  Fighting against noise is crucial for NISQ devices to demonstrate practical
quantum applications. In this work, we give a new paradigm of quantum error
mitigation based on the vectorization of density matrices. Different from the
ideas of existing quantum error mitigation methods that try to distill
noiseless information from noisy quantum states, our proposal directly changes
the way of encoding information and maps the density matrices of noisy quantum
states to noiseless pure states, which is realized by a novel and NISQ-friendly
measurement protocol and a classical post-processing procedure. Our protocol
requires no knowledge of the noise model, no ability to tune the noise
strength, and no ancilla qubits for complicated controlled unitaries. Under our
encoding, NISQ devices are always preparing pure quantum states which are
highly desired resources for variational quantum algorithms to have good
performance in many tasks. We show how this protocol can be well-fitted into
variational quantum algorithms. We give several concrete ansatz constructions
that are suitable for our proposal and do theoretical analysis on the sampling
complexity, the expressibility, and the trainability. We also give a discussion
on how this protocol is influenced by large noise and how it can be well
combined with other quantum error mitigation protocols. The effectiveness of
our proposal is demonstrated by various numerical experiments.
