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hiiiiii i need help

how do i discretely apply a time evolution operator to a wavefunction in steps of Δt? i'm trying to write something down as an optimization problem with discrete timesteps

@bstacey okay yeah it's obvious i'm an engineer and not a physicist :) i was saying qubit bc the full model has at least seven dominant levels they consider, but for optimization we truncate to 3, and we're actually trying to minimize leakage to |3〉

thank you for your help! the free evolution hamiltonian for this qutrit is actually diagonalizable which should make the matrix exponentiation much nicer

@er1n At least now you know the word "qutrit" and can quote it to impress your friends :-)

@er1n It's pronounced like "cubit" because it was literally coined as a joke. Ben Schumacher and Bill Wootters were stumped trying to do an old-school information theory calculation in quantum physics. "Maybe we just need a whole new notion of 'quantum information'!"

"And we can measure it in qubits --- cubits, like Noah's Ark!"

Blake C. Stacey@bstacey@icosahedron.website@er1n How is your wavefunction represented? If it's just stored as a vector, then time evolution is just matrix multiplication. The matrix exponential of a Hamiltonian times (-i) times your timestep Δt divided by Planck's constant will give the time-evolution operator for Δt. If Δt is very small, then this will Taylor-approximate to the identity matrix minus iHΔt / hbar.