Error mitigation with ideal Clifford gates and noisy ancillas

Quantum error mitigation techniques are usually conceived in the context of NISQ devices. Here we explore the potential of quasiprobability-based error mitigation in the context of fault-tolerant quantum computing with perfect Clifford gates and noisy magic states. We derive optimal decompositions of the ideal T gate in terms of Cliffords and noisy T gates obtained via state injection of the available magic states. We study how the technique can be used, depending on the noise level, in place or in conjunction with magic state distillation protocols, such as the Bravyi-Haah protocol, to simulate the output of an ideal quantum computation with the desired accuracy. We conclude by highlighting how these techniques provide us with methods to quantify how close a noisy quantum computer is to an ideal one, and how much advantage it provides with respect to a classical computation based on the same method.