Diploma thesis
In 2005 I completed my Diploma thesis in the quantum information group at the University of Potsdam. Questions on linear optics including how to exploit different degrees of freedom were of central interest.
PhD
Between October 2005 and October 2008 I was a PhD student in the Quantum Information Theory group at the Institute for Mathematical Sciences, Imperial College London, sponsored by Microsoft Research through the European PhD Scholarship. The Physics behind the effects I was interested in are described by Quantum Optics. More precisely, my PhD project is concerned with the capabilities of linear optics as possible hardware to realize quantum information processing devices.
That means on the one hand to find methods to describe and solve the problem of how to implement given unitaries on dual-rail encoding with beam splitters. Particularly interesting is, of course, to find the optimal solutions to these problem, i.e., the solutions that work with the highest probability of success within the set of rules defined in the beginning.
A more relaxed version of this task is concerned with the generation of special quantum states. Given a certain input (e.g., single photons), how to produce a given state.
On the other hand, given certain quantum gates that are implemented in linear optics (and therefore only work probabilistically), how to apply them to given resources (e.g., EPR pairs) to generate other states, such that the resource requirement is the least possible. Actually, this task is an entirely classical problem.
Further, questions for fundamental limits inherent in linear optics were addressed.
The final version of my PhD thesis can be found here, a PDF suitable for eBook-readers is available here.
Research Interest
At the moment I am a postdoctoral researcher at the University of Potsdam.
Besides various questions in linear optics I am investigating optomechanical systems. These are, for example,
tiny mirrors which are probed with classical or quantum states of light. Signatures of quantum behaviour of this
mesoscopic mechanical system and effects of the environment can be identified.
A BibTeX file of my publications can be found here.
Publications
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Konrad Kieling.
Linear Optics Methods in Quantum Information ProcessingQuantum 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.,
University of Potsdam,
2005
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Konrad Kieling and David Gross and Jens Eisert.
Minimal resources for linear optical one-way computingWe 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.,
J. Opt. Soc. Am. B 24 (184),
2007
[pdf]
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David Gross and Konrad Kieling and Jens Eisert.
Potential and limits to cluster-state quantum computing using probabilistic gatesWe 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.,
Phys. Rev. A 74 (042343),
2006
[pdf]
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Konrad Kieling and Terry Rudolph and Jens Eisert.
Percolation, renormalization, and quantum computing with non-deterministic gatesWe 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.,
Phys. Rev. Lett. 99 (130501),
2007
[pdf]
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N. M. VanMeter and P. Lougovski and D. B. Uskov and K. Kieling and J. Eisert and Jonathan P. Dowling.
General linear-optical quantum state generation scheme: Applications to maximally path-entangled statesWe 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.,
Phys. Rev. A 76 (063808),
2007
[pdf]
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Konrad Kieling and David Gross and Jens Eisert.
Cluster state preparation using gates operating at arbitrary success probabilitiesSeveral 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.,
New J. Phys. 9 (200),
2007
[pdf]
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Konrad Kieling and Jens Eisert.
Percolation in quantum computation and communication in “Quantum and Semi-classical Percolation and Breakdown in Disordered Solids”,
Lecture Notes in Physics 762,
2007
[pdf]
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Konrad Kieling and Jeremy O'Brien and Jens Eisert.
On photonic controlled phase gatesAs 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.,
New Journal of Physics 12 (013003),
2010
[pdf]
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Posters
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Minimal resources for linear optical one-way computingWe 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 ver y significant reduction in resource consumption.,
2007
[pdf]
.
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Percolation, renormalization, and quantum computing with non-deterministic gatesWe apply a notion of static renormalization to the preparation of cluster 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 linear optical architectures, where probabilistic gates are inevitable. We demonstrate how to efficiently construct cluster states without the need for rerouting, thereby avoiding a massive amount of feed-forward and conditional dynamics, and furthermore show that except for a single layer of fusion measurements during the preparation, all further measurements can be shifted to the final adapted single qubit measurements. Remarkably, the cluster state preparation is achieved using essentially the same scaling in resources as if deterministic gates were available.,
2007
[pdf]
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Talks
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Linear optics state preparationAs the linear optical toolbox does not allow for interactions between single photons, these nonlinearities are simulated by projective measurements. This results in a probabilistic nature of any quantum computational scheme based entirely on linear optics. As already shown by KLM arbitrarily high success probabilities (ie. near deterministic operation of the gates) are possible in linear optics. The tradeo one has to accept are daunting overheads of optical devices and the need for expensive resource state. When it comes to experimental realization of quantum gates the question of optimal operation with limited resources arises. This includes linear optical Bell state discrimination, nonlinear sign-shift gates (building blocks for KLM s CNOT) and the CNOT gate itself. Recent results are discussed and simple tools and methods useful for adressing the question of optimal success will be presented. Especially linear optical implementations of the controlled NOT gate will be of interest.,
IQING 4 (Paris),
2005
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Optimal strategies for fusing optical cluster statesWe investigate and solve the problem of how to optimally build up cluster states for quantum computing with linear optical means using fusion gates, entirely from the perspective of classical control. We develop a notion of classical strategies and identify the optimal one to prepare linear cluster states with probabilisitic gates. We find that this globally optimal strategy gives rise to an advantage of more than an order of magnitude in the number of maximally entangled pairs already when building chains with an expected length of L = 100, compared to another strategy that could equally well be thought as being optimal. For twodimensional cluster states, we present a proof of global optimality of the asymptotic behavior in the resources. This analysis shows that the choice of appropriate classical control may lead to a very significant reduction in resource consumption.,
DPG Spring Meeting (Frankfurt),
2006
