  One of the challenges in quantum computing is the synthesis of unitary
operators into quantum circuits with polylogarithmic gate complexity. Exact
synthesis of generic unitaries requires an exponential number of gates in
general. We propose a novel approximate quantum circuit synthesis technique by
relaxing the unitary constraints and interchanging them for ancilla qubits via
block-encodings. This approach combines smaller block-encodings, which are
easier to synthesize, into quantum circuits for larger operators. Due to the
use of block-encodings, our technique is not limited to unitary operators and
can also be applied for the synthesis of arbitrary operators. We show that
operators which can be approximated by a canonical polyadic expression with a
polylogarithmic number of terms can be synthesized with polylogarithmic gate
complexity with respect to the matrix dimension.
