  Near-term quantum computers have been built as intermediate-scale quantum
devices and are fragile against quantum noise effects, namely, NISQ devices.
Traditional quantum-error-correcting codes are not implemented on such devices
and to perform quantum computation in good accuracy with these machines we need
to develop alternative approaches for mitigating quantum computational errors.
In this work, we propose quantum error mitigation (QEM) scheme for quantum
computational errors which occur due to couplings with environments during gate
operations, i.e., decoherence. To establish our QEM scheme, first we estimate
the quantum noise effects on single-qubit states and represent them as groups
of quantum circuits, namely, quantum-noise-effect circuit groups. Then our QEM
scheme is conducted by subtracting expectation values generated by the
quantum-noise-effect circuit groups from that obtained by the quantum circuits
for the quantum algorithms under consideration. As a result, the quantum noise
effects are reduced, and we obtain approximately the ideal expectation values
via the quantum-noise-effect circuit groups and the numbers of elementary
quantum circuits composing them scale polynomial with respect to the products
of the depths of quantum algorithms and the numbers of register bits. To
numerically demonstrate the validity of our QEM scheme, we run noisy quantum
simulations of qubits under amplitude damping effects for four types of quantum
algorithms. Furthermore, we implement our QEM scheme on IBM Q Experience
processors and examine its efficacy. Consequently, the validity of our scheme
is verified via both the quantum simulations and the quantum computations on
the real quantum devices.
