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Quantum Information and Computation

An efficient conversion of quantum circuits to a linear nearest neighbor architecture

HirataYuichi, NakanishiMasaki, YamashitaShigeru, NakashimaYasuhiko

Published Jan 1, 2011• 48 citations
Publisher

Abstract

Several promising implementations of quantum computation rely on a Linear NearestNeighbor (LNN) architecture, which arranges quantum bits on a line, and allows neighborinteractions only. Therefore,...
DOI
10.5555/2011383.2011393

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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.
A variety of quantum circuits have been designed.Most of them assume that arbitrary pairs of qubits can interact.However, 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 technique for an arbitrary circuit has not been established.Therefore, this paper gives an efficient method that converts an arbitrary quantum circuit to one on an LNN architecture.Our method achieves small overhead 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, our method also achieves smaller overhead for some known circuits designed on an LNN architecture.