The Thermodynamic Cost of Ignorance: Thermal State Preparation with One Ancilla Qubit

Understand

In this work we investigate a model of thermalization wherein a single ancillary qubit randomly interacts with the system to be thermalized.

• This not only sheds light on the emergence of Gibbs states in nature, but also provides a routine for preparing arbitrary thermal states on a digital quantum computer.
• For desired $\beta$ and random interaction $G$ the routine boils down to time independent Hamiltonian simulation and is represented by the channel $\Phi : \rho \mapsto \mathbb{E}_G {\rm Tr}_{\rm Env} \left[ e^{-i(H + \alpha G)t} \left(\rho \otimes \frac{e^{-\beta H_E}}{\mathcal{Z}}\right) e^{i (H + \alpha G)t} \right]$.
• We rigorously prove that these dynamics reduce to a Markov chain process in the weak-coupling regime with the thermal state as the approximate fixed point.