Abstract
We consider decomposition for a controlled-Rn gate with a standard set of universal gates. For this problem, a method exists that uses a single ancillary qubit to reduce the number of gates. In this work, we extend this method to three ends. First, we find a method that can decompose into fewer gates than the best known results in decomposition of controlled-Rn. We also confirm that the proposed method reduces the total number of gates of the quantum Fourier transform. Second, we propose another efficient decomposition that can be mapped to a nearest-neighbor architecture with only local CNOT gates. Finally, we find a method that can minimize the depth to 5 gate steps in a nearest-neighbor architecture with only local CNOT gates.
Highlights
Approximation of Rn gate.An Rn gate is defined as follows: Rn = 10 0 e iπ/2n −1 (1)The R2 gate is an S gate, and the R3 gate is a T gate
We propose an improvement whereby the controlled-Rn consists of a lower total number of gates keeping one Rn gate
We present an efficient decomposition of a controlled-Rn gate without using nonlocal CNOT gates
Summary
We propose efficient controlled-Rn decomposition methods as a technique to help enhance the benefits of quantum computation. When we approximate the controlled-Rn with precision 10−10, the total number of gates is 761 on average from Table 1. Circuit implementing a controlled-Rn gate with a single ancillary qubit 0 11,12,18. If we consider only one ancillary qubit, T-depth 5 and T-count 9 are the best results in decomposition of controlled-T gate.
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