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Optimizing random local Hamiltonians by dissipation
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A central challenge in quantum simulation is to prepare low-energy states of strongly interacting many-body systems. In this work, we study the problem of preparing a quantum state that optimizes a random all-to-all, sparse or dense, spin or fermionic $k$-local Hamiltonian. We prove that a simplified quantum Gibbs sampling algorithm achieves a $\Omega(\frac{1}{k})$-fraction approximation of the optimum, giving an exponential improvement on the $k$-dependence over the prior best (both classical and quantum) algorithmic guarantees. Combined with the circuit lower bound for such states, our results suggest that finding low-energy states for sparsified (quasi)local spin and fermionic models is quantumly easy but classically nontrivial. This further indicates that quantum Gibbs sampling may be a suitable metaheuristic for optimization problems.
Forward citations
Cited by 3 Pith papers
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Simulating Thermal Properties of Bose-Hubbard Models on a Quantum Computer
A new rigorous Gibbs sampling method is given for bosonic models by proving that their dissipative generators have positive spectral gaps, enabling efficient quantum preparation of thermal states for Bose-Hubbard Hami...
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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-sp...
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Exponential Lindbladian fast forwarding and exponential amplification of certain Gibbs state properties
Quantum algorithms achieve exponential fast-forwarding for structured Lindbladian dynamics and coherence-dependent exponential speedup in Gibbs state property estimation.
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