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Robust Quantum Entanglement at (Nearly) Room Temperature

Author Lior Eldar

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Lior Eldar
  • Yifat, Israel

Acknowledgements

The author thanks Dorit Aharonov, Simon Apers, Aram Harrow, Matthew Hastings and Anthony Leverrier for their useful comments and suggestions. He also thanks anonymous reviewers for their helpful comments and suggestions.

Cite AsGet BibTex

Lior Eldar. Robust Quantum Entanglement at (Nearly) Room Temperature. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 49:1-49:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ITCS.2021.49

Abstract

We formulate an average-case analog of the NLTS conjecture of Freedman and Hastings (QIC 2014) by asking whether there exist topologically ordered systems with corresponding local Hamiltonians for which the thermal Gibbs state for constant temperature cannot even be approximated by shallow quantum circuits. We then prove this conjecture for nearly optimal parameters: we construct a quantum error correcting code whose corresponding (log) local Hamiltonian has the following property: for nearly constant temperature (temperature decays as 1/log²log(n)) the thermal Gibbs state of that Hamiltonian cannot be approximated by any circuit of depth less than log(n), and it is highly entangled in a well-defined way. This implies that appropriately chosen local Hamiltonians can give rise to ground-state long-range entanglement which can survive without active error correction at temperatures which are nearly independent of the system size: thereby improving exponentially upon previously known bounds.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum complexity theory
Keywords
  • Quantum error-correcting codes
  • Quantum Entanglement
  • Quantum Locally-Testable Codes
  • Local Hamiltonians
  • quantum PCP
  • NLTS

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References

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