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Integer Arithmetic With Hybrid Quantum-Classical Circuits

Quantum circuits which perform integer arithmetic could potentially outperform their classical counterparts. In this paper, a quantum circuit is considered which performs a specific computational pattern on classically represented integers to accelerate the computation. Such a hybrid circuit could be embedded in a conventional computer architecture as a quantum device or accelerator. In particular, a quantum multiply-add circuit (QMAC) using a Quantum Fourier Transform (QFT) is proposed which can perform the calculation on conventional integers faster than its conventional counterpart. Whereas classically applying a multiply-adder (MAC) $n$ times to $k$ bit integers would require $O(n \log k)$ parallel steps, the hybrid QMAC needs only $O(n + k)$ steps for the exact result and $O(n + \log k)$ steps for an approximate result.