We provide evidence that commonly held intuitions when designing quantum circuits can be misleading. In particular we show that: a) reducing the T-count can increase the total depth; b) it may be beneficial to trade CNOTs for measurements in NISQ circuits; c) measurement-based uncomputation of relative phase Toffoli ancillae can make up to 30\% of a circuit's depth; d) area and volume cost metrics can misreport the resource analysis. Our findings assume that qubits are and will remain a very scarce resource. The results are applicable for both NISQ and QECC protected circuits. Our method uses multiple ways of decomposing Toffoli gates into Clifford+T gates. We illustrate our method on addition and multiplication circuits using ripple-carry. As a byproduct result we show systematically that for a practically significant range of circuit widths, ripple-carry addition circuits are more resource efficient than the carry-lookahead addition ones. The methods and circuits were implemented in the open-source QUANTIFY software.

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关于量子算术电路的现实最坏情况分析

我们提供的证据表明，设计量子电路时通常持有的直觉可能会产生误导。特别地，我们表明：a）减少T数可以增加总深度；b）交易CNOT以在NISQ电路中进行测量可能是有益的；c）基于测量的相对相Toffoli辅助词的计算可能占电路深度的30％；d）面积和体积成本指标可能会误报资源分析。我们的发现假设量子位是并且将仍然是非常稀缺的资源。结果适用于NISQ和QECC保护的电路。我们的方法使用多种方法将Toffoli门分解为Clifford + T门。我们说明了使用脉动进位的加法和乘法电路的方法。作为副产品的结果，我们系统地表明，在实际上很大的电路宽度范围内，纹波进位加法电路比超前进位加法电路更节省资源。该方法和电路在开源QUANTIFY软件中实现。