Efficient learning algorithms for energy estimation imply that stable quantum algorithms cannot prepare low-energy states in systems exhibiting the quantum overlap gap property, as proven for a sparsified quantum p-spin model.
Bottlenecks in quantum channels and finite temperature phases of matter
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The unitary contribution from weak system-bath coupling in collision-model thermal state preparation tightens the fixed-point error bound, scaling rigorously as J² where J is the coupling strength.
k-local quantum Hamiltonians admit system-size-independent spectral gap for Gibbs samplers at high temperature, enabling FPT quantum approximation algorithms for partition functions.
Metastability timescales near first-order transitions in driven-dissipative systems with hidden time-reversal symmetry are analytically predictable via purification of the steady state.
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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Quantum Glassiness From Efficient Learning
Efficient learning algorithms for energy estimation imply that stable quantum algorithms cannot prepare low-energy states in systems exhibiting the quantum overlap gap property, as proven for a sparsified quantum p-spin model.
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Rigorous error bounds for dissipative thermal state preparation from weak system-bath coupling
The unitary contribution from weak system-bath coupling in collision-model thermal state preparation tightens the fixed-point error bound, scaling rigorously as J² where J is the coupling strength.
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Fast mixing of all-to-all quantum systems at high temperatures
k-local quantum Hamiltonians admit system-size-independent spectral gap for Gibbs samplers at high temperature, enabling FPT quantum approximation algorithms for partition functions.
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Exact metastability in a class of driven-dissipative quantum many-body systems
Metastability timescales near first-order transitions in driven-dissipative systems with hidden time-reversal symmetry are analytically predictable via purification of the steady state.
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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.