Quantum computing with four-particle decoherence-free states in an ion trap

Much effort has been put into quantum computing over the past few years due to great advantages of quantum computing over the computation made in existing computers for solving classically intractable problems @1,2# and finding tractable solutions more rapidly @3#. Some systems @4# such as nuclear magnetic resonance, trapped ions, cavity quantum electrodynamics, and optical photons have been proven to meet the requirement of quantum computing. There are some special advantages for each of the systems referred to above, while we will focus in the present work on the discussion of quantum gates on trapped ions. Since the proposal of Cirac and Zoller @5#, many elaborate ideas have been put forward on quantum computing with trapped ions @6,7# and some experiments showing the possibility of quantum computing with a few trapped ions have been achieved @8–10#. However, to our knowledge, no specific robust scheme of quantum computing with trapped ions has been proposed so far, which can keep decoherence away from qubits in quantum-information processing, although various proposals @11–13# have been put forward to resist the attack of decoherence by using decoherence-free states ~DFS!. We noticed an experiment @14# made recently with trapped ions that encodes qubits in DFS. Although what it demonstrated is the simplest case of DFS, i.e., two-qubit DFS resisting collective dephasing, the effectiveness of DFS in information storage was clearly shown. However, it is natural for us to ask how to use these DFS for quantum computing and if it is possible to build an actual ion-trap quantum computer based on DFS. These questions are the motivation of the present