Hybrid quantum information processing under noise

Quantum information processing holds the promise of practical applications in quantum computation and quantum communication, with the possibility to solve problems no classical device could, or establishing secure communication. However, to make use of such quantum advantages, it is crucial to overcome the influence of noise and decoherence, and to protect quantum information against their detrimental effects. Quantum error correction and entanglement purification have been established as tools to provide such a protection. However, there are stringent requirements on the accuracy of local control operations and gates, and the necessary overheads, such that these methods can be successfully applied. For practical applications it is crucial to provide optimized schemes with minimal overheads, and with large tolerable errors. For this purpose, new avenues and approaches need to be considered. Using elements of measurement-based quantum information processing is one such approach. In contrast to the standard gate-based approach, elementary building blocks such as decoding circuits or encoded gates are realized in a measurement-based way, without the need of coherent entangling gates that might be difficult to realize. Entangled states that can be pre-prepared offline are used as a resource to establish the desired information processing by measurements only. The key challenge is to prepare certain entangled states with a sufficiently high fidelity, where recent investigations indicate that such an approach might offer significant advantages in terms of acceptable error rates. In this project we will investigate the application of such measurement-based elements in hybrid schemes for quantum communication and computation in the presence of noise and decoherence, where they are combined in an optimized way with circuit based approaches. In particular, we plan to carry out the following work: Investigation andanalysis of novel schemes for long-distance quantum communication using measurement-based elements. Proposals and analysis for the usage of measurement-based elements in fault- tolerant universal quantum computation, including justification of error models, threshold analysis and applicability with limited resources. Design and analysis of measurement-based schemes for entanglement purification, magic state distillation, quantum cryptography and other quantum information processing tasks, including security proof for quantum cryptography. Investigation of optimized small-scale implementations for quantum error correction and entanglement purification for the usage in quantum communication networks, including proposals for experimental realization with photons and ions.

Quantum information processing offers unprecedented possibilities by using quantum features, which allow one to solve problems no classical device could, or to achieve tasks such as provable secure communication or precision measurements with improved accuracy. However, to make use of such quantum advantages, it is crucial to overcome the influence of noise and decoherence, and to protect quantum information against their detrimental effects. In this project we have put forward novel approaches to deal with the influence of noise and imperfections in quantum computation, quantum communication and other quantum information processing tasks. One key ingredient of our theoretical studies is the usage of measurement-based elements for quantum information processing, which uses quantum entanglement as a resource to perform desired operations and tasks by measuring individual systems. We have shown that such an approach offers significantly larger error thresholds and tolerances (of up to tens of percent per qubit) as a comparable gate-based approach. The key results we found are in different areas and include: Quantum computation: Establishing (hybrid) schemes with very high error thresholds, including the justification of used error model and efficient construction of required resource states. Quantum networks and quantum communication: Noise-resistant schemes for long- distance quantum communication for big quantum data in bipartite and multipartite settings. Design of quantum communication networks beyond point-to-point communication, including theoretical development and experimental realizations for long-distance distribution of multipartite entangled states using 2D quantum repeaters. Such schemes may be a key ingredient in future large-scale multi-user quantum networks. A security proof for secure classical and quantum communication based on the usage of entanglement purification, extending and simplifying security proofs for quantum cryptography.Noisy quantum metrology: Various proposals of how to deal with the influence of noise and imperfections in quantum metrology, including ultimate limits imposed by noise and possible ways to maintain improved quantum scaling using fast control or encodings. A unified approach to quantum metrology using a universal resource state for sensing Limitations on large-scale quantum effects Establishing limits on the preparation, maintenance and detection of large-scale quantum states and effects, e.g. the requirement of a measurement device the size of the earth to detect a cat in a superposition state.