  Quantum error mitigation is a key approach for extracting target state
properties on state-of-the-art noisy machines and early fault-tolerant devices.
Using the ideas from flag fault tolerance and virtual state purification, we
develop the virtual channel purification (VCP) protocol, which consumes similar
qubit and gate resources as virtual state purification but offers up to
exponentially stronger error suppression with increased system size and more
noisy operation copies. Furthermore, VCP removes most of the assumptions
required in virtual state purification. Essentially, VCP is the first quantum
error mitigation protocol that does not require specific knowledge about the
noise models, the target quantum state, and the target problem while still
offering rigorous performance guarantees for practical noise regimes. Further
connections are made between VCP and quantum error correction to produce one of
the first protocols that combine quantum error correction and quantum error
mitigation beyond concatenation. We can remove all noise in the channel while
paying only the same sampling cost as low-order purification, reaching beyond
the standard bias-variance trade-off in quantum error mitigation. Our protocol
can also be adapted to key tasks in quantum networks like channel capacity
activation and entanglement distribution.
