@diplomathesis{Kieling05a,
docarc = {http://konrad.familie-kieling.de/cgi-bin/docarc/public.pl?rm=search;queryfield=bibtexid;relation=equals;limit=1;categories=0;query=Kieling05a},
category = {papers},
printed = {0},
author = {Konrad Kieling},
title = {Linear Optics Methods in Quantum Information Processing},
year = {2005},
language = {english},
school = {University of Potsdam},
abstract = {Quantum computing is a promising attempt for the next step in the evolution of computation technnology. In this thesis, methods that can be used for implementing quantum circuits with optics are studied. This is particularly done within the framework of linear optics. The linear optics toolbox is developed and the common problem of whether the access to multiple degrees of freedom of photons may enhance linear optics' efficiency is addressed. Except for some special small-scale computation problems, exploiting multiple degrees of freedom does not seem to result in an efficiency gain. Consequences of the restriction to linear elements include the probabilistic nature of elementary quantum gates, giving rise to several schemes of computation that shift this drawback to the step of resource preparation. Procedures of how to generate these resource states are investigated for some gate model based schemes as well as for the cluster model. Further, the question of how to use the allowed tools most e ciently is investigated. Different strategies for cluster state preparation, one of the most efficient strategies among them, are proposed and numerically simulated.},
}
@article{KGE06,
file = {7D31043B-BDB9-137E-C5014987C88EB74D_125556.pdf},
docarc = {http://konrad.familie-kieling.de/cgi-bin/docarc/public.pl?rm=search;queryfield=bibtexid;relation=equals;limit=1;categories=0;query=KGE06},
category = {papers},
printed = {0},
author = {Konrad Kieling and David Gross and Jens Eisert},
title = {Minimal resources for linear optical one-way computing},
journal = {J. Opt. Soc. Am. B},
volume = {24},
number = {2},
year = {2007},
language = {english},
pages = {184},
eprint = {quant-ph/0601190},
abstract = {We address the question of how many maximally entangled pairs are needed in order to build up cluster states for quantum computing using the toolbox of linear optics. As the needed gates in dual-rail encoding are necessarily probabilistic with known optimal success probability, this question amounts to finding the optimal strategy for building up cluster states, from the perspective of classical control. We develop a notion of classical strategies, and present rigorous statements on the ultimate maximal and minimal use of resources of the globally optimal strategy. We find that this strategy - being also the most robust with respect to decoherence - gives rise to an advantage of already more than an order of magnitude in the number of maximally entangled pairs when building chains with an expected length of L=40, compared to other legitimate strategies. For two-dimensional cluster states, we present a first scheme achieving the optimal quadratic asymptotic scaling. This analysis shows that the choice of appropriate classical control leads to a very significant reduction in resource consumption.},
}
@article{GKE06,
file = {PhysRevA_74_042343.pdf},
docarc = {http://konrad.familie-kieling.de/cgi-bin/docarc/public.pl?rm=search;queryfield=bibtexid;relation=equals;limit=1;categories=0;query=GKE06},
category = {papers},
printed = {0},
author = {David Gross and Konrad Kieling and Jens Eisert},
title = {Potential and limits to cluster-state quantum computing using probabilistic gates},
journal = {Phys. Rev. A},
volume = {74},
year = {2006},
language = {english},
pages = {042343},
month = {oct},
url = {http://link.aps.org/abstract/PRA/v74/e042343},
eprint = {quant-ph/0605014},
abstract = {We establish bounds to the necessary resource consumption when building up cluster states for one-way computing using probabilistic gates. Emphasis is put on state preparation with linear optical gates, as the probabilistic character is unavoidable here. We identify rigorous general bounds to the necessary consumption of initially available maximally entangled pairs when building up one-dimensional cluster states with individually acting linear optical quantum gates, entangled pairs, and vacuum modes. As the known linear optics gates have a limited maximum success probability, as we show, this amounts to finding the optimal classical strategy of fusing pieces of linear cluster states. A formal notion of classical configurations and strategies is introduced for probabilistic nonfaulty gates. We study the asymptotic performance of strategies that can be simply described, and prove ultimate bounds to the performance of the globally optimal strategy. The arguments employ methods of random walks and convex optimization. This optimal strategy is also the one that requires the shortest storage time, and necessitates the fewest invocations of probabilistic gates. For two-dimensional cluster states, we find, for any elementary success probability, an essentially deterministic preparation of a cluster state with quadratic, hence optimal, asymptotic scaling in the use of entangled pairs. We also identify a percolation effect in state preparation, in that from a threshold probability on, almost all preparations will be either successful or fail. We outline the implications on linear optical architectures and fault-tolerant computations.},
doi = {10.1103/PhysRevA.74.042343},
}
@article{KRE06,
file = {PhysRevLett_99_130501.pdf},
docarc = {http://konrad.familie-kieling.de/cgi-bin/docarc/public.pl?rm=search;queryfield=bibtexid;relation=equals;limit=1;categories=0;query=KRE06},
category = {papers},
printed = {1},
