Spin transport and quasi 2D architectures for donor-based quantum computing

Through the introduction of a new electron spin transport mechanism, a 2D donor electron spin quantum computer architecture is proposed. This design addresses major technical issues in the original Kane design, including spatial oscillations in the exchange coupling strength and cross-talk in gate control. It is also expected that the introduction of a degree of non-locality in qubit gates will significantly improve the scaling fault-tolerant threshold over the nearest-neighbour linear array.Comment: 4 pages, 5 figures, v2 reference adde

Towards the Design Automation of Quantum Circuits

Quantum mechanics based computing systems are expected to have high capabilities and are considered good candidates to replace classical cryptography and supercomputing systems. Among many implementations, quantum optics systems provide a promising platform to implement universal quantum computers, since they link quantum computation and quantum communication in the same framework. Recently, several quantum gates, circuits, and protocols have been experimentally realized using optics. Despite the fact that big advances in building the physical quantum computers were achieved, there are no currently available industrial computer aided tools that can perform the modeling, analysis, and verification of optical quantum computing systems. In this thesis, we tackle the idea of design automation for quantum circuits, where we use a sound language, higher order logic, to model and reason about quantum circuits formally. In particular, we propose a framework for the hierarchical modeling and automated verification of quantum computing circuits. The modeling approach captures quantum models built hierarchically from quantum gates, which models are readily available in a library. The analysis and verification of composed circuits is done seamlessly based on dedicated mathematical foundations formalized in the theorem prover. Specifically, the tensor product and linear projection are used to extract the quantum circuit outputs. Subsequently, a rich library of quantum gates which includes 1-qubit, 2-qubit, and 3-qubit gates is formalized. In order to automate the analysis process, we developed a decision procedure to eliminate the need of user guidance throughout the formal proofs. To demonstrate the effectiveness of the proposed framework, we conduct the formal analysis of a benchmark of quantum circuits including the Shor's integer factorization algorithm, the Grover's oracle, and the quantum full adder

Quantum State Transfer with Spin Chains

The thesis covers various aspects of quantum state transfer in permanently coupled spin systems.Comment: PhD thesis, December 2006, University College London, 142 page

Understanding Quantum Technologies 2022

Understanding Quantum Technologies 2022 is a creative-commons ebook that provides a unique 360 degrees overview of quantum technologies from science and technology to geopolitical and societal issues. It covers quantum physics history, quantum physics 101, gate-based quantum computing, quantum computing engineering (including quantum error corrections and quantum computing energetics), quantum computing hardware (all qubit types, including quantum annealing and quantum simulation paradigms, history, science, research, implementation and vendors), quantum enabling technologies (cryogenics, control electronics, photonics, components fabs, raw materials), quantum computing algorithms, software development tools and use cases, unconventional computing (potential alternatives to quantum and classical computing), quantum telecommunications and cryptography, quantum sensing, quantum technologies around the world, quantum technologies societal impact and even quantum fake sciences. The main audience are computer science engineers, developers and IT specialists as well as quantum scientists and students who want to acquire a global view of how quantum technologies work, and particularly quantum computing. This version is an extensive update to the 2021 edition published in October 2021.Comment: 1132 pages, 920 figures, Letter forma

