Utilizing Numerical Instantiation to Enable Circuit Resizing

Mid-circuit measurement and reset (MMR) is a combination of primitive operations that various quantum technologies manufacturers have integrated into their platforms, including superconducting, trapped-ion, and neutral-atom-based quantum hardware vendors. MMR's original purpose was to implement quantum error correcting codes, but it has also enabled new circuit optimization approaches in the NISQ-era. These approaches optimize a circuit by reducing their required number of qubits in a technique called circuit resizing, allowing users to execute larger programs on cheaper, smaller quantum chips with potentially fewer gates. Not all circuits are resizable; previous algorithms can only resize circuits when they satisfy certain gate dependence relationships, severely restricting the potential set of programs that can benefit from this optimization. This work introduces a numerical-instantiation-based resynthesis algorithm that restructures non-resizable circuits into resizable ones. Our algorithm is resource-efficient and topology-aware, removing the need for expensive mapping and increasing the potential for optimization. We reduce the number of qubits by 21.4% in otherwise un-resizable circuits. When compiling to linear and T topologies, we show a CNOT gate reduction of 34.9% and 48.5%, respectively, compared against state-of-the-art compilation pipelines.