  While showing great promise, circuit synthesis techniques that combine
numerical optimization with search over circuit structures face scalability
challenges due to a large number of parameters, exponential search spaces, and
complex objective functions. The LEAP algorithm improves scaling across these
dimensions using iterative circuit synthesis, incremental re-optimization,
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 can compile
four qubit unitaries up to $59\times$ faster than QSearch and five and six
qubit unitaries with up to $1.2\times$ fewer CNOTs compared to the QFAST
package. LEAP can reduce the CNOT count by up to $36\times$, or $7\times$ on
average, compared to the CQC Tket compiler. Despite its heuristics, LEAP has
generated optimal circuits for many test cases with a priori known solutions.
The techniques introduced by LEAP are applicable to other
numerical-optimization-based synthesis approaches.
