Curator's Take
This research reveals a fascinating sweet spot in quantum thermodynamics where external magnetic fields can transform otherwise simple high-temperature quantum states into computationally complex, entangled systems that are classically hard to simulate. The key insight is that even at high temperatures where quantum effects typically wash out, carefully tuned external fields can induce enough entanglement to create computational hardness while still allowing efficient preparation on quantum computers. This work provides a concrete pathway for demonstrating quantum advantage through state preparation tasks, offering a more accessible alternative to complex many-body systems that require extreme cooling or precise control. The mathematical framework also advances our understanding of how external perturbations can dramatically alter the computational landscape of quantum thermal states, with potential applications in quantum simulation and algorithm design.
— Mark Eatherly
Summary
Gibbs states are a natural model of quantum matter at thermal equilibrium. We investigate the role of external fields in shaping the entanglement structure and computational complexity of high-temperature Gibbs states. External fields can induce entanglement in states that are otherwise provably separable, and the crossover scale is $h\asymp β^{-1} \log(1/β)$, where $h$ is an upper bound on any on-site potential and $β$ is the inverse temperature. We introduce a quasi-local Lindbladian that satisfies detailed balance and rapidly mixes to the Gibbs state in $\mathcal{O}(\log(n/ε))$ time, even in the presence of an arbitrary on-site external field. Additionally, we prove that for any $β<1$, there exist local Hamiltonians for which sampling from the computational-basis distribution of the corresponding Gibbs state with a sufficiently large external field is classically hard, under standard complexity-theoretic assumptions. Therefore, high-temperature Gibbs states with external fields are natural physical models that can exhibit entanglement and classical hardness while also admitting efficient quantum Gibbs samplers, making them suitable candidates for quantum advantage via state preparation.