Entanglement Dynamics in 1D Quantum Cellular Automata

Several proposed schemes for the physical realization of a quantum computer consist of qubits arranged in a cellular array. In the quantum circuit model of quantum computation, an often complex series of two-qubit gate operations is required between arbitrarily distant pairs of lattice qubits. An alternative model of quantum computation based on quantum cellular automata (QCA) requires only homogeneous local interactions that can be implemented in parallel. This would be a huge simplification in an actual experiment. We find some minimal physical requirements for the construction of unitary QCA in a 1 dimensional Ising spin chain and demonstrate optimal pulse sequences for information transport and entanglement distribution. We also introduce the theory of non-unitary QCA and show by example that non-unitary rules can generate environment assisted entanglement.Comment: 12 pages, 8 figures, submitted to Physical Review

Universal quantum interfaces

To observe or control a quantum system, one must interact with it via an interface. This letter exhibits simple universal quantum interfaces--quantum input/output ports consisting of a single two-state system or quantum bit that interacts with the system to be observed or controlled. It is shown that under very general conditions the ability to observe and control the quantum bit on its own implies the ability to observe and control the system itself. The interface can also be used as a quantum communication channel, and multiple quantum systems can be connected by interfaces to become an efficient universal quantum computer. Experimental realizations are proposed, and implications for controllability, observability, and quantum information processing are explored.Comment: 4 pages, 3 figures, RevTe

Computation on a Noiseless Quantum Code and Symmetrization

Let ${\cal H}$ be the state-space of a quantum computer coupled with the environment by a set of error operators spanning a Lie algebra ${\cal L}.$ Suppose ${\cal L}$ admits a noiseless quantum code i.e., a subspace ${\cal C}\subset{\cal H}$ annihilated by ${\cal L}.$ We show that a universal set of gates over $\cal C$ is obtained by any generic pair of ${\cal L}$-invariant gates. Such gates - if not available from the outset - can be obtained by resorting to a symmetrization with respect to the group generated by ${\cal L}.$ Any computation can then be performed completely within the coding decoherence-free subspace.Comment: One result added, to appear in Phys. Rev. A (RC) 4 pages LaTeX, no figure

Universal quantum control in irreducible state-space sectors: application to bosonic and spin-boson systems

We analyze the dynamical-algebraic approach to universal quantum control introduced in P. Zanardi, S. Lloyd, quant-ph/0305013. The quantum state-space $\cal H$ encoding information decomposes into irreducible sectors and subsystems associated to the group of available evolutions. If this group coincides with the unitary part of the group-algebra \CC{\cal K} of some group $\cal K$ then universal control is achievable over the ${\cal K}$-irreducible components of $\cal H$. This general strategy is applied to different kind of bosonic systems. We first consider massive bosons in a double-well and show how to achieve universal control over all finite-dimensional Fock sectors. We then discuss a multi-mode massless case giving the conditions for generating the whole infinite-dimensional multi-mode Heisenberg-Weyl enveloping-algebra. Finally we show how to use an auxiliary bosonic mode coupled to finite-dimensional systems to generate high-order non-linearities needed for universal control.Comment: 10 pages, LaTeX, no figure

On Quantum Control via Encoded Dynamical Decoupling

I revisit the ideas underlying dynamical decoupling methods within the framework of quantum information processing, and examine their potential for direct implementations in terms of encoded rather than physical degrees of freedom. The usefulness of encoded decoupling schemes as a tool for engineering both closed- and open-system encoded evolutions is investigated based on simple examples.Comment: 12 pages, no figures; REVTeX style. This note collects various theoretical considerations complementing/motivated by the experimental demonstration of encoded control by Fortunato et a

Universal control of quantum subspaces and subsystems

We describe a broad dynamical-algebraic framework for analyzing the quantum control properties of a set of naturally available interactions. General conditions under which universal control is achieved over a set of subspaces/subsystems are found. All known physical examples of universal control on subspaces/systems are related to the framework developed here.Comment: 4 Pages RevTeX, Some typos fixed, references adde

Levels of extra-pair paternity are associated with parental care in penduline tits (Remizidae)

In most passerine birds, individuals attempt to maximise their fitness by providing parental care while also mating outside their pair bond. A sex-specific trade-off between these two behaviours is predicted to occur since the fitness benefits of extra-pair mating differs between the sexes. We use nest observations and parentage analysis to reveal a negative association between male care and the incidence of extra-pair paternity across three species of penduline tit (Remizidae)

On the relationship between continuous- and discrete-time quantum walk

Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. But whereas a continuous-time random walk can be obtained as the limit of a sequence of discrete-time random walks, the two types of quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-time case. In this article, I describe a precise correspondence between continuous- and discrete-time quantum walks on arbitrary graphs. Using this correspondence, I show that continuous-time quantum walk can be obtained as an appropriate limit of discrete-time quantum walks. The correspondence also leads to a new technique for simulating Hamiltonian dynamics, giving efficient simulations even in cases where the Hamiltonian is not sparse. The complexity of the simulation is linear in the total evolution time, an improvement over simulations based on high-order approximations of the Lie product formula. As applications, I describe a continuous-time quantum walk algorithm for element distinctness and show how to optimally simulate continuous-time query algorithms of a certain form in the conventional quantum query model. Finally, I discuss limitations of the method for simulating Hamiltonians with negative matrix elements, and present two problems that motivate attempting to circumvent these limitations.Comment: 22 pages. v2: improved presentation, new section on Hamiltonian oracles; v3: published version, with improved analysis of phase estimatio

A BQP-complete problem related to the Ising model partition function via a new connection between quantum circuits and graphs

We present a simple construction that maps quantum circuits to graphs and vice-versa. Inspired by the results of D.A. Lidar linking the Ising partition function with quadratically signed weight enumerators (QWGTs), we also present a BQP-complete problem for the additive approximation of a function over hypergraphs related to the generating function of Eulerian subgraphs for ordinary graphs. We discuss connections with the Ising partition function.Comment: 12 pages, 2 figure

Multipartite Entanglement and Quantum State Exchange

We investigate multipartite entanglement in relation to the theoretical process of quantum state exchange. In particular, we consider such entanglement for a certain pure state involving two groups of N trapped atoms. The state, which can be produced via quantum state exchange, is analogous to the steady-state intracavity state of the subthreshold optical nondegenerate parametric amplifier. We show that, first, it possesses some 2N-way entanglement. Second, we place a lower bound on the amount of such entanglement in the state using a novel measure called the entanglement of minimum bipartite entropy.Comment: 12 pages, 4 figure