Fig. 2: Numerical results of Hamiltonian reshaping.
From: Mitigating errors in analog quantum simulation by Hamiltonian reshaping or Hamiltonian rescaling
The eigen-energy differences Eba = Eb − Ea for 100 randomly chosen pairs of eigenstates (a, b) are estimated. We consider the Hamiltonian in Eq. (20) with parameters n = 6, νz = 4, νx = 1, and J = 4. The Lindblad operators are assumed to be \({L}_{k}=\sqrt{\kappa }(i\left\vert 0\right\rangle {\left\langle 0\right\vert }_{k}+\left\vert 1\right\rangle {\left\langle 1\right\vert }_{k})\otimes {{\bf{I}}}_{{\rm{others}}}\) for k = 1, …, n, and the error Hamiltonian is \({H}^{(1)}=\kappa \beta \mathop{\sum }\nolimits_{j = 1}^{n}{Z}_{j}\). Parameters are set to β = 0.01, ΔT = 0.0001, and L = 2000. For each numerical experiment, κ = γ∣Eba∣ is used to reflect the relative error strength. The red line represents the average estimated relative error before error mitigation. Error mitigation is performed using 100 Pauli reshaped Hamiltonians, with the black line showing the average result after mitigation. The blue line indicates the mitigation result using reshaped Hamiltonians with \(\left\{{I}^{\otimes n},{X}^{\otimes n},{Y}^{\otimes n},{Z}^{\otimes n}\right\}\). When the error rate is small, this method performs better due to reduced statistical errors, as discussed in “Results“. The violin plot illustrates the distribution of relative errors before or after mitigation for these 100 Eba values.
