  Quantum error mitigation is essential for computing on the noisy quantum
computer with a limited number of qubits. In this paper, we propose a practical
protocol of error mitigation by virtually purifying the quantum state without
qubit overhead or requiring only one ancillary qubit. In dual-state
purification, we effectively generate a purified state with increased fidelity
using the erroneous state and its dual state, respectively, prepared with the
noisy quantum circuit and the dual map of its inverse circuit. Combined with
tomography purification, we can make sure that the final estimate of an
observable is obtained from a pure state. The numerical result suggests that
our protocol reduces the error by a rescaling factor decreasing with the qubit
number and circuit depth, i.e. the performance of purification is better for
larger circuits. On a cloud quantum computer, we successfully demonstrate the
reduced error with a quantum variational eigensolver circuit.
