  Virtual distillation has been proposed as an error mitigation protocol for
estimating the expectation values of observables in quantum algorithms. It
proceeds by creating a cyclic permutation of $M$ noisy copies of a quantum
state using a sequence of controlled-swap gates. If the noise does not shift
the dominant eigenvector of the density operator away from the ideal state,
then the error in expectation-value estimation can be exponentially reduced
with $M$. In practice, subsequent error mitigation techniques are required to
suppress the effect of noise in the cyclic permutation circuit itself, leading
to increased experimental complexity. Here, we perform a careful analysis of
the effect of uncorrelated, identical noise in the cyclic permutation circuit
and find that the estimation of expectation value of observables are robust
against dephasing noise. We support the analytical result with numerical
simulations and find that $67\%$ of errors are reduced for $M=2$, with physical
dephasing error probabilities as high as $10\%$. Our results imply that a broad
class of quantum algorithms can be implemented with higher accuracy in the
near-term with qubit platforms where non-dephasing errors are suppressed, such
as superconducting bosonic qubits and Rydberg atoms.
