Sign Resolved Measurements In Quantum Simulations

Quantum simulations provide a powerful framework to explore strongly correlated many-body systems. However, in many cases, the weights of quantum paths can become negative, invalidating their interpretation as probabilities, i.e., the sign problem. Neglecting the sign S of configurations can yield qualitatively incorrect results. A striking example arises in auxiliary-field Quantum Monte Carlo studies of the Hubbard model, where disregarding the sign suppresses the d-wave pairing response as temperature decreases, while proper inclusion reveals the opposite trend. Here, we investigate this issue through a sign-resolved analysis of observables in the 2D Hubbard model. We compute histograms of quantities such as density, kinetic energy, double occupancy, antiferromagnetic structure factor, and d-wave susceptibility separately for S=+1 and S=−1 configurations. The Wasserstein distance between histograms grows with temperature, reflecting increasing decorrelation. Interestingly, the d-wave susceptibility histograms converge at low temperatures, becoming identical at zero temperature. We interpret these findings via an equation, which links observable expectations to the inverse average sign, and further analyze the four sign sectors defined by spin-determinant parity combinations.