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Reducing the impact of errors and decoherence in near-term quantum computers,such as noisy intermediate-scale quantum (NISQ) devices, is critical for theirpractical implementation. These factors significantly limit the applicabilityof quantum algorithms, necessitating a comprehensive understanding of theirphysical origins to establish effective error mitigation strategies. In thisstudy, we present a non-Markovian model of quantum state evolution and aquantum error mitigation cost function tailored for NISQ devices interactingwith an environment represented by a set of simple harmonic oscillators as anoise source. Employing the projection operator formalism and both advanced andretarded propagators in time, we derive the reduced-density operator for theoutput quantum states in a time-convolutionless form by solving the quantumLiouville equation. We examine the output quantum state fluctuations for bothidentity and controlled-NOT (CNOT) gate operations in two-qubit operationsusing a range of input states. Subsequently, these results are compared withexperimental data from ion-trap and superconducting quantum computing systemsto estimate the crucial parameters of the cost functions for quantum errormitigation. Our findings reveal that the cost function for quantum errormitigation increases as the coupling strength between the quantum system andits environment intensifies. This study underscores the significance ofnon-Markovian models in understanding quantum state evolution and highlightsthe practical implications of the quantum error mitigation cost function whenassessing experimental results from NISQ devices.

Non-Markovian noise sources for quantum error mitigation