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...

Abstract. In discrete time, coined quantum walks, the coin degrees of freedom offer the potential for a wider range of controls over the evolution of the walk than are available in the continuous time quantum walk. This paper explores some of the possibilities on regular graphs, and also reports periodic behaviour on small cyclic graphs.

We present a study of the effects of decoherence in the operation of a discrete quantum walk on a line, cycle and hypercube. We find high sensitivity to decoherence, increasing with the number of steps in the walk, as the particle is becoming more delocalised with each step. However, the effect of a small amount of decoherence is to enhance the properties of the quantum walk that are desirable for the development of quantum algorithms. Specifically, we observe a highly uniform distribution on the line, a very fast mixing time on the cycle, and more reliable hitting times across the hypercube.Comment: (Imperial College London) 6 (+epsilon) pages, 6 embedded eps figures, RevTex4. v2 minor changes to correct typos and refs, submitted version. v3 expanded into article format, extra figure, updated refs, Note on "glued trees" adde

We introduce the quantum quincunx, which physically demonstrates the quantum walk and is analogous to Galton's quincunx for demonstrating the random walk by employing gravity to draw pellets through pegs on a board, thereby yielding a binomial distribution of final peg locations. In contradistinction to the theoretical studies of quantum walks over orthogonal lattice states, we introduce quantum walks over nonorthogonal lattice states ͑specifically, coherent states on a circle͒ to demonstrate that the key features of a quantum walk are observable albeit for strict parameter ranges. A quantum quincunx may be realized with current cavity quantum electrodynamics capabilities, and precise control over decoherence in such experiments allows a remarkable decrease in the position noise, or spread, with increasing decoherence. Galton's quincunx ͓1͔ is a valuable device for demonstrating the random walk ͑RW͒: gravity draws pellets through a pyramidal structure of pegs, yielding a binomial distribution. The RW is of fundamental importance as the underlying process for dissipation and fluctuation ͓2͔ and as a central concept in research into computer algorithms, which has motivated research into the quantum walk ͑QW͒ ͓3-6͔ as a quantum counterpart to the RW. The QW exhibits surprising features such as a quadratic enhancement of fluctuations and possible exponential speedups ͓7͔ over the RW. In addition, the QW could be useful for bench marking the performance of certain quantum devices ͓8͔. Following Galton's classical example, we describe a cavity quantum electrodynamic ͑CQED͒ device that exhibits the QW, with controllable decoherence that can yield a continuous transition from the QW to the RW. Although the ͑energy-conserving͒ QW on a circle has been studied ͓4͔, and a physical realization in the context of the ion trap has been introduced ͓8͔, ideal lattice states have always been assumed; however, orthogonal localized lattice states are not realized physically-typically they would be constructed as nonorthogonal Gaussian ͑e.g., coherent͒ states. We prove here that the QW is viable using such nonorthogonal lattice states for a restricted range of energies, still exhibiting the dramatic features characterizing the QW. Moreover, whereas the fluctuation-dissipation theorem yields increased fluctuations as losses increase, this ''quantum quincunx'' exhibits the counterintuitive result that fluctuations decrease as losses increase.Microwave CQED provides an excellent technology for realizing the quantum quincunx. The combined atomϩcavity system can be effectively isolated from the environment, and decoherence can be controllably introduced ͓9͔; furthermore, new technologies allow the atom to be struck by a periodic sequence of off-axis microwave pulses ͓10͔. Whereas the RW utilizes a random number ͑a coin toss͒ to determine right or left steps by the ''walker,'' the unitary evolution of the QW demands a ''quantum coin'' that is rotated from the heads (ϩ) or tails (Ϫ) state into an equal superposition of these states via the ...

Decoherence-free subspaces allow for the preparation of coherent and entangled qubits for quantum computing. Decoherence can be dramatically reduced, yet dissipation is an integral part of the scheme in generating stable qubits and manipulating them via one-and two-bit gate operations. How this works can be understood by comparing the system with a three-level atom exhibiting a macroscopic dark period. In addition, a dynamical explanation is given for a scheme based on atoms inside an optical cavity in the strong-coupling regime and we show how spontaneous emission by the atoms can be highly suppressed.