We investigate properties of quantum mechanical systems in the light of quantum information theory. We put an emphasize on systems with infinite-dimensional Hilbert spaces, so-called continuous-variable systems'', which are needed to describe quantum optics beyond the single photon regime and other Bosonic quantum systems. We present methods to obtain a description of such systems from a series of measurements in an efficient manner and demonstrate the performance in realistic situations by means of numerical simulations. We consider both unconditional quantum state tomography, which is applicable to arbitrary systems, and tomography of matrix product states. The latter allows for the tomography of many-body systems because the necessary number of measurements scales merely polynomially with the particle number, compared to an exponential scaling in the generic case. We also present a method to realize such a tomography scheme for a system of ultra-cold atoms in optical lattices. Furthermore, we discuss in detail the possibilities and limitations of using continuous-variable systems for measurement-based quantum computing. We will see that the distinction between Gaussian and non-Gaussian quantum states and measurements plays an crucial role. We also provide an algorithm to solve the large and interesting class of naturally occurring Hamiltonians, namely frustration free ones, efficiently and use this insight to obtain a simple approximation method for slightly frustrated systems. To achieve this goals, we make use of, among various other techniques, the well developed theory of matrix product states, tensor networks, semi-definite programming, and matrix analysis. / Die stürmische Entwicklung der Quanteninformationstheorie in den letzten Jahren brachte einen neuen Blickwinkel auf quantenmechanische Probleme. Insbesondere die fundamentale Eigenschaft der Verschränkung von Quantenzuständen spielt hierbei eine Schlüsselrolle. Einstein, Podolsky und Rosen haben 1935 versucht die Unvollständigkeit der Quantenmechanik zu demonstrieren, indem sie zeigten, dass sie keine lokale, realistische Therie ist und der Ausgang einer Messung an einem Ort von Messungen abhängen kann, die an beliebig weit entfernten Orten gemacht wurden. John Bell stellte 1964 eine, später nach ihm benannte, Ungleichung auf, die eine Grenze an mögliche Korrelationen von Messergebnissen in lokalen, realistischen Theorien gibt. Die Vorhersagen der Quatenmechanik verletzen diese Ungleichung, eine Tatsache, die 1981 von Alain Aspect und anderen auch experimentell bestätigt wurde. Solche nicht-lokalen Quantenzustände werden verschränkt'' genannt. In neuerer Zeit wurde Verschränkung nicht mehr nur als mysteriöse Eigenschaft der Quantenmechanik sondern auch als Resource für Aufgaben der Informationsverarbeitung gesehen. Ein Computer, der sich diese Eigenschaften der Quantenmechanik zu nutze macht, ein sogenannter Quantencomputer, würde es erlauben gewisse Aufgaben schnell zu lösen für die normale'' Computer zu lange brauchen. Das wichtigste Beispiel hierfür ist die Zerlegung von großen Zahlen in ihre Primfaktoren, für die Shor 1993 einen Quantenalgorithmus präsentierte. In dieser Arbeit haben wir uns mit den Eigenschaften von Quantensystemen, die durch sogenannte kontinuierliche Variablen beschrieben werden, beschäftigt. Diese sind nicht nur theoretisch sonder auch experimentell von besonderem Interesse, da sie quantenoptische Systeme beschreiben, die sich verhältnismäßig leicht im Labor präparieren, manipulieren und messen lassen. Wenn man eine vollständige Beschreibung eines Quantenzustandes erhalten will, braucht man, auf Grund der Heisenberg'schen Unschärferelation, mehrere Kopien von ihm an denen man dann Messungen durchführt. Wir haben eine Methode, compressed-sensing genannt, eingeführt um die Anzahl der nötigen Messungen substantiell zu reduzieren. Wir haben die theoretische Effizienz dieser Methode bewiesen und durch numerische Simulationen auch ihre Praktikabilität demonstriert. Desweiteren haben wir beschrieben, wie man compressed-sensing für die schon erwähnten optischen Systemen sowie für ultrakalte Atome experimentell realisieren kann. Ein zweites Hauptthema dieser Arbeit war messbasiertes Quantenrechnen. Das Standardmodell des Quantenrechnens basiert auf sogenannten Gattern, die eine genaue Kontrolle der Wechselwirkung zwischen den Bestandteilen des Quantencomputers erfordern. Messbasiertes Quantenrechnen hingegen kommt mit der Präparation eines geeigneten Quantenzustands, Resource genannt, gefolgt von einfachen Messungen auf diesem Zustand aus. Wir haben gezeigt, dass Systeme mit kontinuierlichen Variablen eine vorteilhafte Realisierung eines Quantencomputers in diesem Paradigma erlauben, es jedoch auch wichtige Beschränkungen gibt, die kompliziertere Zustandspräparationen und Messungen nötig machen.

