qhash

Create quantum operators using a global excitation number cutoff

The code in this repository is based on algorithms described in the excellent paper J. M. Zhang and R. X. Dong, European Journal of Physics 31, 591 (2010)

In this example, we want to simulate a system with 6 modes and keeping up to 3 total excitations. In the normal way of tensoring up individual subsystems, if we kept 3+1 states in each mode, this requires a Hilbert-space size of 4^6=4096. Here, by instead keeping only 3 total excitations in the system we require a Hilbert-space size of only 84.

from qhash import Hashing

num_excitations = 3
num_modes = 6
two_mode_hash = Hashing(num_excitations, num_modes)
hilbert_dim = two_mode_hash.hilbert_dim()  # 84

We can now extract the raising and lowering operators of each mode by specifying the mode index

a_0 = two_mode_hash.a_operator(0)
a_1 = two_mode_hash.a_operator(1)

And so on. These ndarray objects can now be passed to your favorite tool for performing quantum simulations. The ordering of the basis vectors can be found from calling

basis_vectors = two_mode_hash.basis_vectors()

which returns a list of the basis vectors.