Quantum Transport and Quantum Information Processing in Single Molecular Junctions

Abstract

Superposition states and entanglement in quantum bits (qubits) are inherently required in quantum computations (Benenti et al., 2004; Miyano & Furusawa, 2008; Nielsen & Chuang, 2004; Sagawa & Yoshida, 2003). Electron and nuclear spins have been identified as attractive candidates for qubits (Ladd et al., 2010), and the prominent properties involved in quantum spins have been observed in liquid state molecules (Vandersypen et al., 2001) and solid state materials such as doped silicon (Kane, 1998) and nitrogen-vacancy (NV) center in diamond (Childress et al., 2006). An impressive demonstration of quantum computations on Shor’s algorithm was carried out by Vandersypen and co-workers by using a liquid state system, in which each molecule includes seven nuclear spin qubits (Vandersypen et al., 2001). The operations for single and double qubits were implemented through bulk nuclear magnetic resonance (NMR) technique, in which radio-frequency (RF) pulse sequences were constructed so as to manipulate nuclear spin states along the design of quantum gates for the factorization. The RF pulse applications were succeeded in the precise control of nuclear spin states, and in turn in the factorization of a small number (N=15) in Shor’s algorithm. However, the liquid NMR signals are inherently averaged signals from a huge number of molecules, and therefore problems on initialization of qubits and pseudo-entanglement appear in the liquid NMR system, which make the liquid system difficult for the quantum computations using a larger number of qubits, although the operations in NMR are in principle robust.