Η κατασκευή ενός ολοκληρωμένου κβαντικού υπολογιστή αποτελεί μια πρόκληση για τη σύγχρονη επιστήμη. Ο κβαντικός υπολογιστής μας δίνει την ελπίδα πως κάποια στιγμή στο κοντινό μέλλον, θα είμαστε σε θέση να λύνουμε προβλήματα ταχύτερα και πιο αποδοτικά από ότι κάνει ένας κλασσικός υπολογιστής σήμερα. Για παράδειγμα, ο κβαντικός αλγόριθμος παραγοντοποίησης του Shor [3] πετυχαίνει εκθετική επιτάχυνση έναντι του κλασσικού, κάτι που σημαίνει πως η χρήση του πρωτόκολλου κρυπτογράφησης RSA δεν θα είναι όσο ασφαλής είναι σήμερα. Αυτό θα έχει ως αποτέλεσμα μεγάλες αλλαγές στις επικοινωνίες και στις συναλλαγές στο προσεχές μέλλον. Στην παρούσα διπλωματική εργασία θα περιγράψουμε τις αρχές που πρέπει να πληρεί ένα κβαντικό σύστημα για να θεωρηθεί κβαντικός υπολογιστής, πώς υλοποιούμε ένα qubit που είναι η μονάδα πληροφορίας του και τέλος θα μιλήσουμε για το πώς κωδικοποιούμε την κβαντική πληροφορία ώστε να είμαστε σε θέση να τη διορθώσουμε. Αρχίζουμε με τη διατύπωση των αρχών της κβαντικής μηχανικής , όπως προκύπτουν από την πειραματική διαδικασία. Συνεχίζουμε με την υπεραγωγιμότητα, το φαινόμενο που μας επιτρέπει να χειριζόμαστε μακροσκοπικά της κβαντικές ιδιότητες της ύλης, όπως και κάποια ακόμα φαινόμενα, όπως αυτό του Meissner, που μας δίνουν τη δυνατότητα να δημιουργήσουμε το κυκλώμα που υλοποιεί το qubit. Τέλος, περιγράφουμε θεωρητικά ένα καθολικό σύνολο από κβαντικές πύλες και τα κυκλώματα διόρθωσης λαθών κβαντικού κώδικα. / The construction of an integrated quantum computer is a challenge for modern science. The quantum computer gives us hope that sometime in the near future, we will be able to solve problems faster and more efficiently than does a conventional computer today. For example, the Shor's quantum algorithm for factoring [3] gave exponential acceleration compared to the classical one, which means that the use of RSA encryption protocol will not be safe as it is today. This will result large changes in communications and transactions in the near future. In this paper we describe the principles that must meet a quantum system to be considered as a quantum computer, how do we implement a qubit which is the unit of information, and finally we'll talk about how we encode quantum information in order to be able to fix it . We begin with the formulation of the principles of quantum mechanics, derived from the experimental procedure. We continue with the superconductivity phenomenon that allows us to manipulate the macroscopic quantum properties of matter, and even some phenomena such as the Meissner, who enable us to create a circuit that implements the qubit. Finally, we describe theoretically a universal set of quantum gates and circuits of error correcting quantum code.

No description available.

One way of realizing a quantum computer is to use an ion trap. The research group Trapped Ion Quantum Technologies at Stockholm university were operating an ion trap with strontium ions. To increase the coherence time they installed a magnetic field shielding. Therefore the experimental setup had to be partially rebuilt. A new 405 nm laser was installed in order to speed up the ionization step of neutral strontium atoms. The characterization of the laser was performed and it showed that the laser could be operated at the required wavelength. The wavelength was characterized with respect to temperature and power. A scan of the 422 nm Doppler cooling laser was also performed and it showed that the Doppler cooling worked as intended. Lastly, Rabi oscillations were performed to see if coherent manipulation of the ion's quantum state worked as intended. This experiment was also successful but it showed some differences between having the magnetic shielding door open or closed which should be investigated further.

The performances of two D-Wave 2 machines (476 and 496 qubits) and of a 1097-qubit D-Wave 2X were investigated. Each chip has a Chimera interaction graph G. Problem input consists of values for the fields hj and for the two-qubit interactions Ji,j of an Ising spin-glass problem formulated on G. Output is returned in terms of a spin configuration {sj}, with sj = +1 or -1. We generated random spanning trees (RSTs) uniformly distributed over all spanning trees of G. On the 476-qubit D-Wave 2, RSTs were generated on the full chip with Ji,j = -1 and hj = 0 and solved one thousand times. The distribution of solution energies and the average magnetization of each qubit were determined. On both the 476- and 1097-qubit machines, four identical spanning trees were generated on each quadrant of the chip. The statistical independence of the these regions was investigated.

