Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence

We propose a family of exactly solvable toy models for the AdS/CFT correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. Our building block is a special type of tensor with maximal entanglement along any bipartition, which gives rise to an isometry from the bulk Hilbert space to the boundary Hilbert space. The entire tensor network is an encoder for a quantum error-correcting code, where the bulk and boundary degrees of freedom may be identified as logical and physical degrees of freedom respectively. These models capture key features of entanglement in the AdS/CFT correspondence; in particular, the Ryu-Takayanagi formula and the negativity of tripartite information are obeyed exactly in many cases. That bulk logical operators can be represented on multiple boundary regions mimics the Rindler-wedge reconstruction of boundary operators from bulk operators, realizing explicitly the quantum error-correcting features of AdS/CFT recently proposed by Almheiri et. al in arXiv:1411.7041.Comment: 40 Pages + 25 Pages of Appendices. 38 figures. Typos and bibliographic amendments and minor correction

QUANTUM EVOLUTIONARY ALGORITHM FOR QUANTUM CIRCUIT SYNTHESIS

Quantum computing area has a lot research attention due to opportunities that possessing such device could provide. For example, quantum computers could deliver new insights to previously unsolvable problems. The reason for that is higher parallel capabilities of such devices. In addition, since quantum computers are naturally reversible, no heat dissipation occurs during computation [21]. This property could serve as a viable solution to the problem that computer chip production industry faces. Moreover, since the chip manufacturing industry reaches nanometer scale of size of elements, the effects that could cause unexpected information behavior in classical paradigm are part of the technology of quantum devices [31, 14]. Considering possible benefits that could be achieved by quantum computing devices, the new areas of Quantum Information Theory, Quantum Cryptography, Quantum Algorithms and Logic Design and many others emerged at the end of the twentieth century [31]. These areas are concentrating their efforts on solving problems of designing communication protocols, ensuring the security of the new systems, constructing appropriate algorithms. Computers that could be advancing in finding solutions in problems listed above require quantum circuits that have optimal structure and could implement error correction. This is the main motivation for this thesis work to explore the problem of circuit design. The approach that we investigate is circuit construction by the means of Quantum Evolutionary Algorithms. We propose a version of an algorithm that accounts with specificity and constraints of quantum paradigm. We use its Graphic Processing Unit (GPU) accelerated classical implementation to evaluate the behavior and performance of the proposed algorithm. Later we discuss additional complexity introduced by accounting with these constraints. We support our ideas with results of synthesis of small circuits and compare the performance with classical genetic algorithm on similar task

Conceptual understanding through efficient automated design of quantum optical experiments

Artificial intelligence (AI) is a potentially disruptive tool for physics and science in general. One crucial question is how this technology can contribute at a conceptual level to help acquire new scientific understanding. Scientists have used AI techniques to rediscover previously known concepts. So far, no examples of that kind have been reported that are applied to open problems for getting new scientific concepts and ideas. Here, we present Theseus, an algorithm that can provide new conceptual understanding, and we demonstrate its applications in the field of experimental quantum optics. To do so, we make four crucial contributions. (i) We introduce a graph-based representation of quantum optical experiments that can be interpreted and used algorithmically. (ii) We develop an automated design approach for new quantum experiments, which is orders of magnitude faster than the best previous algorithms at concrete design tasks for experimental configuration. (iii) We solve several crucial open questions in experimental quantum optics which involve practical blueprints of resource states in photonic quantum technology and quantum states and transformations that allow for new foundational quantum experiments. Finally, and most importantly, (iv) the interpretable representation and enormous speed-up allow us to produce solutions that a human scientist can interpret and gain new scientific concepts from outright. We anticipate that Theseus will become an essential tool in quantum optics for developing new experiments and photonic hardware. It can further be generalized to answer open questions and provide new concepts in a large number of other quantum physical questions beyond quantum optical experiments. Theseus is a demonstration of explainable AI (XAI) in physics that shows how AI algorithms can contribute to science on a conceptual level

Quantum logic and entanglement by neutral Rydberg atoms: methods and fidelity

Quantum gates and entanglement based on dipole-dipole interactions of neutral Rydberg atoms are relevant to both fundamental physics and quantum information science. The precision and robustness of the Rydberg-mediated entanglement protocols are the key factors limiting their applicability in experiments and near-future industry. There are various methods for generating entangling gates by exploring the Rydberg interactions of neutral atoms, each equipped with its own strengths and weaknesses. The basics and tricks in these protocols are reviewed, with specific attention paid to the achievable fidelity and the robustness to the technical issues and detrimental innate factors.Comment: 57 pages, 10 figure