Decoherence bounds on fidelity of operations going outside of the computational subspace

The fidelity of operations performed on qubits is often limited by incoherent errors, which typically can be modeled by fundamental Markovian noise processes such as amplitude damping and dephasing. In [Phys. Rev. Lett. 129, 150504 (2021)], a simple formula for the fidelity reduction of a general multiqubit operation in terms of the dissipative rates and the corresponding Lindblad jump operators is presented. This reduction is independent of the specific operation when the ideal evolution is confined to the computational subspace. Here we address quantum operations that utilize the states from outside of the computational subspace and find a closed expression for the fidelity reduction under the dissipation acting independently on the individual qubits. Using this expression we calculate the correction to the fidelity for a few well-known operations under various dissipation processes. These results are useful for understanding the error budgets of quantum gates while scaling up quantum computers.