see this

https://www.nature.com/articles/s42005-021-00556-w

Thank you for your suggestion

Dont understand

A discrete variable is a contradiction of terms.

However,

A gaussian state can be a quantum state , ie. the ground state of an harmonic oscillator.

Normally you ask about the Gaussian state of a Quantum system (Not a variable)

You are right. A possible choice is "Gaussian states of discrete-variable quantum systems". Thank you very much.

in Physics.

Our concept of Hilbert space is like an infinite vector space where the vectors are functions, with an inner product (Psi(n), Psi(m)) = delta(n,m) if

orthonormalized. and the Psi(n) are eigenfunctions of some hermitian Hamiltonian H

H Psi(n) = E(n) Psi(n)

You would use a finite matrix for H? In some QM problems this is also valid.

It is correct to say a space of functions.

The finite-dimensional Hilbert spaces are also used in Physics.

For example, a qubit is a quantum system described by a two-dimensional Hilbert space. For a review see:

Vourdas A, Quantum systems with finite Hilbert space, Rep. Prog. Phys. 67 (2004) 267-320. In this case the matrix of H is a finite matrix.

Thanks

Yes, sometimes simple molecules are studied this way in Quantum Chemistry,

with a finite matrix.

Im not into Quantum Computing so that detail escapes me.

However eigenvalues normally are not integers and in QM and have units of energy. The eigenvalues are the predictive quantities in QM.

However I suppose you can bend the meaning of QM a bit, especially from mathematicians, and use it in computing.

Hooke's_atom and related harmonium type models?

Thank you for your interesting suggestion.

I shall analyze it carefully.