While showing great promise, circuit synthesis techniques that combine numerical optimization with search over circuit structures face scalability challenges due to large number of parameters, exponential search spaces, and complex objective functions. The LEAP algorithm improves scaling across these dimensions using iterative circuit synthesis, incremental reoptimization, dimensionality reduction, and improved numerical optimization. LEAP draws on the design of the optimal synthesis algorithm QSearch by extending it with an incremental approach to determine constant prefix solutions for a circuit. By narrowing the search space, LEAP improves scalability from four to six qubit circuits. LEAP was evaluated with known quantum circuits such as QFT and physical simulation circuits like the VQE, TFIM and QITE. LEAP is able to compile four qubit unitaries up to $59times$ faster than QSearch and five and six qubit unitaries with up to $1.2times$ fewer CNOTs compared to the advanced QFAST package. LEAP is able to reduce the CNOT count by up to $48times$, or $11times$ on average, compared to the IBM Qiskit compiler. Although employing heuristics, LEAP has generated optimal depth circuits for all test cases where a solution is known a priori. The techniques introduced by LEAP are applicable to other numerical optimization based synthesis approaches.
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