Optimizing quantum circuits using higher-dimensional Hilbert spaces

Abstract

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.