BalancedUniformPauli

class samplomatic.distributions.BalancedUniformPauli(num_subsystems: int)

Bases: Distribution

The balanced uniform distribution over virtual Pauli gates.

Here, balanced means that on every qubit, each of the four Paulis appears the same number of times, provided that the requested number of samples is a multiple of four. Moreover, when the number of samples is a multiple of two, it is promised that, for each qubit, X or Y is sampled the same number of times as I or Z.

The sampling algorithm is simply to draw four times fewer n-qubit Paulis uniformly and iid than requested, and then replicate each four times with respective multiplications by $I^{\otimes}n$, $X^{\otimes}n$, $Z^{\otimes}n$, and $Y^{\otimes}n$, truncating the samples if their requested number is not a multiple of four. Randomizations are ordered such that the four replications are consecutive. The particular ordering of the four multiplicative terms— $I$ then $X$ then $Z$ then $Y$ —is what provides the guarantee that for each qubit, X or Y is sampled the same number of times as I or Z, even if the number of samples is even but not a multiple of four.

Parameters

num_subsystems – The number of subsystems this distribution samples.

Attributes Summary

Methods Summary

Attributes Documentation

register_type

Methods Documentation

sample