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Quantum Gibbs state sampling algorithms generally suffer from either scalingexponentially with system size or requiring specific knowledge of spectralproperties \textit{a priori}. Also, these algorithms require a large overheadof bath or scratch/ancilla qubits. We propose a method, termed the minimaleffective Gibbs ansatz (MEGA), which uses a quantum computer to determine aminimal ensemble of pure states that accurately reproduce thermal averages oftypical observables. This technique employs properties of correlation functionsthat can be split into a lesser and greater part; here, we primarily focus onsingle-particle Green's functions. When properly measured, these correlationfunctions provide a simple test to indicate how close a given pure state orensemble of pure states are to providing accurate thermal expectation values.Further, we show that when properties such as the eigenstate thermalizationhypothesis hold, this approach leads to accurate results with a sparse ensembleof pure states; sometimes only one suffices. We illustrate the ansatz usingexact diagonalization simulations on small clusters for the Fermi-Hubbard andHubbard-like models. Even if MEGA becomes as computationally complex as otherGibbs state samplers, it still gains an advantage due to its ease ofimplementation without any \textit{a priori} information about the Hamiltonianand in the efficient allocation of available qubits by eliminating bath qubitsand using a minimal number of ancilla.

Minimal Effective Gibbs Ansatz (MEGA): A simple protocol for extracting an accurate thermal representation for quantum simulation