Fig. 10: Eigenvalue Estimation.
From: Long-time simulations for fixed input states on quantum hardware
a Determining the eigenstates overlapped by the initial state: The 3-qubit XY Hamiltonian was diagonalized on a quantum simulator in the subspace of initial state \(\left|{\psi }_{0}\right\rangle =\left|110\right\rangle\) to obtain θopt and γopt. Here we show the output of measuring \(W{({{{{\boldsymbol{\theta }}}}}_{{{{\rm{opt}}}}})}^{{\dagger} }\left|{\psi }_{0}\right\rangle\) in the computational basis on ibmq_boeblingen. The 4 non-zero states correspond to the 4 eigenvectors overlapped by \(\left|{\psi }_{0}\right\rangle\). b Eigenvalue Estimation using QEE. Here we show the result of implementing QEE (using fsVFF as a pre-processing step) on ibmq_santiago to calculate the eigenvalues of the eigenvectors in the subspace overlapped by \(\left|011\right\rangle\). The solid yellow, red, blue and green lines represent the eigenvalues obtained for the \(\left|000\right\rangle\), \(\left|001\right\rangle\), \(\left|100\right\rangle\) and \(\left|101\right\rangle\) states, with exact corresponding energies of {−2.828, 0, 0, 2.828}, indicated by the dotted lines. The eigenvalues are plotted as phases since for Δt = 1 there is a one to one correspondence.
