Non-Markovian cost function for quantum error mitigation with Dirac Gamma matrices representation
Doyeol Ahn Department of Electrical,Computer Engineering,University of Seoul,Seoul,Inc.,R Korea +5 more
- 23 May 2023
TL;DR: In this paper , a 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, are explored.
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Abstract: 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.
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Figures
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Table 4 offers an encapsulation of theoretical projections concerning the fluctuations in quantum states during the execution of an Identity operation, an essential quantum gate operation. Contrary to the previous section, the Identity operation does not interchange the states of two qubits, but rather leaves the state of a qubit unchanged. This becomes increasingly crucial when these operations are impacted by non-Markovian noise sources. These predictions explore the possible alterations and dynamic responses of quantum states during the Identity operation. Non-Markovian noise, representing a more intricate noise pattern, highlights the system's dependence not merely on its current state, but also its past states. This inclusion of historical states introduces memory effects into the system, subsequently complicating the noise process and intensifying the challenge of managing it. 
Table 3: Quantum state fluctuations under the SWAP operation for ibm_guadalupe 
Table 2: Quantum state fluctuations under the SWAP operation for IonQ 
Table 1: Quantum state fluctuations of SWAP operation with non-Markovian noise sources
Citations
Quantum algorithm for nonlinear Burgers' equation for high-speed compressible flows
Esmaeil Esmaeilifar,Doyeol Ahn,R.S. Myong +2 more
TL;DR: Researchers propose a novel quantum algorithm for solving the nonlinear Burgers' equation, overcoming linearity limitations by employing multiple state vector copies and advanced quantum techniques, achieving linear scaling in time and demonstrating excellent agreement with classical simulations.
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