How do I pick a random Clifford operation in Stim?

Question

I want to sample random n-qubit Clifford operations. How do I do that in Stim?

(Self-answering because this was requested when the feature already existed)

Answer 1

The method stim.Tableau.random(n) generates a uniformly random n-qubit Clifford operation, using the algorithm from "Hadamard-free circuits expose the structure of the Clifford group", and returns its stabilizer tableau.

example

import stim
t = stim.Tableau.random(10)
print(repr(t))

sample output

stim.Tableau.from_conjugated_generators(
    xs=[
        stim.PauliString("-ZZXZZY__YX"),
        stim.PauliString("-___XXXZZZ_"),
        stim.PauliString("+YXZY_Y_Z__"),
        stim.PauliString("-YZYXXXY_YY"),
        stim.PauliString("+YZXZYXZ__Y"),
        stim.PauliString("+ZZZXZYYY__"),
        stim.PauliString("-_YZ___ZYXY"),
        stim.PauliString("+_YXYZXYY_Y"),
        stim.PauliString("-Y__YZ_____"),
        stim.PauliString("+ZZXZ_Z_XYY"),
    ],
    zs=[
        stim.PauliString("+_YZXXZZYZZ"),
        stim.PauliString("-YXZXYXY_XY"),
        stim.PauliString("-_YXXXZYYYX"),
        stim.PauliString("+_YYZYZ_ZYX"),
        stim.PauliString("-_XY___YYZY"),
        stim.PauliString("-ZX_ZZYZ_YY"),
        stim.PauliString("-_Y_XXXZYXZ"),
        stim.PauliString("-Y__ZYXY_XX"),
        stim.PauliString("-Y_X_YZXZYY"),
        stim.PauliString("+Y__ZXZY_XX"),
    ],
)

performance

This method has asymptotic cubic scaling (eg. it performs a schoolbook matrix multiplication).

>>> %time t = stim.Tableau.random(10)
Wall time: 253 µs
>>> %time t = stim.Tableau.random(100)
Wall time: 11.3 ms
>>> %time t = stim.Tableau.random(1000)
Wall time: 289 ms
>>> %time t = stim.Tableau.random(10000)
Wall time: 2min 20s