  We introduce a domain-specific algorithm for numerical optimization
operations used by quantum circuit instantiation, synthesis, and compilation
methods. QFactor uses a tensor network formulation together with analytic
methods and an iterative local optimization algorithm to reduce the number of
problem parameters. Besides tailoring the optimization process, the formulation
is amenable to portable parallelization across CPU and GPU architectures, which
is usually challenging in general purpose optimizers (GPO). Compared with
several GPOs, our algorithm achieves exponential memory and performance savings
with similar optimization success rates. While GPOs can handle directly
circuits of up to six qubits, QFactor can process circuits with more than 12
qubits. Within the BQSKit optimization framework, we enable optimizations of
100+ qubit circuits using gate deletion algorithms to scale out linearly with
the hardware resources allocated for compilation in GPU environments.
