  Contemporary quantum computers have relatively high levels of noise, making
it difficult to use them to perform useful calculations, even with a large
number of qubits. Quantum error correction is expected to eventually enable
fault-tolerant quantum computation at large scales, but until then it will be
necessary to use alternative strategies to mitigate the impact of errors. We
propose a near-term friendly strategy to mitigate errors by entangling and
measuring $M$ copies of a noisy state $\rho$. This enables us to estimate
expectation values with respect to a state with dramatically reduced error,
$\rho^M/ \mathrm{Tr}(\rho^M)$, without explicitly preparing it, hence the name
"virtual distillation". As $M$ increases, this state approaches the closest
pure state to $\rho$, exponentially quickly. We analyze the effectiveness of
virtual distillation and find that it is governed in many regimes by the
behavior of this pure state (corresponding to the dominant eigenvector of
$\rho$). We numerically demonstrate that virtual distillation is capable of
suppressing errors by multiple orders of magnitude and explain how this effect
is enhanced as the system size grows. Finally, we show that this technique can
improve the convergence of randomized quantum algorithms, even in the absence
of device noise.
