Generate Clifford gates in matrix form

[ghost]

Hi Stefan:

I am thinking about generating all 24 single-qubit Clifford gates in matrix form. Is there a function to do that? Thanks

[Krastanov]

Yes, enumerate_cliffords and enumerate_phases.

julia> length(collect(enumerate_phases(enumerate_cliffords(1))))
24

[ghost]

Hi Stefan:

Yes this can generate all 24 single qubit clifford gates. But is there a simple way to get the matrix of each gate?

Thanks

[Krastanov]

With the release of 0.8.12 today, this is easier.

• stab_to_gf2 can be used to generate the binary matrix representing the gate
• Operator from QuantumOptics.jl can be used to convert CliffordOperator into a unitary matrix

If I understand correctly, you can do what you want by writing:

julia> using QuantumClifford, QuantumOptics

julia> all_1q_clifford_unitaries = Operator.(enumerate_phases(enumerate_cliffords(1)));

julia> all_1q_clifford_unitaries[12]
Operator(dim=2x2)
  basis: Spin(1/2)
  0.5+0.0im  0.0-0.5im
 -0.5+0.0im  0.0-0.5im