End-to-End Complexity Analysis for Quantum Simulation of the Extended Jaynes-Cummings Models

• URL: http://arxiv.org/abs/2509.13546v1
• Date: Tue, 16 Sep 2025 21:23:53 GMT
• Title: End-to-End Complexity Analysis for Quantum Simulation of the Extended Jaynes-Cummings Models
• Authors: Nam Nguyen, Michael Yu, Alan Robertson, Hiromichi Nishimura, Samuel J. Elman, Benjamin Koltenbah,
• Abstract summary: We present an end-to-end framework for the quantum simulation of the Jaynes-Cummings model (eJCM)<n>We develop explicit quantum algorithms and circuits for simulating the system's time evolution.<n>This work establishes a complete roadmap for simulating the eJCM on future quantum computers.
• Score: 2.5789509846010574
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The extended Jaynes-Cummings model (eJCM) is a foundational framework for describing multi-mode light-matter interactions, with direct applications in quantum technologies such as photon addition and quasi-noiseless amplification. However, the model's complexity makes classical simulation intractable for large systems that could be of practical interest. In this work, we present a comprehensive, end-to-end framework for the quantum simulation of the eJCM. We develop explicit quantum algorithms and circuits for simulating the system's time evolution using first and second-order product formulas, analyzing the dynamics in both the Schrodinger and interaction pictures. Our analysis includes rigorous, closed-form error bounds that guide the choice of simulation parameters, and we extend the methodology to efficiently handle both pure and mixed quantum states. Furthermore, we validate our theoretical cost models with numerical simulations and provide a detailed fault-tolerant resource analysis, compiling the simulation circuits for a surface-code architecture to yield concrete estimates for physical qubit counts and execution times. This work establishes a complete roadmap for simulating the eJCM on future quantum computers.

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