I'd like to have pretty thorough benchmarking for all of the propagators (as a Literate.jl fiile that gets included in the documentation).
For each method, let's benchmark the (wallclock) runtime and memory usage for
the "initialization" (creating the workspace, e.g. ChebyWrk) depending on the size of the Hilbert space
a single time step, depending on the size of the Hilbert space
a single time step for a fixed size Hilbert space (>1000) depending on the sparsity of the Hamiltonian
the propagation over a time grid for a fixed size Hilbert space (>1000), depending on the number of time steps
For the polynomial methods, in addition to wallclock runtime, we might also want "number matrix-vector products"
In each case, we'll want to look at both dense and sparse Hamiltonians:
Use a random dense (Hermitian or non-Hermitian) matrix as the Hamiltonian
Use a random sparse (Hermitian or non-Hermitian) matrix as the Hamiltonian, with several fixed "sparsity values"
Use the Hamiltonian for two transmons with the cavity included as a "realistic" sparse Hamiltonian. Since we can choose where to truncate each transmon and the cavity, and random pulses should easily populate all levels, this is a good system for having "realistic" Hamiltonians of varying size n * n * m where n is the number of transmon levels and m is the number of cavity levels.
There is no point in doing a dense Liouvillian: that's the same as propagating a dense Hamiltonian of the same size. So the different Liouvillians should always be sparse, but derive from the above dense/sparse Hamiltonians, and using Lindblad operators for spontaneous decay and dephasing from all levels with random decay rates.
I'd like to have pretty thorough benchmarking for all of the propagators (as a
Literate.jlfiile that gets included in the documentation).For each method, let's benchmark the (wallclock) runtime and memory usage for
ChebyWrk) depending on the size of the Hilbert spaceFor the polynomial methods, in addition to wallclock runtime, we might also want "number matrix-vector products"
In each case, we'll want to look at both dense and sparse Hamiltonians:
n * n * mwherenis the number of transmon levels andmis the number of cavity levels.There is no point in doing a dense Liouvillian: that's the same as propagating a dense Hamiltonian of the same size. So the different Liouvillians should always be sparse, but derive from the above dense/sparse Hamiltonians, and using Lindblad operators for spontaneous decay and dephasing from all levels with random decay rates.