Robust Quantum Entanglement at (nearly) Room Temperature
summary
Constructs a family of local Hamiltonians whose thermal state remains hard to prepare: the Hamiltonian is topologically ordered and its thermal state has circuit complexity Ω(log n) even at β = Θ(log log n) (temperature decays like 1/log log n). The proof models thermal noise via Metropolis-Hastings, uses quantum locally testable codes (projective code of Leverrier et al., boosted to constant soundness), proves typical errors have max connected component = O(log n), and implements a shallow decoder (Sipser–Spielman style) that recovers the entangled ground state.
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chapters (19)
- 0:00Intro
- 0:12Schroedinger's Ket
- 0:55When in doubt - blame decoherence...
- 1:36Theory vs. Real Life
- 2:28Entanglement at room temperature?
- 3:02A local quantum circuit
- 3:24Quantum circuit complexity
- 5:10Main Theorem
- 6:14Take-home message
- 6:57Let's recap
- 7:24Main idea
- 8:30Main problem
- 8:55Change regimes
- 10:17Still not enough...
- 11:13Thermal state in terms of errors
- 12:37Required ingredients
- 13:37The recipe
- 14:51Summary
- 15:34Conclusions
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