Weighted Graph States Research Articles

Renormalization algorithm with graph enhancement

We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underlie the density-matrix renormalization-group approach by combining them with weighted graph states. States within this class may (i) possess arbitrarily long-ranged two-point correlations, (ii) exhibit an arbitrary degree of block entanglement entropy up to a volume law, (iii) be taken translationally invariant, while at the same time (iv) local properties and two-point correlations can be computed efficiently. This variational class of states can be thought of as being prepared from matrix product states, followed by commuting unitaries on arbitrary constituents, hence truly generalizing both matrix product and weighted graph states. We use this class of states to formulate a renormalization algorithm with graph enhancement and present numerical examples, demonstrating that improvements over density-matrix renormalization-group simulations can be achieved in the simulation of ground states and quantum algorithms. Further generalizations, e.g., to higher spatial dimensions, are outlined.

Compact Toffoli gate using weighted graph states

We introduce three compact graph states that can be used to perform a measurement-based Toffoli gate. Given a weighted graph of six, seven, or eight qubits, we show that success probabilities of $1∕4$, $1∕2$, and 1, respectively, can be achieved. Our study puts a measurement-based version of this important quantum logic gate within the reach of current experiments. As the graphs are setup independent, they could be realized in a variety of systems, including linear optics and ion traps.

Graphical description of local Gaussian operations for continuous-variable weighted graph states

The form of a local Clifford [LC, also called local Gaussian (LG)] operation for the continuous-variable (CV) weighted graph states is presented in this paper, which is the counterpart of the LC operation of local complementation for qubit graph states. The property of the CV weighted graph states is shown, which can be expressed by the stabilizer formalism. It is distinctively different from the qubit weighted graph states, which cannot be expressed by the stabilizer formalism. The corresponding graph rule, stated in purely graph theoretical terms, is described, which completely characterizes the evolution of CV weighted graph states under this LC operation. This LC operation may be applied repeatedly on a CV weighted graph state, which can generate the infinite LC equivalent graph states of this graph state. This work is an important step to characterize the LC equivalence class of CV weighted graph states.

Random circuits by measurements on weighted graph states

Random quantum circuits take an input quantum state and randomize it. This is a task with a growing number of identified uses in quantum-information processing. We suggest a scheme to implement random circuits in a weighted graph state. The input state is entangled with the weighted graph state and a random circuit is implemented when the experimenter performs local measurements in one fixed basis only. The scheme uses no classical random numbers and is a new and natural application of weighted graph states.

Entanglement of group-II-like atoms with fast measurement for quantum information processing

We construct a scheme for the preparation, pairwise entanglement via exchange interaction, manipulation, and measurement of individual group-II-like neutral atoms (Yb, Sr, etc.). Group-II-like atoms proffer important advantages over alkali metals, including long-lived optical-transition qubits that enable fast manipulation and measurement. Our scheme provides a promising approach for producing weighted graph states, entangled resources for quantum communication, and possible application to fundamental tests of Bell inequalities that close both detection and locality loopholes.

Unifying Variational Methods for Simulating Quantum Many-Body Systems

We introduce a unified formulation of variational methods for simulating ground state properties of quantum many-body systems. The key feature is a novel variational method over quantum circuits via infinitesimal unitary transformations, inspired by flow equation methods. Variational classes are represented as efficiently contractible unitary networks, including the matrix-product states of density matrix renormalization, multiscale entanglement renormalization (MERA) states, weighted graph states, and quantum cellular automata. In particular, this provides a tool for varying over classes of states, such as MERA, for which so far no efficient way of variation has been known. The scheme is flexible when it comes to hybridizing methods or formulating new ones. We demonstrate the functioning by numerical implementations of MERA, matrix-product states, and a new variational set on benchmarks.

Entangling identical bosons in optical tweezers via exchange interaction

We first devise a scheme to perform a universal entangling gate via controlled collisions between pairs of atomic qubits trapped with optical tweezers. Second, we present a modification to this scheme to allow for the preparation of atomic Bell pairs via selective excitation, suitable for quantum-information-processing applications that do not require universality. Both these schemes are enabled by the inherent symmetries of identical composite particles, as originally proposed by Hayes et al. Our scheme provides a technique for producing weighted graph states, entangled resources for quantum communication, and a promising approach to performing a “loophole free” Bell test in a single laboratory.PACS Nos.: 03.65.Ud, 03.67.Mn, 32.80.Pj, 42.50.Vk

A variational method based on weighted graph states

In a recent article Anders et al 2006 Phys. Rev. Lett. 97 107206, we have presented a class of states which is suitable as a variational set to find ground states in spin systems of arbitrary spatial dimension and with long-range entanglement. Here, we continue the exposition of our technique, extend from spin 1/2 to higher spins and use the boson Hubbard model as a non-trivial example to demonstrate our scheme.

Weighted graph states and applications to spin chains, lattices and gases

Weighted graph states naturally arise when spin systems interact via an Ising-type interaction. First, we abstractly define the class of weighted graph states and demonstrate its computational accessibility. We show how reduced density matrices of a small number of spins (≈10) can be computed from arbitrarily large systems using weighted graph techniques and projected entangled pair techniques, and we discuss various entanglement measures accessible from these reduced density matrices. Second, we apply these findings to spin chains and lattices with long-range interactions and analytically derive area laws for the scaling of block-wise entanglement. Then, we turn to disordered spin systems, spin gases, which are connected to random weighted graph states and which share their entanglement properties. Finally, we use a spin gas as a bath that introduces decoherence in single as well as multipartite spin systems. The microscopic, exact decoherence model we obtain can operate in different regimes and exhibit non-Markovian features as well as spatially correlated noise effects.

Ground-State Approximation for Strongly Interacting Spin Systems in Arbitrary Spatial Dimension

We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These states allow for the efficient computation of all local observables (e.g., energy) and include states with diverging correlation length and unbounded multiparticle entanglement. As a demonstration, we apply our approach to the Ising model on 1D, 2D, and 3D square lattices. We also present generalizations to higher spins and continuous-variable systems, which allows for the investigation of lattice field theories.