Multipartite entanglement and quantum algorithms

[eng] Quantum information science has grown from being a very small subfield in the 70s until being one of the most dynamic fields in physics, both in fundamentals and applications. In the theoretical section, perhaps the feature that has attracted most interest is the notion of entanglement, the ghostly relation between particles that dazzled Einstein and has provided fabulous challenges to build a coherent interpretation of quantum mechanics. While not completely solved, we have today learned enough to feel less uneasy with this fundamental problem, and the focus has shifted towards its potential powerful applications. Entanglement is now being studied from different perspectives as a resource for performing information processing tasks. With bipartite entanglement being largely understood nowadays, many questions remain unanswered in the multipartite case. The first part of this thesis deals with multipartite entanglement in different contexts. In the first chapters it is studied within the whole corresponding Hilbert space, and we investigate several entanglement measures searching for states that maximize them, including violations of Bell inequalities. Later, focus is shifted towards hamiltonians that have entangled ground states, and we investigate entanglement as a way to establish a distance between theories and we study frustration and methods to efficiently solve hamiltonians that exhibit it. In the practical section, the most promised upcoming technological advance is the advent of quantum computers. In the 90s some quantum algorithms improving the performance of all known classical algorithms for certain problems started to appear, while in the 2000s the first universal computers of few atoms began to be built, allowing implementation of those algorithms in small scales. The D-Wave machine already performs quantum annealing in thousands of qubits, although some controversy over the true quantumness of its internal workings surrounds it. Many countries in the planet are devoting large amounts of money to this field, with the recent European flagship and the involvement of the largest US technological companies giving reasons for optimism. The second part of this thesis deals with some aspects of quantum computation, starting with the creation of the field of cloud quantum computation with the appearance of the first computer available to the general public through internet, which we have used and analysed extensively. Also small incursions in quantum adiabatic computation and quantum thermodynamics are present in this second part.[cat] La informació quàntica ha crescut des d'un petit subcamp als anys setanta fins a esdevenir un dels camps més dinàmics de la física actualment, tant en aspectes fonamentals com en les seves aplicacions. En la secció teòrica, potser la propietat que ha atret més interès és la noció d'entrellaçament, la relació fantasmagòrica entre partícules que va deixar estupefacte Einstein i que ha suposat un enorme desafiament per a construir una interpretació coherent de la mecànica quàntica. Sense estar totalment solucionat, hem après prou per sentir-nos menys incòmodes amb aquest problema fonamental i el focus s'ha desplaçat a les seves aplicacions potencials. L'entrellaçament s'estudia avui en dia des de diferents perspectives com a recurs per realitzar tasques de processament de la informació. L'entrellaçament bipartit està ja molt ben comprès, però en el cas multipartit queden moltes qüestions obertes. La primera part d'aquesta tesi tracta de l'entrellaçament multipartit en diferents contextos. Estudiem l'hiperdeterminant com a mesura d'entrellaçament el cas de 4 qubits, analitzem l'existència i les propietats matemàtiques dels estats absolutament màximament entrellaçats, trobem noves desigualtats de Bell, estudiem l'espectre d'entrellaçament com a mesura de distància entre teories i estudiem xarxes tensorials per tractar eficientment sistemes frustrats. En l'apartat pràctic, el més prometedor avenç tecnològic del camp és l'adveniment dels ordinadors quàntics. La segona part de la tesi tracta d'alguns aspectes de computació quàntica, començant per la creació del camp de la computació quàntica al núvol, amb l'aparició del primer ordinador disponible per al públic general, que hem usat extensament. També fem petites incursions a la computació quàntica adiabàtica i a la termodinàmica quàntica en aquesta segona par

Notes on Quantum Computation and Information

We discuss fundamentals of quantum computing and information - quantum gates, circuits, algorithms, theorems, error correction, and provide collection of QISKIT programs and exercises for the interested reader.Comment: v2: 86 pages, 97 references. Refined the text, fixed several typos, added some text on continuous variables, and added few solved example problems. v1: 72 pages, 76 references. Suggestions, comments, and corrections are very welcome

La Logistica del Computer Quantistico e l'Informatica Relativa

Notizie da giornali e siti web riportato sempre più enfaticamente i successi relativi a computer quantistici. È pertanto naturale porsi delle domante circa questi computer, su come essi operano, su dove sono fisicamente, su cosa serve alla loro gestione. Anzi, è doveroso porsi domande, poiché i titoli delle notizie possono indurre ad intenderli come “supercomputer” effettivamente esistenti, capaci di risolvere in pochi secondi dei problemi di calcolo che i computer classici impiegherebbero millenni a processare. Questo lavoro propone quindi una review degli attuali Computer Quantistici, con particolare riguardo, ove possibile, alla relativa logistica. Nel panorama dell’Informatica Quantistica, si intende approfondire come potrà essere il futuro delle infrastrutture ad essi legate e quali saranno i sistemi base di algoritmi relativi al Calcolo Quantistico. In definitiva, si cercherà di comprendere quale sarà la futura logistica, intesa come nuova «arte del computare». Particolare attenzione verrà data al vantaggio quantistico, la strategia di medio termine relativa alla progettazione di algoritmi per le prossime generazioni di computer quantistici. Tali algoritmi sono richiesti da un ventaglio di applicazioni strategiche. Attualmente sono principalmente algoritmi di simulazione di fisica e chimica quantistica. Si illustreranno due metodi di calcolo: quello basato sulla computazione quantistica abiabatica, che si ottiene attraverso il quantum annealing (sistemi D-Wave), e quello che utilizza un array di porte quantistiche (sistemi IBM, Google ed altri). Si vedranno, con maggiore dettaglio, le simulazioni basate sul metodo del Variational Quantum Eigensolver. Alcune nozioni relative ai qubit, alle porte quantistiche ed alle Hamiltoniane ad esse legate verranno proposte. Oltre a parlare di qubit, si parlerà di qumode. L’arte del computare quantistico ha infatti due facce, quella basata sul qubit e quella basata sul qumode. Il quantum computer Borealis di Xanadu è capace di sviluppare un sistema ibrido, con una emulazione di qubit di tipo GKP insieme a luce squeezed. Verrà inoltre menzionato il primo desktop a tre qubits di SpinQ. Verrà anche fornito un accenno alla comunicazione quantistic

