![]() ![]() Specifically:ĭefinition 1 Let H n be a 2 n-dimensional Hilbert space (n qubits), and let C be a K-dimensional subspace of H n. Quantum error correction could be used to combat noise in starlight captured by telescopes. (9.45)). A proposed solution to this issue is Quantum Error Correction (QEC), which aims to rectify the corrupted qubit state through a three-step process: (i) detection: identifying the presence of an error, (ii) decoding: pinpointing the location (s) of the affected qubit (s), and (iii) correction: restoring the faulty qubits to their original states. In general, a quantum error-correcting code is a subspace of a Hilbert space designed so that any of a set of possible errors can be corrected by an appropriate quantum operation. where the ith row corresponds to finite geometry representation of the generator g i (see Eq. The theory of fault-tolerant quantum computation tells us how to perform operations on states encoded in a quantum error-correcting code without compromising the code's ability to protect against errors. To build a quantum computer, we face an even more daunting task: If our quantum gates are imperfect, everything we do will add to the error. ![]() Currently, we are actively involved in a number of. By adding extra qubits and carefully encoding the quantum state we wish to protect, a quantum system can be insulated to great extent against errors. Quantum error correction works by encoding the quantum information in a way that allows errors to be detected and corrected. According to Franco Nori, 'Machine learning can play a pivotal role in addressing large-scale quantum computation and optimization challenges. The theory of quantum error-correcting codes has been developed to counteract noise introduced in this way. Any qubit stored unprotected or one transmitted through a communications channel will inevitably come out at least slightly changed. Building a quantum computer or a quantum communications device in the real world means having to deal with errors.
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