LEAP: Scaling Numerical Optimization Based Synthesis Using an Incremental Approach

Synthesis provides a valuable tool for quantum circuit optimization.The best techniques combine numerical optimization with search over structures, but face scalability challenges due to: 1) large number of of parameters; 2) exponential search space; and 3) complex objective function.
The LEAP compiler scales synthesis along these dimensions using an incremental approach, where it iteratively determines stable prefix solutions for a circuit, which are then removed. LEAP explores:
1) heuristics to bind parameters and circuit structure; 2) rnumerical optimization using multi-start; and 3) incremental re-optimization.

Our baseline is the optimal depth QSearch algorithm which successfully handles circuits up to 4 qubits.
LEAP is able to compile 4 qubit unitaries up to 59x faster than QSearch and 5 and 6 qubit unitaries with up to 14x fewer CNOTS compared to the QFAST state-of-the art package. Workload includes known quantum circuits such as QFT and physical simulation circuits such as the VQE, TFIM and Qite. LEAP is able to reduce the CNOT count by up to 48x, or 11x on average when compared with the IBM Qiskit and T|ket compilers.

LEAP has been released as part of the BQSkit (Berkeley Quantum Synthesis Toolkit) infrastructure and it is integrated into IBM Qiskit.