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We provide evidence that commonly held intuitions when designing quantumcircuits can be misleading. In particular we show that: a) reducing the T-countcan increase the total depth; b) it may be beneficial to trade CNOTs formeasurements in NISQ circuits; c) measurement-based uncomputation of relativephase Toffoli ancillae can make up to 30\% of a circuit's depth; d) area andvolume cost metrics can misreport the resource analysis. Our findings assumethat qubits are and will remain a very scarce resource. The results areapplicable for both NISQ and QECC protected circuits. Our method uses multipleways of decomposing Toffoli gates into Clifford+T gates. We illustrate ourmethod on addition and multiplication circuits using ripple-carry. As abyproduct result we show systematically that for a practically significantrange of circuit widths, ripple-carry addition circuits are more resourceefficient than the carry-lookahead addition ones. The methods and circuits wereimplemented in the open-source QUANTIFY software.

On the realistic worst case analysis of quantum arithmetic circuits