Simultaneous global optimization

[wcairnx]

Is it possible to optimize the shape of a single control waveform with multiple different overall amplitudes for multiple objectives? The idea is that I have a single fast control signal that can be multiplied by a different scalar amplitude for each of wo qubits, and I would like to perform distinct gates on the two qubits. I would like to optimize both the control waveform shape and the two amplitudes to achieve robust but different gates on the two qubits.

[goerz]

That's an interesting problem! It's not something you can do out of the box, exactly, but QuantumControl.jl will certainly be helpful in this.

We don't have any global optimization methods. So you could write your own code or use some other package to create a swarm or grid for the two coupling parameters, and then use QuantumControl.jl with GRAPE or Krotov to optimize the amplitudes at each coupling parameter point. Then refine the swarm/grid based on for which points you had the most success in the amplitude optimization. That's pretty much exactly what we did in Goerz et al. npj Quantum Information 3, 37 (2017).

The alternative approach (although I haven't maybe fully thought this through) is to calculate a combined gradient for the amplitude values and the two coupling parameters. The calculation of gradients for parametrized pulses is still work-in-progress. We only recently defined the notion of a ParametrizedFunction, of which a tunable coupling strength would be an example. Calculating gradients for such parameters would happen with the help of QuantumGradientGenerator, along the lines of GOAT, see Machnes et al. Phys. Rev. Lett. 120, 150401 (2018).

Once that's implemented, you could supposedly copy the amplitude gradient calculation from GRAPE and the parameter gradient calculation from GOAT and combine them into a single gradient vector and pass that to LBFGS.

But as I said, the parameter gradient calculation is still work-in-progress and even then, it would require a fair amount of problem-specific code to put everything together. So for the time being, I'd go with option 1, even though it's pretty costly in terms of numerical resources (hopefully, you have a cluster or a workstation with a significant number of cores)