Fig. 3: Experimental results for the BayesMGD algorithm and final energy errors with respect to the VQE ground state. | Nature Communications

Fig. 3: Experimental results for the BayesMGD algorithm and final energy errors with respect to the VQE ground state.

From: Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer

Fig. 3

a Progress of VQE for 1 × 8 and 2 × 4 Fermi-Hubbard instances at half-filling, as measured by the error between energy at parameters θk and VQE ground energy \({E}_{\min }\) (main plot log scale, inset linear scale). “Estimate” is the energy estimated by the BayesMGD algorithm during the VQE procedure based on measurement results, “exact” is the true energy at the corresponding parameters. b Final errors in measured energy following error mitigation on the final state. “Raw”: no error mitigation. “PS”: only postselection on occupation number. “+Sym”: also time-reversal symmetry. “+TFLO”: also Training with Fermionic Linear Optics32. “+Coh”: also coherent error correction in TFLO. “+PHS”: also particle-hole symmetry. Raw/PS shown with different scale for clarity. Reduction in error using all techniques is e.g. ~46× at half-filling. Each error mitigation method is applied as well as all previous methods. Plots show a piecewise linear interpolation between integer occupations. Error bars were calculated according to the procedure described in Methods section and are often too small to be visible.

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