Broken Symmetry in a Two-Qubit Quantum Control Landscape

On this page, you can find the supplementary videos to the paper Broken Symmetry in a Two-Qubit Quantum Control Landscape [1].

For the symmetrically-coupled two-qubit problem, we present four movies showing protocols in the symmetry-broken glassy phase (green in Fig. 1 from paper) for the protocol duration $T=2.0$. The movies come in symmetry-related pairs a-b, and show the existence of exactly degenerate driving protocols close to optimality.

In all movies, we trace one one qubit and plot the reduced density matrix of the other on the Bloch sphere. The target state is shown in red, while the instantaneous state - in green. On the upper left of the movies, we show the entanglement entropy of a single qubit. On the right-hand side, we show the instantaneous fidelity.

Stochastic Descent. Movies 1 a,b show two nearly optimal degenerate protocols found using Stochastic Descent [2] for $T=2.0$. The protocol time step size is $\delta t=0.01$. Movie 1a, Movie 1b.
Symmetry-breaking Variational Ansatz. Movies 2 a,b show two nearly optimal degenerate protocols found using the Variational ansatz (see Supplemental Material from paper) for $T=2.0$. The protocol time step size is $\delta t=0.001$. Movie 2a, Movie 2b.

References:
[1] M.B., A.G.R. Day, D. Sels, P. Weinberg, A. Polkovnikov, and P. Mehta, arXiv: 1711.09109 (2017).
[2] M.B., A.G.R. Day, P. Weinberg, A. Polkovnikov, P. Mehta, and D. Sels, Phys. Rev. A 97, 052114 (2018).