Quantum Computing Using Dissipation to Remain in a Decoherence-Free Subspace

Abstract

We propose a new approach to the implementation of quantum gates in which decoherence during the gate operations is strongly reduced. This is achieved by making use of an environment induced quantum Zeno effect that confines the dynamics effectively to a decoherence-free subspace.PACS numbers: 03.67. Lx, 42.50.Lc Quantum computing has attracted much interest since it became clear that quantum computers are in principle able to solve hard computational problems more efficiently than present classical computers [1][2][3]. The main obstacle inhibiting realizations arises from the difficulty of isolating a quantum mechanical system from its environment. This leads to decoherence and the loss of information stored in the system, which limits for instance factoring to small numbers [4]. Schemes have been proposed to correct for errors induced by decoherence and other imperfections [5]. Alternatively, the use of decoherence-free subspaces [6][7][8][9] has been proposed for which the dependence on error correction codes may be much reduced. Nevertheless, the error rate of each operation must not exceed 10 25 if quantum computers are ever to work fault tolerantly [10].In contrast to the widely held folk belief that decoherence is to be avoided, we show here that dissipation can be used to implement nearly decoherence-free quantum gates with a success rate which can, at least in principle, be arbitrarily close to unity. The main requirement for this to work is the existence of a decoherence-free subspace (DFS) in the system under consideration. States in the DFS will be called decoherence-free (DF) states. Examples of DFS are known [9,11], but until now, it was not known how to manipulate states within a DFS in general [12].In this Letter we propose a concrete example of a DFS whose states can be used to obtain DF qubits for quantum computing. In contrast to earlier proposals, we assume that all other states couple strongly to the environment. A state with no overlap with DF states should (nearly immediately) lead to dissipation. We show that we can interpret the effect of the environment on the system as that of rapidly repeated measurements of whether the system is DF or not. This effect, which we call an environment induced quantum Zeno effect [13], leads to the fact that a weak interaction changes only the state of the system inside the DFS. This allows for a wide range of new possibilities to perform DF gate operations between the qubits. As an example we describe a CNOT operation between two qubits that is almost DF yet rather simple: A single laser pulse suffices. We will show that the system proposed fulfills all criteria for a quantum computer proposed by DiVincenzo [14].The system we propose consists of N identical threelevel atoms with a L configuration. We denote the split ground states of atom i by j0͘ i and j1͘ i , and the excited state by j2͘ i . The atoms are assumed to be stored in a line, which can be for instance in a linear ion trap, an optical lattice, or on top of a wire on an atom chip [15]. To r...

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