Synthesis of Quantum Barrel Shifters

A barrel shifter is a common component of high-speed processor, which can realize the displacement operation of the specified number of data word in a single cycle. On the basis of the inverse logic circuit, a displacement device with n inputs and m control bits is proposed, which is denoted as (n, m) shifter, and a set of control inputs that specify how to shift in data between input and output. On the basis of the quantum reversible logic circuits, for synthesizing the barrel shifter, we present the novel method based on the decomposition of the permutation group and some Construction Rules. It only uses (3, 1) shifter and controlled swap gate to quickly synthesize any controlled shifter with low quantum cost, and any (n, k) barrel shifter can be got by cascading the least of k corresponding (n, 1) shifters. The quantum circuit shifters generated by this method can reduce the number of quantum gates, reduce the quantum cost and improve the efficiency of the algorithm, so that all kinds of reversible barrel shifter can be rapidly designed. In this article, we mainly give the ways on qubit left circular shifts, bit permutation and line permutations, and other types of basic shift circuits are also designed.

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