Optimizing random local Hamiltonians by dissipation

• URL: http://arxiv.org/abs/2411.02578v1
• Date: Mon, 04 Nov 2024 20:21:16 GMT
• Title: Optimizing random local Hamiltonians by dissipation
• Authors: Joao Basso, Chi-Fang Chen, Alexander M. Dalzell,
• Abstract summary: We prove that a simplified quantum Gibbs sampling algorithm achieves a $Omega(frac1k)$-fraction approximation of the optimum. Our results suggest that finding low-energy states for sparsified (quasi)local spin and fermionic models is quantumly easy but classically nontrivial.
• Score: 44.99833362998488
• License:
• Abstract: 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.

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