Efficient Quantum Algorithm for Heisenberg Spin Systems
summary
Shows that a Suzuki‑Fisher family of Heisenberg models (including the antiferromagnet on any bipartite graph and certain sign‑problem cases) has a spectral gap ∝ Z‑field and so admits an efficient quantum adiabatic algorithm that estimates ground energy to ε in time poly(N, J, 1/ε) and prepares the ground state. Proof uses a new inequality bounding the relative spectral gap of positive semidefinite Lee‑Yang tensors, contraction/Hurwitz arguments and Schwarz lemma; yields exact algorithm for EPR/quantum max‑cut on bipartite graphs.
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chapters (7)
- 0:00Introduction to spin systems
- 14:06Quantum advantage and models
- 16:27Non-stoquastic systems
- 20:02Lee-Yang tensors
- 27:35Relative spectral gaps
- 34:52Adiabatic quantum algorithm
- 39:30Future directions and questions
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