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Quantum error seminar6/3/2023 ![]() Ensuring high-fidelity entanglement has always been a challenging task owing to interaction with the hostile channel environment created due to quantum noise and decoherence. Quantum entanglement is a unique criterion of the quantum realm and an essential tool to secure quantum communication. Our results, which are in good agreement with those obtained using quantum simulators, reveal the potential of matrix product density operators for the investigation of the performance of quantum devices with a large number of qubits and deep noisy quantum circuits. On the other, zero-noise extrapolation may be employed to recover quantum revivals of the Loschmidt echo, which would be completely missed in the absence of mitigation, and to retrieve faithfully noise-free inter-site correlations. On the one hand, interestingly, noise alters systematically the behavior of the Loschmidt echo at the dynamical phase transition times, doubling the number of non-analytic points, and hence inducing an error that, inherently, cannot be mitigated. Our analysis, based on matrix product density operators, of the transverse-field Ising model with depolarizing noise, reveals both advantages and inherent problems associated with zero-noise extrapolation when simulating non-equilibrium many-body dynamics. ![]() Zero-noise extrapolation provides an especially useful error mitigation method for noisy intermediate-scale quantum devices. ![]() Basic subjects as well as advanced theory and a survey of topics from cutting-edge research make this book invaluable both as a pedagogical introduction at the graduate level and as a reference for experts in quantum information science. The book is not limited to a single approach, but reviews many different methods to control quantum errors, including topological codes, dynamical decoupling and decoherence-free subspaces. This comprehensive text, written by leading experts in the field, focuses on quantum error correction and thoroughly covers the theory as well as experimental and practical issues. Scalable quantum computers require a far-reaching theory of fault-tolerant quantum computation. To achieve large scale quantum computers and communication networks it is essential not only to overcome noise in stored quantum information, but also in general faulty quantum operations. Quantum computation and information is one of the most exciting developments in science and technology of the last twenty years.
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