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arXiv:2201.03068

Study of the effect of quantum noise on the accuracy of the Schrodinger equation simulation on a quantum computer using the Zalka-Wiesner method

Yu. I. Bogdanov, Н. А. Богданова, Dmitriy V. Fastovets, V. F. Lukichev

Published Jan 9, 2022• 2 citations
arXivHTMLPDF

Abstract

The study of the effect of quantum noise on the accuracy of modeling quantum systems on a quantum computer using the Zalka-Wiesner method is carried out. The efficiency of the developed methods and algorithms is demonstrated by the example of solving the nonstationary Schrodinger equation with allowance for quantum noise for a particle moving in the Poschl-Teller potential. The analysis and prediction of accuracy for the Zalka-Wiesner method are carried out taking into account the complexity of the quantum system and the strength of quantum noise. In our opinion, the considered problem provides a useful test for assessing the quality and efficiency of quantum computing devices on various physical platforms currently being developed. The obtained results are essential for the development of high-precision methods for controlling the technologies of quantum computations.

DOI
10.48550/arxiv.2201.03068

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The study of the effect of quantum noise on the accuracy of modeling quantum systems on a quantum computer using the Zalka-Wiesner method is carried out. The efficiency of the developed methods and algorithms is demonstrated by the example of solving the nonstationary Schrodinger equation with allowance for quantum noise for a particle moving in the Poschl-Teller potential. The analysis and prediction of accuracy for the Zalka-Wiesner method are carried out taking into account the complexity of the quantum system and the strength of quantum noise. In our opinion, the considered problem provides a useful test for assessing the quality and efficiency of quantum computing devices on various physical platforms currently being developed. The obtained results are essential for the development of high-precision methods for controlling the technologies of quantum computations.
The study of the effect of quantum noise on the accuracy of modeling quantum systems on a quantum computer using the Zalka-Wiesner method is carried out. The efficiency of the developed methods and algorithms is demonstrated by the example of solving the nonstationary Schrödinger equation with allowance for quantum noise for a particle moving in the Pöschl–Teller potential. The analysis and prediction of accuracy for the Zalka-Wiesner method are carried out taking into account the complexity of the quantum system and the strength of quantum noise. In our opinion, the considered problem provides a useful test for assessing the quality and efficiency of quantum computing devices on various physical platforms currently being developed. The obtained results are essential for the development of high-precision methods for controlling the technologies of quantum computations.
The simulation of quantum systems on a quantum computer using the Zalka–Wiesner algorithm including quantum noise has been considered. The efficiency of developed methods and algorithms has been demonstrated by example of the solution of the time-dependent Schrödinger equation for a particle in the Pöschl–Teller potential. The developed analytical theory of the effect of quantum noise on the accuracy of simulation has been compared with Monte Carlo simulations. The accuracy of the solution of the Schrödinger equation for a many-electron system has been forecasted as a function of the number of electrons and for different levels of noise.
In recent years, quantum information systems have attracted increasing attention of researchers in the field of computer science and physics. However, the introduction and practical application of quantum computing is limited by the influence of noise and errors that occur in quantum systems. To implement effective control and improve the reliability of quantum information systems, it is necessary to develop methods that can suppress and correct errors in the process of quantum computing. The purpose of this work is to develop and study a control model based on noise-immune quantum computing, as well as methods for suppressing and correcting errors in quantum computing. The paper proposes a combination of different approaches, including the use of error correction codes, noise suppression algorithms, and methods for optimal control of quantum information systems. In the course of the study, a control model was developed that allows efficient processing of information in quantum systems, taking into account the presence of noise and errors. Experiments were carried out using real quantum devices to evaluate the effectiveness of the proposed model. The experimental results show that the developed method can significantly improve the reliability and accuracy of quantum computing. The proposed control model based on noise-immune quantum computing and methods for suppressing and correcting errors represent a significant contribution to the development of quantum information systems. Further development and optimization of the proposed approach can lead to the creation of more reliable and efficient quantum systems capable of solving complex computational problems.
In recent years, quantum information systems have attracted increasing attention of researchersin the field of computer science and physics. However, the introduction and practicalapplication of quantum computing is limited by the influence of noise and errors that occur inquantum systems. To implement effective control and improve the reliability of quantum informationsystems, it is necessary to develop methods that can suppress and correct errors in theprocess of quantum computing. The purpose of this work is to develop and study a control modelbased on noise-immune quantum computing, as well as methods for suppressing and correctingerrors in quantum computing. The paper proposes a combination of different approaches, includingthe use of error correction codes, noise suppression algorithms, and methods for optimal controlof quantum information systems. In the course of the study, a control model was developedthat allows efficient processing of information in quantum systems, taking into account the presenceof noise and errors. Experiments were carried out using real quantum devices to evaluate theeffectiveness of the proposed model. The experimental results show that the developed method cansignificantly improve the reliability and accuracy of quantum computing. The proposed controlmodel based on noise-immune quantum computing and methods for suppressing and correctingerrors represent a significant contribution to the development of quantum information systems.Further development and optimization of the proposed approach can lead to the creation of morereliable and efficient quantum systems capable of solving complex computational problems.
Quantum computing is expected to introduce the next era of computing speed and power, and its software - quantum program is gaining increasing research interest in the software engineering community. A significant characteristic of quantum computing is the existence of noise. Unlike classical computers where the output of a program is usually deterministic, the execution of a quantum program may be affected by quantum noise. Such a difference may cause difficulties or misunderstandings for developers shifting from classical programming to quantum programming. To understand the impact of quantum noise on quantum programs and its implications for software developers, we conduct a series of studies with real-world quantum programs and quantum computing environments. Specifically, we first measure and analyze the noise in a real quantum computer by testing it with a basic quantum program. We find that a non-neglectable amount of quantum noise generally exists in real quantum computers. Then we investigate the robustness of quantum programs against different quantum noises by testing 18 real-world quantum programs and 50,000 randomly generated quantum circuits in simulated and real environments. We observe that quantum noise can significantly influence the correctness of quantum programs, and different quantum circuit structures show diverse sensitivity patterns under the same noise. Based on the observations, we build a machine learning model to predict the fidelity of a quantum program under certain quantum noise. The model achieves a small average fidelity prediction error, meaning the impact of noise can be precisely estimated statistically.
A major challenge in realizing efficient and powerful quantum algorithms is quantum noise. Quantum noise itself is a sophisticated topic that is not seen in the classical domain. In this paper, we explore the impact of noise on quantum algorithms in Noisy Intermediate-Scale Quantum (NISQ) systems. This paper first introduces the origins of quantum noise. Next, it proposes a common treatment to simplify the view of quantum noise. Finally, it presents a case study to investigate the impact of noise on quantum Fourier transform algorithm.