Is there any package that does quantum operator algebra (i.e., algebra with non-commuting operators) in Julia? I need to calculate numerous commutators of fermions, so I hope the package can do the job with small time and memory costs.

Do you have a more specific problem to calculate? There are some that do simple symbolic calculations, most are numerical packages AFAIK

I need to calculate numerous commutators of fermions, so I hope the package can do the job with small time and memory costs. Both numerical and symbolic packages are okay with me. Could you share a little bit more details?

I don’t know if there is many packages do fermions, but there is GitHub - QuantumBFS/FLOYao.jl: A fermionic linear optics simulator backend for Yao.jl does the fermionic linear optics (FLO) circuits

I do not know of anything that exactly fits your needs, but QuantumCumulants does do some commutation algebra for simplifying expectation values: Theoretical background · QuantumCumulants.jl

Excising their internal methods that do the simplification might be a good starting point. They would also welcome contributions and feature requests.

Have you looked at GitHub - qojulia/QuantumOptics.jl: Library for the numerical simulation of closed as well as open quantum systems.?

It might be able to do that. I think I used it for something similar some time ago.

I haven’t used this before, but by name this seems to be what you are looking for?