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Quantum Information Processing

Efficient quantum computing between remote qubits in linear nearest neighbor architectures

Preethika Kumar

Published Sep 21, 2012• 10 citations
Publisher
DOI
10.1007/s11128-012-0485-5

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We show how to construct an efficient quantum circuit for computing a good approximation of the quantum Fourier transform on a linear nearest neighbor architecture. The constructed circuit uses no ancillary qubits and its depth and size are O(n)O(n)O(n) and O(nlog⁡n)O(n\log n)O(nlogn), respectively, where nnn is the length of the input. The circuit is useful for decreasing the size of Fowler et al.'s quantum circuit for Shor's factoring algorithm on a linear nearest neighbor architecture.
Several promising implementations of quantum computation rely on a Linear Nearest Neighbor (LNN) architecture, which arranges quantum bits on a line, and allows neighbor interactions only. Therefore, several specific circuits have been designed on an LNN architecture. However, a general and efficient conversion method for an arbitrary circuit has not been established. Therefore, this paper gives an efficient conversion technique to convert quantum circuits to an LNN architecture. When a quantum circuit is converted to an LNN architecture, the objective is to reduce the size of the additional circuit added by the conversion and the time complexity of the conversion. The proposed method requires less additional circuitry and time complexity compared with naive techniques. To develop the method, we introduce two key theorems that may be interesting on their own. In addition, the proposed method also achieves less overhead than some known circuits designed from scratch on an LNN architecture.