Fig. 5: Time-evolution results.
From: Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer
a Dynamical Quantum Phase Transition in the Quantum Ising Model: The dynamics of the transverse field Ising model can be obtained analytically and form a good basis for the comparison with our quantum circuits. These are shown in blue and compared with dynamics obtained from numerically exact optimisation of the principal eigenvalue of the transfer matrix within our ansatz shown in orange, and the numerical optimisation of the circuits shown in Fig. 4 in the absence of noise shown in green. The results show that the circuit cost function can faithfully track the dynamics. b Cost-function evaluated on Rainbow: The cost function evaluated along a linear interpolation in the eight parameters from U and extending through the exact update is shown for each of the indicated time-steps in (a). The cost-function is rescaled by a Loschmidt echo obtained by overlapping the left hand of the circuit in (a), including the time-evolution operator, with its Hermitian conjugate. The optimum value of the rescaled circuit coincides with that calculated in a classical simulation without error.
