Predicting Gibbs-State Expectation Values with Pure Thermal Shadows

Understand

The preparation and computation of many properties of quantum Gibbs states is essential for algorithms such as quantum semidefinite programming and quantum Boltzmann machines.

• We propose a quantum algorithm that can predict $M$ linear functions of an arbitrary Gibbs state with only $\mathcal{O}(\log{M})$ experimental measurements.
• Our main insight is that for sufficiently large systems we do not need to prepare the $n$-qubit mixed Gibbs state explicitly but, instead, we can evolve a random $n$-qubit pure state in imaginary time.
• The result then follows by constructing classical shadows of these random pure states.