Quantum computation has been a rich field of study for decades because it promises possible spectacular advances, some of which may run counter to our classically rooted intuitions. At the same time, quantum computation is still in its infancy in both theoretical and practical areas. Efficient quantum algorithms are very limited in number and scope; no real breakthrough has yet been achieved in physical implementations. Grover's search algorithm can be applied to a wide range of problems; even problems not generally regarded as searching problems can be reformulated to take advantage of quantum parallelism and entanglement leading to algorithms which show a square root speedup over their classical counterparts. This dissertation discusses a systematic way to formulate such problems and gives as an example a quantum scheduling algorithm for an R||C_max problem. This thesis shows that quantum solution to such problems is not only feasible but in some cases advantageous. The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting only a single error per error correction cycle. Yet, time-correlated errors are common for physical implementations of quantum systems; an error corrected during a certain cycle may reoccur in a later cycle due to physical processes specific to each physical implementation of the qubits. This dissertation discusses quantum error correction for a restricted class of time-correlated errors in a spin-boson model. The algorithm proposed allows the correction of two errors per error correction cycle, provided that one of them is time-correlated. The algorithm can be applied to any stabilizer code, perfect or non-perfect, and simplified the circuit complexity significantly comparing to the classic quantum error correction codes.

<p dir="ltr">Quantum computing is advancing rapidly, with variational quantum algorithms (VQAs) showing great promise for demonstrating quantum advantage on near-term devices. A critical component of VQAs is the ansatz, a parameterized quantum circuit that is iteratively optimized. However, compiling ansatz circuits for specific quantum hardware is challenging due to topological constraints, gate errors, and decoherence. This thesis presents a series of techniques to efficiently generate and optimize quantum circuits, with a focus on VQAs. We first introduce AccQOC, a framework combining static pre-compilation with accelerated dynamic compilation to transform quantum gates to hardware pulses using quantum optimal control (QOC). AccQOC generates pulses for frequently used gate sequences in advance and stores them in a lookup table. For new gate sequences, it utilizes a Minimum Spanning Tree based approach to find the optimal compilation order that maximizes the similarity between consecutive sequences, thereby accelerating the compilation process. By leveraging pre-computed pulses and employing a similarity-based approach, AccQOC achieves a 9.88×speedup in compilation time compared to standard QOC methods while maintaining a 2.43×latency reduction over gate-based compilation. Building on AccQOC, we propose EPOC, an extended framework integrating circuit partitioning, ZX-calculus optimization, and synthesis methods. EPOC operates at a finer granularity compared to previous coarse-grained approaches, decomposing circuits into smaller sub-circuits based on the number of qubits and circuit depth. It then applies synthesis techniques to identify equivalent representations with reduced gate count. The optimized sub-circuits are then grouped into larger unitary matrices, which are used as inputs for QOC. This approach enables increased parallelism and reduced latency in the resulting quantum pulses. Compared to the state-of-the-art pulse optimization framework, EPOC achieves a 31.74% reduction in circuit latency and a 76.80% reduction compared to gate-based methods. To construct hardware-efficient ansatz for VQAs, we introduce two novel approaches. TopGen is a topology-aware bottom-up approach that generates sub-circuits according to the connectivity constraints of the target quantum device. It starts by generating a library of subcircuits that are compatible with the device topology and evaluates them based on metrics 17 like expressibility and entangling capability. The sub-circuits with the best properties are then selected and progressively combined using different techniques. TopGen also employs dynamic circuit growth, where small sub-circuits are appended to the ansatz during training, and gate pruning, which removes gates with small parameters. Evaluated on a range of VQA tasks, TopGen achieves an average reduction of 50% in circuit depth after compilation compared to previous methods. NAPA takes a more direct approach by utilizing devicenative parametric pulses as the fundamental building blocks for constructing the ansatz. It uses cross-resonance pulses for entangling qubits and DRAG pulses for single-qubit rotations. The ansatz is constructed in a hardware-efficient manner. By using the better flexibility and expressivity of parametric pulses, NAPA demonstrates up to 97.3% latency reduction while maintaining accuracy comparable to gate-based approaches when evaluated on real quantum devices. Finally, we explore error mitigation techniques for VQAs at the pulse level. We develop a fidelity estimator based on reversed pulses, that enables randomized benchmarking of parametric pulses. This estimator compares the final state obtained after applying a sequence of pulses followed by their reversed counterparts to the initial state, using the probability of successful trials as a proxy for fidelity. Furthermore, we adapt the zero-noise extrapolation (ZNE) technique to the pulse level, enabling the error mitigation for quantum pulses. Applied to VQE tasks for H2 and HeH+ molecules, pulse-level ZNE reduces the deviation from ideal expectation values by an average of 54.1%. The techniques developed in this thesis advance the efficiency and practicality of VQAs on near-term quantum devices. The introduced frameworks, AccQOC and EPOC, provide efficient pulse optimization, while TopGen and NAPA can construct hardware-efficient ansatz. Besides, the pulse-level error mitigation techniques presented in this thesis improve the resilience of VQAs against the inherent noise and imperfections of NISQ devices. Together, these contributions help unlock the full potential of quantum computing and realize practical quantum advantages in the near future.</p>

