Exploiting the Benefits of Clean Ancilla Based Toffoli Gate Decomposition Across Architectures

Abstract

Elementary gate decomposition of larger Toffoli operations is often carried out using additional qubits (ancilla). The number of gates and the circuit depth vary in such transformation depending on the type of ancilla used (clean or dirty). The present Noisy Intermediate Scale Quantum (NISQ) devices have limited number of coherent qubits with faulty native operation support. Superconducting devices also have coupling restrictions or Nearest-Neighbor (NN) constraints, which require additional gates to map the transformed netlist for execution. While the mapping overhead is correlated with the number of 2-qubit gates and involved qubits, the fidelity of execution is inversely proportional to the number of gates and circuit depth. There is a tradeoff in devising the transpilation (i.e. low-level transformation and mapping) approach — dirty ancilla demands less qubits and overhead at the expense of more gates and depth as compared to clean ancilla, which involves less gates and depth at the expense of more qubits and overhead. This paper analyzes the disparity in gates, depth and qubits between: (i) the low-level transformation approaches without considering device coupling information, and (ii) the mapping schemes based on netlist transformation using a specific type of ancilla. We analyze the benefits of using NN-constraints at the transformation stage, and the impact of distributing clean ancilla across architectures. We have carried out experiments on IBM Q20 and Hexagonal Q20 architectures, which show improvements of 17% and 13% respectively in terms of number of gates.