints of the quantum device.
  In this paper we introduce a novel qubit mapping approach, string-based qubit
mapping. The key insight is to prioritize the mapping of logical qubits that
appear in longest repeating non-overlapping substrings of qubit pairs accessed.
This mapping method is complemented by allocating qubits according to their
global frequency usage. We evaluate and compare our new mapping scheme against
two quantum compilers (QISKIT and TKET) and two device topologies, the IBM
Manhattan (65 qubits) and the IBM Kolkata (27 qubits). Our results demonstrate
that combining both mapping mechanisms often achieve better results than either
one individually, allowing us to best QISKIT and TKET baselines, yielding
between 13% and 17% average improvement in several group sizes, up to 32%
circuit depth reduction and 63% gate volume improvement.
Blake Gerard Martin Kong