Evolutionary algorithms for hard quantum control

Although quantum control typically relies on greedy (local) optimization, traps (irregular critical points) in the control landscape can make optimization hard by foiling local search strategies. We demonstrate the failure of greedy algorithms as well as the (nongreedy) genetic-algorithm method to realize two fast quantum computing gates: a qutrit phase gate and a controlled-not gate. We show that our evolutionary algorithm circumvents the trap to deliver effective quantum control in both instances. Even when greedy algorithms succeed, our evolutionary algorithm can deliver a superior control procedure, for example, reducing the need for high time resolution.

Figure 1

Logarithmic infidelity $L$ vs iteration number $ı$ for (a) the qutrit gate and (b) the cnot gate using the quasi-Newton method with (a) $T=10\pi$ (red solid lines), $T=4\pi$ (blue lines with “$+$” markers), and $T=3\pi$ (green lines with “$\times$” markers) such that $K=50$ in all cases, and with (b) $T=30$ and $K=30$ (red solid lines), $T=10$ and $K=10$ (blue lines with “$+$” markers), and $T=4$ and $K=4$ (green lines with “$\times$” markers).

Figure 2

Logarithmic-infidelity $L$ vs iteration number $ı$ for ($\square$) GA, ($\times$) DE, ($\circ$) Common PSO, (☆) PSO1, ($*$) PSO2, ($\diamond$) PSO3, ($⊳$) quasi-Newton, (✶) simplex, and ($▿$) Krotov with $R=80$ ($R=40$) for greedy (evolutionary) algorithms. Median-run performance is depicted in (a) and (c); best run performance is depicted in (b) and (d). The qutrit phase gate is the target ($T=2.5\pi$ and $K=10$) in (a) and (b); cnot is the target ($T=3.2$ and $K=4$) in (c) and (d).