Limitations of quantum computing with Gaussian cluster states

We discuss the potential and limitations of Gaussian cluster states for measurement-based quantum computing. Using a framework of Gaussian projected entangled pair states (GPEPS), we show that no matter what Gaussian local measurements are performed on systems distributed on a general graph, transport and processing of quantum information is not possible beyond a certain influence region, except for exponentially suppressed corrections. We also demonstrate that even under arbitrary non-Gaussian local measurements, slabs of Gaussian cluster states of a finite width cannot carry logical quantum information, even if sophisticated encodings of qubits in continuous-variable (CV) systems are allowed for. This is proven by suitably contracting tensor networks representing infinite-dimensional quantum systems. The result can be seen as sharpening the requirements for quantum error correction and fault tolerance for Gaussian cluster states, and points towards the necessity of non-Gaussian resource states for measurement-based quantum computing. The results can equally be viewed as referring to Gaussian quantum repeater networks.Comment: 13 pages, 7 figures, details of main argument extende

Percolation, renormalization, and quantum computing with non-deterministic gates

We apply a notion of static renormalization to the preparation of entangled states for quantum computing, exploiting ideas from percolation theory. Such a strategy yields a novel way to cope with the randomness of non-deterministic quantum gates. This is most relevant in the context of optical architectures, where probabilistic gates are common, and cold atoms in optical lattices, where hole defects occur. We demonstrate how to efficiently construct cluster states without the need for rerouting, thereby avoiding a massive amount of conditional dynamics; we furthermore show that except for a single layer of gates during the preparation, all subsequent operations can be shifted to the final adapted single qubit measurements. Remarkably, cluster state preparation is achieved using essentially the same scaling in resources as if deterministic gates were available.Comment: 5 pages, 4 figures, discussion of strategies to deal with further imperfections extended, references update

Directly estimating non-classicality

We establish a method of directly measuring and estimating non-classicality - operationally defined in terms of the distinguishability of a given state from one with a positive Wigner function. It allows to certify non-classicality, based on possibly much fewer measurement settings than necessary for obtaining complete tomographic knowledge, and is at the same time equipped with a full certificate. We find that even from measuring two conjugate variables alone, one may infer the non-classicality of quantum mechanical modes. This method also provides a practical tool to eventually certify such features in mechanical degrees of freedom in opto-mechanics. The proof of the result is based on Bochner's theorem characterizing classical and quantum characteristic functions and on semi-definite programming. In this joint theoretical-experimental work we present data from experimental optical Fock state preparation, demonstrating the functioning of the approach.Comment: 4+1 pages, 2 figures, minor change

Directed percolation effects emerging from superadditivity of quantum networks

Entanglement indcued non--additivity of classical communication capacity in networks consisting of quantum channels is considered. Communication lattices consisiting of butterfly-type entanglement breaking channels augmented, with some probability, by identity channels are analyzed. The capacity superadditivity in the network is manifested in directed correlated bond percolation which we consider in two flavours: simply directed and randomly oriented. The obtained percolation properties show that high capacity information transfer sets in much faster in the regime of superadditive communication capacity than otherwise possible. As a byproduct, this sheds light on a new type of entanglement based quantum capacity percolation phenomenon.Comment: 6 pages, 4 figure

On photonic controlled phase gates

As primitives for entanglement generation, controlled phase gates take a central role in quantum computing. Especially in ideas realizing instances of quantum computation in linear optical gate arrays a closer look can be rewarding. In such architectures, all effective non-linearities are induced by measurements: Hence the probability of success is a crucial parameter of such quantum gates. In this note, we discuss this question for controlled phase gates that implement an arbitrary phase with one and two control qubits. Within the class of post-selected gates in dual-rail encoding with vacuum ancillas we identify the optimal success probabilities. We construct networks that allow for an implementation by means of todays experimental capabilities in detail. The methods employed here appear specifically useful with the advent of integrated linear optical circuits, providing stable interferometers on monolithic structures.Comment: 9 pages, 6 figures, final versio

Experimental implementation of the optimal linear-optical controlled phase gate

We report on the first experimental realization of optimal linear-optical controlled phase gates for arbitrary phases. The realized scheme is entirely flexible in that the phase shift can be tuned to any given value. All such controlled phase gates are optimal in the sense that they operate at the maximum possible success probabilities that are achievable within the framework of any postselected linear-optical implementation. The quantum gate is implemented using bulk optical elements and polarization encoding of qubit states. We have experimentally explored the remarkable observation that the optimum success probability is not monotone in the phase.Comment: 4 pages, 5 figures, 1 tabl

Enhancement of Entanglement Percolation in Quantum Networks via Lattice Transformations

We study strategies for establishing long-distance entanglement in quantum networks. Specifically, we consider networks consisting of regular lattices of nodes, in which the nearest neighbors share a pure, but non-maximally entangled pair of qubits. We look for strategies that use local operations and classical communication. We compare the classical entanglement percolation protocol, in which every network connection is converted with a certain probability to a singlet, with protocols in which classical entanglement percolation is preceded by measurements designed to transform the lattice structure in a way that enhances entanglement percolation. We analyze five examples of such comparisons between protocols and point out certain rules and regularities in their performance as a function of degree of entanglement and choice of operations.Comment: 12 pages, 17 figures, revtex4. changes from v3: minor stylistic changes for journal reviewer, minor changes to figures for journal edito

General linear-optical quantum state generation scheme: Applications to maximally path-entangled states

We introduce schemes for linear-optical quantum state generation. A quantum state generator is a device that prepares a desired quantum state using product inputs from photon sources, linear-optical networks, and postselection using photon counters. We show that this device can be concisely described in terms of polynomial equations and unitary constraints. We illustrate the power of this language by applying the Grobner-basis technique along with the notion of vacuum extensions to solve the problem of how to construct a quantum state generator analytically for any desired state, and use methods of convex optimization to identify bounds to success probabilities. In particular, we disprove a conjecture concerning the preparation of the maximally path-entangled |n,0)+|0,n) (NOON) state by providing a counterexample using these methods, and we derive a new upper bound on the resources required for NOON-state generation.Comment: 5 pages, 2 figure