Quantum mechanics has a long history of helping computer science. For a long time, it provided help only at the hardware level by giving a better understanding of the properties of matter and thus allowing the design of ever smaller and ever more efficient components. For the last few decades, much research has been dedicated to finding whether one can change computer science even more radically by using the principles of quantum mechanics at both the hardware and algorithm levels. This field of research called Quantum Information Processing (QIP) has rapidly seen interesting theoretical developments: it was in particular shown that using superposition of states leads to computers that could outperform classical ones. The experimental side of QIP however lags far behind as it requires an unprecedented amount of control and understanding of quantum systems. Much effort is spent on finding which particular systems would provide the best physical implementation of QIP concepts. Because of their nearly endless versatility and the high degree of control over their synthesis, organic materials deserve to be assessed as a possible route to quantum computers. This thesis studies the QIP potential of spin degrees of freedom in several such organic compounds. Firstly, a study on low-spin antiferromagnetic rings is presented. It is shown that in this class of molecular nanomagnets the relaxation times are much longer than previously expected and are in particular long enough for up to a few hundred quantum operations to be performed. A detailed study of the relaxation mechanisms is presented and, with it, routes to increasing the phase coherence time further by choosing the suitable temperature, isotopic and chemical substitution or solvent. A study of higher-spin systems is also presented and it is shown that the relaxation mechanisms are essentially the same as in low-spin compounds. The route to multi-qubit system is also investigated: the magnetic properties of several supermolecular assemblies, in particular dimers, are investigated. Coupling between neighbouring nanomagnets is demonstrated and experimental issues are raised concerning the study of the coherent dynamics of dimers. Finally a study of the purely organic compound phenanthrene is reported. In this molecule the magnetic moment does not result from the interactions between several transition metal ions as in molecular nanomagnets but from the photoexcitation of an otherwise diamagnetic molecule. The interest of such a system in terms of QIP is presented and relaxation times and coupling to relevant nuclei are identified.

This thesis is based on top of the previous thesis "Security of modern encryption protocols" where we introduced a new paradigm for constructing quantum circuits. We have built circuits for modular arithmetic (addition, multiplication and exponentiation) in order to break El-Gamal asymmetric cryptosystem. Current thesis reviews all proposed circuits and discusses possibilities of their further optimization in goal of lowering the number of used qbits at least by an order of magnitude. It also shows that this is not possible due to existence of COPY gates which make the design inherently unoptimizable. Getting rid of COPY gates is, however, not possible without substantial rewrite of the whole paradigm. The overall estimate of number of qbits used in circuits thus remains O(log(m)log^2(N)) where m is a processed number and N is a modulus. The thesis also proposes optimization of the modular multiplication circuit that, if issues with COPY gates are resolved, allows us to lower the number of used qbits by about O(log(m)) at the price of a longer execution time.

Image charge detection is presented as a possible candidate to realise deterministic ion implantation. The deterministic placement of single impurities in solid substrates will enable a variety of novel applications, using their quantum mechanical properties for sensors or qubit registers. In this work, experimental techniques are used together with theoretical calculations to develop, characterise and optimise the detection of charged objects in a single pass through an image charge detector. In the main experimental part, ion bunches are employed as a model system for highly charged ions in proof-of-principle measurements with detector prototypes built in our labs. Image charge signals are characterised in the time and frequency domain. Using a statistical measurement and data analysis protocol, the noise and signal probability density functions are determined to calculate error and detection rates. It was found that even at an extremely low signal-to-noise ratio of 2, error rates can be suppressed effectively for high fidelity implantation. Aiming to improve the sensitivity, the maximum possible signal-to-noise ratio is calculated and discussed in dependence on the design parameters of an optimised image charge detector and the kinetic ion parameters. Lastly, a new ion implantation set-up combining focused ion beam technology with a source able to produce highly charged ions is introduced.