Open AccessOptimizing quantum circuits using higher-dimensional Hilbert spaces
Author(s) -
Kai Liu,
Wendong Li,
Wenzhao Zhang,
Peng Shi,
Chao Ren,
Gu Yong-Jian
Publication year - 2012
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.61.120301
Subject(s) - qubit , toffoli gate , quantum gate , hilbert space , quantum circuit , controlled not gate , computer science , dimension (graph theory) , quantum , electronic circuit , quantum computer , topology (electrical circuits) , quantum error correction , quantum mechanics , mathematics , physics , algorithm , pure mathematics , combinatorics
Inspired by Lanyon (B. P. Lanyon et al. 2008 Nature Physics. 5 134) successfully simplifying the three-qubit Toffoli gate, we present a novel scheme that optimizes universal quantum logic circuits using assisted higher-dimensional Hilbert space. We construct a more efficient two-qubit circuit and a more effective three-qubit universal quantum circuit by using assisted dimension, Cosine-Sine Decomposition (CSD) and Quantum Shannon Decomposition (QSD). Meanwhile, we present the formula for the complexity of arbitrary n-qubit universal quantum gate. We propose the physical implementation of this scheme by linear optical circuits and cavity-QED. The results show that the two-qubit and three-qubit universal quantum circuits are respectively close and superior to the current optimal scheme in complexity. And with the increase of the number of qubits, the advantage of our scheme will become increasingly prominent.