Quantum information dynamics

Presented is a study of quantum entanglement from the perspective of the theory of quantum information dynamics. We consider pairwise entanglement and present an analytical development using joint ladder operators, the sum of two single-particle fermionic ladder operators. This approach allows us to write down analytical representations of quantum algorithms and to explore quantum entanglement as it is manifested in a system of qubits.;We present a topological representation of quantum logic that views entangled qubit spacetime histories (or qubit world lines) as a generalized braid, referred to as a super-braid. The crossing of world lines may be either classical or quantum mechanical in nature, and in the latter case most conveniently expressed with our analytical expressions for entangling quantum gates. at a quantum mechanical crossing, independent world lines can become entangled. We present quantum skein relations that allow complicated superbraids to be recursively reduced to alternate classical histories. If the superbraid is closed, then one can decompose the resulting superlink into an entangled superposition of classical links. Also, one can compute a superlink invariant, for example the Jones polynomial for the square root of a knot.;We present measurement-based quantum computing based on our joint number operators. We take expectation values of the joint number operators to determine kinetic-level variables describing the quantum information dynamics in the qubit system at the mesoscopic scale. We explore the issue of reversibility in quantum maps at this scale using a quantum Boltzmann equation. We then present an example of quantum information processing using a qubit system comprised of nuclear spins. We also discuss quantum propositions cast in terms of joint number operators.;We review the well known dynamical equations governing superfluidity, with a focus on self-consistent dynamics supporting quantum vortices in a Bose-Einstein condensate (BEC). Furthermore, we review the mutual vortex-vortex interaction and the consequent Kelvin wave instability. We derive an effective equation of motion for a Fermi condensate that is the basis of our qubit representation of superfluidity.;We then present our quantum lattice gas representation of a superfluid. We explore aspects of our model with two qubits per point, referred to as a Q2 model, particularly its usefulness for carrying out practical quantum fluid simulations. We find that it is perhaps the simplest yet most comprehensive model of superfluid dynamics. as a prime application of Q2, we explore the power-law regions in the energy spectrum of a condensate in the low-temperature limit. We achieved the largest quantum simulations to date of a BEC and, for the first time, Kolmogorov scaling in superfluids, a flow regime heretofore only obtainably by classical turbulence models.;Finally, we address the subject of turbulence regarding information conservation on the small scales (both mesoscopic and microscopic) underlying the flow dynamics on the large hydrodynamic (macroscopic) scale. We present a hydrodynamic-level momentum equation, in the form of a Navier-Stokes equation, as the basis for the energy spectrum of quantum turbulence at large scales. Quantum turbulence, in particular the representation of fluid eddies in terms of a coherent structure of polarized quantum vortices, offers a unique window into the heretofore intractable subject of energy cascades

Modern applications of machine learning in quantum sciences

In these Lecture Notes, we provide a comprehensive introduction to the most recent advances in the application of machine learning methods in quantum sciences. We cover the use of deep learning and kernel methods in supervised, unsupervised, and reinforcement learning algorithms for phase classification, representation of many-body quantum states, quantum feedback control, and quantum circuits optimization. Moreover, we introduce and discuss more specialized topics such as differentiable programming, generative models, statistical approach to machine learning, and quantum machine learning