# Quantum Error Correcting Codes in Eigenstates of Translation-Invariant Spin Chains.

@article{Brando2017QuantumEC, title={Quantum Error Correcting Codes in Eigenstates of Translation-Invariant Spin Chains.}, author={Fernando G. S. L. Brand{\~a}o and Elizabeth Crosson and Mehmet Burak Şahinoğlu and John Bowen}, journal={Physical review letters}, year={2017}, volume={123 11}, pages={ 110502 } }

Quantum error correction was invented to allow for fault-tolerant quantum computation. Systems with topological order turned out to give a natural physical realization of quantum error correcting codes (QECC) in their ground spaces. More recently, in the context of the anti-de Sitter/conformal field theory correspondence, it has been argued that eigenstates of CFTs with a holographic dual should also form QECCs. These two examples raise the question of how generally eigenstates of many-body…

## 45 Citations

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The results not only indicate (potentially eﬃcient) randomized constructions of optimal U (1)- and SU ( d )-covariant codes, but also reveal fundamental properties of random symmetric unitaries, which yield important solvable models of complex quantum systems that have attracted great recent interest in quantum gravity and condensed matter physics.

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VarQEC, a noise-resilient variational quantum algorithm to search for quantum codes with a hardware-efficient encoding circuit, sheds new light on the understanding of QECC in general, which may also help to enhance near-term device performance with channel-adaptive error-correcting codes.

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For quantum spin systems in any spatial dimension with a local, translation-invariant Hamiltonian, we prove that asymptotic state convertibility from a quantum state to another one by a…

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This work considers the gapless Heisenberg-XXX model, whose energy eigenstates can be described via Bethe ansatz tensor networks, and shows that it contains — within its low-energy eigenspace — an error-detecting code with the same parameter scaling.

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New and powerful lower bounds on the infidelity of covariant quantum error correction are proved, which not only extend the scope of previous no-go results but also provide a substantial improvement over existing bounds.

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This paper explores the properties of ETH as an error correcting code and shows that there exists an explicit universal recovery channel for the code, and discusses a generalization that all chaotic theories contain error correcting codes.

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