Already existing monomers and dimers can be used to implement our proposal, with an electronic or nuclear spin S (34,41,44,46,47,51,52,54) representing the qudit, coupled to a spin 1/2 ancilla, used for error detection.ĭesign of QEC Codes for Magnetic Molecules. We introduce error-protected states in such a molecular qudit and design the full sequence of magnetic pulses actually realizing the QEC for generic spin systems. To this aim, rather than resorting to codes based on abstract generic error models, (20,21,50) we derive a code which is specific for the class of systems we are considering and hence gives substantially better performance. (49)Ĭonversely, here we show how to encode a single logical qubit into d levels of a molecular nanomagnet ( qudit encoding), endowed with a QEC scheme to protect it against the most harmful errors occurring in molecular qubits, namely, pure dephasing. However, usually this does not work because real hardware errors in these molecular systems do not typically translate into single-qubit errors, thus making standard codes ineffective. (40−44) As far as QEC is concerned, one could think of mapping 2 n molecular levels to n qubits (45,48) and applying standard error-correction codes for independent qubits. Magnetic molecules were also largely investigated as promising platforms for quantum computation: interesting complexes were designed to meet specific schemes (31−39) and were chemically optimized to reach very long coherence times. For instance, careful tailoring of the ligand cage surrounding rare-earth ions enabled the synthesis of bistable single-ion magnets showing high-temperature magnetic hysteresis, (25−30) thus paving the way to data storage at the single-molecule level. Chemical engineering enabled the realization of molecular systems targeted for specific applications. In this respect, molecular nanomagnets represent the ideal platform, offering many accessible (electronic and nuclear) spin states which could be used to encode a protected qubit. (10) A possible way to overcome this hurdle is by employing a single multilevel quantum object to encode a logical qubit. (11−18) However, this makes the practical implementation of QEC and the corresponding quantum computation extremely difficult, because nonlocal quantum gates on a large set of physically distinct objects are needed. In standard approaches these extra-states are obtained by encoding a logical qubit into many physical units. Logical qubits are designed such that errors bring the system in a state outside the computational subspace, making errors in logical qubits detectable and correctable. (10) While non-error-corrected algorithms are based on elementary two-level units called qubits, the idea behind QEC is to encode the quantum information into “logical qubits”, objects with more than two possible energy levels. (4−9) However, protecting quantum information from its intrinsic fragility via quantum error correction (QEC) is the striking roadblock that has to be circumvented to really unleash the power of quantum computers. Basic as well as advanced theory and topics from cutting-edge research make this book invaluable at the graduate level and as a reference for experts in quantum information science.The route toward quantum computers has seen an astonishing boost in the past few years, (1,2) with noisy intermediate-scale devices (3) already available to run nontrivial quantum algorithms. It reviews various methods to control quantum errors and covers experimental and practical issues. This work focuses on quantum error correction. 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. Synopsis: Quantum computation and information is one of the most exciting developments in science and technology of the last twenty years.
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