  We demonstrate a technique for optimizing quantum circuits that is analogous
to classical windowing. Specifically, we show that small table lookups can
allow control qubits to be iterated in groups instead of individually. We
present various windowed quantum arithmetic circuits, including a windowed
modular exponentiation with nested windowed modular multiplications, which have
lower Toffoli counts than previous work at register sizes ranging from tens of
qubits to thousands of qubits.
