Logical shadow tomography: Efficient estimation of error-mitigated observables

In near-term quantum applications, reducing errors and improving device reliability is an essential task. Towards these ends, various techniques have been introduced in recent literature, collectively referred to as quantum error mitigation techniques, for reducing errors in pre-fault-tolerant devices. Here, we introduce logical shadow tomography as a versatile error mitigation method. Our technique uses a stabilizer code to encode information in a logical state.  Instead of doing active error correction, quantum states will be measured at the end of computation via shadow tomography and non-logical errors are projected out in the classical post-processing. Relative to quantum subspace expansion which requires O(2^(M-1)L) experiments to estimate an logical Pauli observable encoded by an [[M, L, d]] code, our technique only requires 2^L experiments, an important practical reduction in resources.