author = {Konrad Kieling and Terry Rudolph and Jens Eisert},
title = {Percolation, renormalization, and quantum computing with non-deterministic gates},
journal = {Phys. Rev. Lett.},
volume = {99},
year = {2007},
language = {english},
pages = {130501},
url = {http://link.aps.org/abstract/PRL/v99/e130501},
eprint = {quant-ph/0611140},
abstract = {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 nondeterministic 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.},
doi = {10.1103/PhysRevLett.99.130501},
}
@article{MLU+07,
file = {PhysRevA_76_063808.pdf},
docarc = {http://konrad.familie-kieling.de/cgi-bin/docarc/public.pl?rm=search;queryfield=bibtexid;relation=equals;limit=1;categories=0;query=MLU+07},
category = {papers},
printed = {0},
author = {N. M. VanMeter and P. Lougovski and D. B. Uskov and K. Kieling and J. Eisert and Jonathan P. Dowling},
title = {General linear-optical quantum state generation scheme: Applications to maximally path-entangled states},
journal = {Phys. Rev. A},
volume = {76},
year = {2007},
language = {english},
pages = {063808},
eprint = {quant-ph/0612154},
url = {http://link.aps.org/abstract/PRA/v76/e063808},
abstract = {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.},
doi = {10.1103/PhysRevA.76.063808},
}
@article{KGE07,
file = {njp7_6_200.pdf},
docarc = {http://konrad.familie-kieling.de/cgi-bin/docarc/public.pl?rm=search;queryfield=bibtexid;relation=equals;limit=1;categories=0;query=KGE07},
category = {papers},
printed = {0},
author = {Konrad Kieling and David Gross and Jens Eisert},
title = {Cluster state preparation using gates operating at arbitrary success probabilities},
journal = {New J. Phys.},
volume = {9},
year = {2007},
language = {english},
pages = {200},
url = {http://www.iop.org/EJ/abstract/1367-2630/9/6/200},
eprint = {quant-ph/0703045},
abstract = {Several physical architectures allow for the sequential preparation of cluster states for measurement-based quantum computing using probabilistic quantum gates. In such an approach, the order in which partial resources are combined to form the final cluster state turns out to be crucially important. We determine the influence of this classical decision process on the expected size of the final cluster. Extending earlier work, we consider different quantum gates operating at various probabilites of success. For finite resources, we employ a computer algebra system to obtain the provably optimal classical control strategy and derive symbolic results for the expected final size of the cluster. Surprisingly, two substantially different regimes can be identified: When the success probability of the elementary gates is high, the influence of the classical control strategy is found to vanish. In that case, other figures of merit become more relevant. For small probabilities of success, the choice of an appropriate strategy is crucial.},
doi = {10.1088/1367-2630/9/6/200},
}
@incollection{KE07,
file = {review18.pdf},
docarc = {http://konrad.familie-kieling.de/cgi-bin/docarc/public.pl?rm=search;queryfield=bibtexid;relation=equals;limit=1;categories=0;query=KE07},
category = {papers},
printed = {0},
author = {Konrad Kieling and Jens Eisert},
title = {Percolation in quantum computation and communication},
booktitle = {Quantum and Semi-classical Percolation and Breakdown in Disordered Solids},
editor = {Asok K. Sen and Kamal K. Bardhan and Bikas K. Chakrabarti},
series = {Lecture Notes in Physics},
volume = {762},
year = {2007},
language = {english},
publisher = {Springer},
pages = {285--317},
}
@article{__52,
file = {njp10_1_013003.pdf},
docarc = {http://konrad.familie-kieling.de/cgi-bin/docarc/public.pl?rm=search;queryfield=docid;relation=equals;limit=1;categories=0;query=52},
category = {papers},
printed = {0},
author = {Konrad Kieling and Jeremy O'Brien and Jens Eisert},
title = {On photonic controlled phase gates},
journal = {New Journal of Physics},
volume = {12},
year = {2010},
language = {english},
pages = {013003},
url = {http://www.iop.org/EJ/abstract/1367-2630/12/1/013003/},
eprint = {0909.2057},
abstract = {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 work, 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.},
doi = {10.1088/1367-2630/12/1/013003},
}
@unpublished{__63,
docarc = {http://konrad.familie-kieling.de/cgi-bin/docarc/public.pl?rm=search;queryfield=docid;relation=equals;limit=1;categories=0;query=63},
category = {papers},
printed = {0},
author = {Matthias Ohliger and Konrad Kieling and Jens Eisert},
title = {Limitations of quantum computing with Gaussian cluster states},
year = {2010},
language = {english},
eprint = {1004.0081},
abstract = {Abstract: 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.},
}
@unpublished{__67,
docarc = {http://konrad.familie-kieling.de/cgi-bin/docarc/public.pl?rm=search;queryfield=docid;relation=equals;limit=1;categories=0;query=67},
category = {papers},
printed = {0},
author = {Andrea Mari and Konrad Kieling and Bo Melholt Nielsen and Eugene S. Polzik and Jens Eisert},
title = {Directly estimating non-classicality},
year = {2010},
language = {english},
eprint = {1005.1665},
abstract = {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 can 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.},
}
@unpublished{__69,
docarc = {http://konrad.familie-kieling.de/cgi-bin/docarc/public.pl?rm=search;queryfield=docid;relation=equals;limit=1;categories=0;query=69},
category = {papers},
printed = {0},
author = {Karel Lemr and Antonin Cernoch and Jan Soubusta and Konrad Kieling and Jens Eisert and Miloslav Dusek},
title = {Experimental implementation of the optimal linear-optical controlled phase gate},
year = {2010},
language = {english},
eprint = {1007.4797},
abstract = {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.},
}