Quantum Error Correction Codes
Optimizing Quantum Error Correction Codes with Reinforcement Learning
... a quantum computation, we ask how the structure of the quantum mechanical system itself can be changed, both a priori and during a compu- ...QEC codes which we apply to a family of surface ...
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Quantum error correction : an introductory guide
... of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to gate compilation strategies at the software ...with quantum coding ...
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Quantum error correction protects quantum search algorithms against decoherence
... When quantum computing becomes a wide-spread commercial reality, Quantum Search Algorithms (QSA) and especially Grover’s QSA will inevitably be one of their main applications, constituting their ...the ...
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The Coherent Parity Check Framework for Quantum Error Correction
... new codes to a classical design ...CPC codes can be mapped to factor graphs of the type commonly seen in classical information theory and machine ...the quantum mechanical aspects of CPC ...
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Stabilizer Codes and Quantum Error Correction
... the error syndrome takes a fair amount of time, the possibility of an error in the data while measuring the syndrome can- not be ...An error in the data in the middle of the syndrome measurement will ...
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Homological Error Correction: Classical and Quantum Codes
... homological error correction codes both classically and ...homological codes saturating the Hamming bound. In the quantum case, we show that for non- orientable surfaces it is ...
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Performance of topological codes for quantum error correction
... Surface Codes The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum ...the error correction process – it is the algorithm which ...
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More Sparse-Graph Codes for Quantum Error-Correction
... dual-containing codes, all of which have sparse graphs. These codes’ properties are promising compared to other quantum error-correcting ...Sparse-Graph Codes for Quantum ...
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Duality of Quantum and Classical Error Correction Codes: Design Principles and Examples
... stabilizer codes must satisfy the stringent sym- plectic product ...QLDPC codes and the non-recursive nature of non-catastrophic ...EA quantum codes was developed in [112], [116]–[118], which ...
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Information Amidst Noise: Preserved Codes, Error Correction, and Fault Tolerance in a Quantum World
... preserved codes, noiseless (i.e., requiring no non-trivial correction), unitarily noiseless and correctable codes, all of which will be carefully ...correctable codes of E are built upon IPSs ...
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Quantum Error Correction with Biased Noise
... discusses codes with S-symmetry, and their use for distilling a non-magic state which is nonetheless useful for completing the Cli↵ord group in circumstances where it is not readily ...-symmetric codes and ...
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Novel Methods in Quantum Error Correction
... private quantum codes now includes a variety of other applica- tions, with realizations both as subspaces and subsystems of Hilbert ...of quantum secret sharing [ 43 , 45 ...the quantum ...
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D.5 Quantum error correction
... III. QUANTUM COMPUTATION Figure III.35: Circuit for quantum error ...m error-correction qubits to yield the encoded state | ...of error operators E j , which alter the ...
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Studies Of A Quantum Scheduling Algorithm And On Quantum Error Correction
... a quantum error correcting code uses a large number of qubits and quantum gates it becomes increasingly more difficult to carry out the encoding and syndrome measurements during a single ...
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Emerging Paradigms in Quantum Error Correction and Quantum Cryptography
... approximate codes, without having to perform a difficult optimization over all recovery maps for every possible ...the quantum storage device possessed by either party is noisy and ...the quantum ...
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Quantum error-correcting output codes
... Because the mapping of arbitrary codewords in the test vectors space onto the codeword contained in M is many to one, the ECOC coding/decoding pro- cess has an intrinsic error correction property. A subset ...
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Classical Error-correcting Codes in Quantum Communications
... of quantum states becomes a physical reality, it is necessary to consider methods of protecting quantum information and controlling errors occurring as a result of interactions with the environment and ...
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More Than Error Correction: Cryptography from Codes
... Chapter 6 Conclusion and Future Work Through the development of code-based cryptography, we can see the huge potential of applying codes to the design of encryption schemes and other security protocols. Dispite ...
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Error correction and degeneracy in surface codes suffering loss
... Note that we can obtain a new logical operator by multi- plying the original one by a plaquette stabilizer, ˜ Z i = P p Z ¯ i . The actions of ¯ Z i and ˜ Z i on the code space are the same, since ˜ Z i |C = P p Z ¯ i ...
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Analysis of Quantum Error Correction Applicability on IBM-Q
... ● In [8], it was stated that the [[4, 2, 2]] code, which can be implemented with merely 5 qubits, can be used to improve a quantum circuit’s fault-tolerance. ● Implementations of [[4, 2, 2]] codes on IBM Q ...
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