For PEPS states with loop-decay, BP with cluster corrections approximates local observables exponentially accurately, and loop-decay necessarily implies exponential decay of connected correlations, ruling out BP at critical points.
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New analytic constructions yield quantum lattice models with continuous symmetry breaking and chiral topological order at arbitrarily high temperatures via entropic stabilization.
Detectability lemma enables Gibbs sampling without Lindbladian simulation, yielding O(M) cost reduction for M-term local Lindbladians and quadratic speedup in spectral gap for frustration-free and commuting cases.
Coupling to mesoscopic reservoirs generates temperature-increasing entropic barriers that suppress topological defect creation and transport, yielding three-regime correlation lengths in 1D Ising chains and double error reduction in finite-size 2D toric codes.
A variational framework assisted by matrix product states prepares approximate thermal Gibbs states for 1D lattices up to 30 sites and 2D lattices up to 6x6 using up to 44 qubits, with a demonstration on IBM Heron hardware.
Benchmarks gradient-ascent algorithms for constrained free energy minimization on quantum Heisenberg models and stabilizer codes, with applications to thermal state design and fixed-temperature quantum encoding.
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Belief Propagation and Tensor Network Expansions for Many-Body Quantum Systems: Rigorous Results and Fundamental Limits
For PEPS states with loop-decay, BP with cluster corrections approximates local observables exponentially accurately, and loop-decay necessarily implies exponential decay of connected correlations, ruling out BP at critical points.
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Exploring Entropic Orders: High Temperature Continuous Symmetry Breaking, Chiral Topological States and Local Commuting Projector Models
New analytic constructions yield quantum lattice models with continuous symmetry breaking and chiral topological order at arbitrarily high temperatures via entropic stabilization.
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Quantum Gibbs sampling through the detectability lemma
Detectability lemma enables Gibbs sampling without Lindbladian simulation, yielding O(M) cost reduction for M-term local Lindbladians and quadratic speedup in spectral gap for frustration-free and commuting cases.
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Entropic Barriers and the Kinetic Suppression of Topological Defects
Coupling to mesoscopic reservoirs generates temperature-increasing entropic barriers that suppress topological defect creation and transport, yielding three-regime correlation lengths in 1D Ising chains and double error reduction in finite-size 2D toric codes.
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Variational Thermal State Preparation on Digital Quantum Processors Assisted by Matrix Product States
A variational framework assisted by matrix product states prepares approximate thermal Gibbs states for 1D lattices up to 30 sites and 2D lattices up to 6x6 using up to 44 qubits, with a demonstration on IBM Heron hardware.
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Constrained free energy minimization for the design of thermal states and stabilizer thermodynamic systems
Benchmarks gradient-ascent algorithms for constrained free energy minimization on quantum Heisenberg models and stabilizer codes, with applications to thermal state design and fixed-temperature quantum encoding.