Archimedes Pavlidis, Dimitris Gizopoulos
We present a novel and efficient, in terms of circuit depth, design for Shor's quantum factorization algorithm. The circuit effectively utilizes a diverse set of adders based on the quantum Fourier transform (QFT) to build more complex arithmetic blocks: quantum multiplier/accumulators by constants and quantum dividers by constants. These arithmetic blocks are effectively architected into a generic modular quantum multiplier which is the fundamental block for the modular exponentiation circuit, the most computational intensive part of Shor's algorithm.The proposed modular exponentiation circuit has a depth of about 2000n2 and requires 9n +2 qubits, where n are the bits of the classic number to be factored. A further depth decrease of more than three times can be achieved if we exploit the approximate QFT implementation of each adder unit. Also, the circuit uses almost exclusively two qubit gates which are more suitable for physical implementation.
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http://arxiv.org/abs/1207.0511
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