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Optimal strategies for fusing cluster states with probabilistic gatesWe investigate and solve the problem of how to optimally build up cluster states for quantum computing with probabilistic gates entirely from the perspective of classical control. As in the context of linear optics non-unit success probabilities occur quite naturally, we will focus especially on this architecture. We develop a notion of classical strategies and identify the optimal one to prepare linear cluster states. For two-dimensional cluster states we present a scheme that shows optimal behavior in the asymptotic scaling in the resources. Further, a method will be presented to achieve this scaling even without the need for expensive feed-forward during the preparation step.,
Baton Rouge,
2006
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Cluster state preparation with probabilistic gatesWe investigate and solve the problem of how to optimally build up cluster states for quantum computing with probabilistic gates entirely from the perspective of classical control. As in the context of linear optics non-unit success probabilities occur quite naturally, we will focus especially on this architecture. We develop a notion of classical strategies and identify the optimal one to prepare linear cluster states. For two-dimensional cluster states we present a scheme that shows optimal behavior in the asymptotic scaling in the resources. Further, a method will be presented to achieve this scaling even without the need for expensive feed-forward during the preparation step, thus decreasing the amount of required quantum memory.,
QUOXIC (Oxford),
2006
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Percolation, renormalization, and quantum computing with non-deterministic gatesWe apply a notion of static renormalization to the preparation of cluster 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 linear optical architectures, where probabilistic gates are inevitable. We demonstrate how to efficiently construct cluster states without the need for rerouting, thereby avoiding a massive amount of feed-forward and conditional dynamics, and furthermore show that except for a single layer of fusion measurements during the preparation, all further measurements can be shifted to the final adapted single qubit measurements. Remarkably, the cluster state preparation is achieved using essentially the same scaling in resources as if deterministic gates were available.,
International Workshop on MBQC (Oxford),
2007
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Percolation, renormalization, and quantum computing with non-deterministic gatesWe apply a notion of static renormalization to the preparation of cluster 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 linear optical architectures, where probabilistic gates are inevitable. We demonstrate how to efficiently construct cluster states without the need for rerouting, thereby avoiding a massive amount of feed-forward and conditional dynamics, and furthermore show that except for a single layer of fusion measurements during the preparation, all further measurements can be shifted to the final adapted single qubit measurements. Remarkably, the cluster state preparation is achieved using essentially the same scaling in resources as if deterministic gates were available. Further, techniques to reduce the size of the required resource states will be presented.,
DPG Spring Meeting (Düsseldorf),
2007
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Percolation, renormalization, and quantum computing with non-deterministic gatesWe apply a notion of static renormalization to the preparation of cluster 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 linear optical architectures, where probabilistic gates are inevitable. We demonstrate how to efficiently construct cluster states without the need for rerouting, thereby avoiding a massive amount of feed-forward and conditional dynamics, and furthermore show that except for a single layer of fusion measurements during the preparation, all further measurements can be shifted to the final adapted single qubit measurements. Remarkably, the cluster state preparation is achieved using essentially the same scaling in resources as if deterministic gates were available. Further, techniques to reduce the size of the required resource states will be presented.,
IQING 5 (Innsbruck),
2007
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Percolation, renormalization, and quantum computing with non-deterministic gatesWe 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. When the gate probabilities exceed some threshold of the underlying lattice, a phase transition gives rise to an asymptotically certain emergence of the desired cluster states. We demonstrate how to efficiently construct cluster states without the need for rerouting, thereby avoiding a massive amount of feed-forward and conditional dynamics. Remarkably, the cluster state preparation is achieved using essentially the same scaling in resources as if deterministic gates were available, or arbitrary conditional dynamics would have been allowed for.,
First European Young Scientists Conference on Quantum Information (Vienna),
2007
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Linear optics unleashedLinear optical architectures for quantum information pro cessing are based on single-photon sources, photon-number preserving optical elements, and photon (number resolving) detectors. Due to the allowed set of tools being narrowed down, specific problems can often be cast into a mathematical framework that allows for the assessment of possible state manipulation, measurement and preparation. The measurement based nature of optical gates and the issue of encoding qubits in a way to easily access them exp erimentally leads to a rich structure of problems. In this talk, we will discuss issues of resource consumption in optical state preparation, optimal success probabilities, and prescriptions of how to build linear optical quantum gates and measurement devices.,
DPG Spring Meeting (Darmstadt),
2008
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Percolation meets linear optical quantum computingWe 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.,
SPIE Optics and Photonics (San Diego),
2008
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Unleashing linear optics -- explicit construction of small networks,
QQQ Meeting (Paul-Drude-Institute Berlin),
2008
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New perspectives in optomechanics,
MINOS Project Meeting (IQOQI Vienna),
2008
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Measuring non-Markovian quantum noise in optomechanical systemsOptomechanical systems offer the perspective of driving mechanical modes to close to the quantum ground state by a suitable radiation pressure coupling to the light field of a cavity. In this work, we study the influence of complex thermal baths to which the mechanical mode is coupled, and discuss effects of non-Ohmic damping. Complementary to efforts of cooling down the mirror to observe quantum mechanical behaviour, a new perspective of using such systems will be presented. We will discuss ideas of using the mechanical mirror at a finite temperature as an ultrasensitive device to probe properties of complex baths
-- which are unaccessible so far. This is done without making any possibly unjustified assumptions: Using the device as a black box in systems identification, one can think of certifiably and quantitatively probing properties of decohering environments.,
DPG Spring Meeting (Hamburg),
2009
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