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.