شبیه‌سازی دینامیک موثر دیراک با استفاده از راه‌پیمایی‌های کوانتومی بر بستر کامپیوترهای کوانتومی دیجیتال

نوع مقاله : کاربردی

نویسنده
گروه آموزشی فیزیک، دانشکده علوم پایه، دانشگاه تفرش، تفرش، ایران
10.22034/jmrph.2026.122919.0
چکیده
نظریه میدان کوانتومی چارچوب بنیادی توصیف ذرات و میدان‌ها در فیزیک مدرن است، اما حل دقیق بسیاری از مدل‌های آن، به‌ویژه در رژیم‌های غیراغتشاشی، با روش‌های تحلیلی و عددی کلاسیک با دشواری‌های جدی روبه‌رو است. یکی از مسیرهای پیشنهادی برای مطالعه چنین سامانه‌هایی استفاده از شبیه‌سازی کوانتومی است که در آن دینامیک یک مدل فیزیکی با بهره‌گیری از سامانه‌های کوانتومی قابل‌کنترل بازنمایی می‌شود. در این کار، امکان مدل‌سازی یک چارچوب گسسته‌ای برای توصیف دینامیک نسبیتی با استفاده از راه‌پیمایی کوانتومی گسسته‌زمان و پیاده‌سازی آن بر بستر کامپیوترهای کوانتومی دیجیتال مورد بررسی قرار می‌گیرد. در این چارچوب، تحول زمانی سامانه با استفاده از عملگرهای یکانی تعریف می‌شود و نشان داده می‌شود که در حد پیوسته و با مقیاس‌بندی مناسب در فضا و زمان، این مدل گسسته می‌تواند دینامیک مؤثری متناظر با معادله دیراک برای یک ذره آزاد در فضای 1+1 بعدی را بازتولید کند. سپس این مدل در قالب مدارهای کوانتومی روی یک سامانه‌ی پنج‌کیوبیتی که گرافی با ۱۶ گره را نمایش می‌دهد پیاده‌سازی می‌شود تا رفتار دینامیک و الگوی تداخلی توزیع احتمال حاصل از راه‌پیمایی کوانتومی در شرایط ایده‌آل و در حضور نویز بررسی شود.
کلیدواژه‌ها

عنوان مقاله English

Simulation of Effective Dirac Dynamic via Quantum Walks on Digital Quantum Computers

نویسنده English

Zeynab Kiamehr
Tafresh UniversityDepartment of Physics, Faculty of Basic Sciences, Tafresh University, Tafresh, Iran
چکیده English

Quantum field theory (QFT) forms the fundamental basis of many areas in physics and is indispensable for our understanding of the universe. This research shows that simulating QFT using digital quantum computers is not merely a numerical computation, but rather a foundational problem in physical modeling that simultaneously depends on the theoretical structure of QFT, the choice of quantum algorithm, the definition of fidelity metrics, and the limitations of existing hardware. Since the equations of quantum field theories are generally complex and analytically intractable, employing quantum walks as a computational framework provides an alternative approach that enables the exploration of these theories in regimes inaccessible to classical methods. Within this framework, digital quantum walks serve as a natural algorithmic implementation for simulating the dynamics of quantum fields, as their discrete structure aligns well with the intrinsic architecture of NISQ-era quantum processors and, in the continuum limit, converges toward fundamental equations such as the Dirac equation. However, simulations and implementations on IBM’s superconducting quantum hardware reveal a high sensitivity to noise: even within non-interacting models, noise effects can fundamentally distort the interference patterns of the probability distributions. Consequently, defining a precise quantitative metric to assess simulation validity becomes crucial. The adoption of Hellinger fidelity as the central measure enables a systematic comparison between the probability distributions obtained from ideal simulations, noisy models, and experimental data, clearly indicating the extent to which the simulated dynamics can be interpreted as a valid representation of QFT.

کلیدواژه‌ها English

Quantum simulation
quantum field theory (QFT)
quantum walk
Hellinger Fidelity
quantum hardware noise
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انتشار آنلاین از 08 مهر 1405