Doyeol Ahn

In this study, we explore the non-Markovian cost function for quantum error mitigation (QEM) and the representation of two-qubit operators using Dirac Gamma matrices, central to the structure of relativistic quantum mechanics. The primary focus of quantum computing research, particularly with noisy intermediate-scale quantum (NISQ) devices, is on reducing errors and decoherence for practical application. While much of the existing research concentrates on Markovian noise sources, the study of non-Markovian sources is crucial given their inevitable presence in most solid-state quantum computing devices. We introduce a non-Markovian model of quantum state evolution and a corresponding QEM cost function for NISQ devices, considering an environment typified by simple harmonic oscillators as a noise source. The Dirac Gamma matrices, integral to areas of physics like quantum field theory and supersymmetry, share a common algebraic structure with two-qubit gate operators. By representing the latter using Gamma matrices, we are able to more effectively analyze and manipulate these operators due to the distinct properties of Gamma matrices. We evaluate the fluctuations of the output quantum state for identity and SWAP gate operations in two-qubit operations across various input states. By comparing these results with experimental data from ion-trap and superconducting quantum computing systems, we estimate the key parameters of the QEM cost functions. Our results reveal that as the coupling strength between the quantum system and its environment increases, so does the QEM cost function. This study underscores the importance of non-Markovian models for understanding quantum state evolution and the practical implications of the QEM cost function when assessing experimental results from NISQ devices.

Reducing the impact of errors and decoherence in near-term quantum computers, such as noisy intermediate-scale quantum (NISQ) devices, is critical for their practical implementation. These factors significantly limit the applicability of quantum algorithms, necessitating a comprehensive understanding of their physical origins to establish effective error mitigation strategies. In this study, we present a non-Markovian model of quantum state evolution and a quantum error mitigation cost function tailored for NISQ devices interacting with an environment represented by a set of simple harmonic oscillators as a noise source. Employing the projection operator formalism and both advanced and retarded propagators in time, we derive the reduced-density operator for the output quantum states in a time-convolutionless form by solving the quantum Liouville equation. We examine the output quantum state fluctuations for both identity and controlled-NOT (CNOT) gate operations in two-qubit operations using a range of input states. Subsequently, these results are compared with experimental data from ion-trap and superconducting quantum computing systems to estimate the crucial parameters of the cost functions for quantum error mitigation. Our findings reveal that the cost function for quantum error mitigation increases as the coupling strength between the quantum system and its environment intensifies. This study underscores the significance of non-Markovian models in understanding quantum state evolution and highlights the practical implications of the quantum error mitigation cost function when assessing experimental results from NISQ devices.