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Iranian Journal of Physics Research

Dynamic Simulation of the Jaynes-Cummings model using the hybrid quantum-classical algorithm

Davoodi Yeganeh, H

Published Sep 1, 2021• 0 citations
Publisher

Abstract

The Jaynes-Cummings model is the canonical model for atom-light interactions, describing ‎a single confined bosonic mode interacting with a two-level system (qubit). This is ‎sufficient to describe a wide range of phenomena in quantum optics and quantum ‎computing. We simulate the dynamics of this model using the hybrid quantum-classical ‎algorithm (HQCA) consisting of quantum and classical computers. The parametric quantum ‎state preparations and quantum measurements are performed on the quantum computer ‎and parameters optimization employ on the classic computer. For implement of hybrid ‎quantum-classical algorithms, the Noisy Intermediate Scale Quantum (NISQ) computer is ‎used. In Noisy Intermediate Scale Quantum computers, we don’t need to error correction. ‎For this purpose, we transform Hamiltonian to qubit form and using an algorithm to obtain ‎the dynamic of the Jaynes-Cummings model. We obtain occupation probability and ‎transition probability in the Jaynes-Cummings model using the hybrid quantum-classical ‎algorithm. The output of the algorithm is compatible with the exact calculation‎‎‎‎.‎

DOI
10.47176/ijpr.21.2.01142

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The Jaynes-Cummings model is the canonical model for atom-light interactions, describing ‎a single confined bosonic mode interacting with a two-level system (qubit). This is ‎sufficient to describe a wide range of phenomena in quantum optics and quantum ‎computing. We simulate the dynamics of this model using the hybrid quantum-classical ‎algorithm (HQCA) consisting of quantum and classical computers. The parametric quantum ‎state preparations and quantum measurements are performed on the quantum computer ‎and parameters optimization employ on the classic computer. For implement of hybrid ‎quantum-classical algorithms, the Noisy Intermediate Scale Quantum (NISQ) computer is ‎used. In Noisy Intermediate Scale Quantum computers, we don’t need to error correction. ‎For this purpose, we transform Hamiltonian to qubit form and using an algorithm to obtain ‎the dynamic of the Jaynes-Cummings model. We obtain occupation probability and ‎transition probability in the Jaynes-Cummings model using the hybrid quantum-classical ‎algorithm. The output of the algorithm is compatible with the exact calculation‎‎‎‎.‎
Today Quantum Computers have a wide range of applications, one of the prominent is quantum simulation. Simulations are used for many industrial and research purposes. Here we understand how can we simulate three atoms heisenberg model interaction on three qubits using real NISQ(Noisy Intermediate-Scale Quantum Computing) device ‘ibmq_jakarta’ first we perform simulation by classical method after that we will go on quantum approach,for 3 qubit simulation its represented by 8×8 matrix. This is because there are 2³ = 8 states in the N =3(N represents number of qubits used) system, if the simulation were 50 particles(N=50) then it would be approx 10¹⁵×10¹⁵! Well beyond the capacity of today's classical computers, but for quantum computers this task will require only 15 qubits.
Quantum parameter estimation is a crucial tool for inferring unknown parameters in physical models from experimental data.The Jaynes-Cummings model is a widely used model in quantum optics that describes the interaction between an atom and a single-mode quantum optical field.In this Letter, we systematically investigate the problem of estimating the atom-light coupling strength in this model and optimize the initial state in the full Hilbert space.We compare the precision limits achievable for different optical field quantum states, including coherent states, amplitude-and phase-squeezed states, and provide experimental suggestions with an easily prepared substitute for the optimal state.Our results provide valuable insights into optimizing quantum parameter estimation in the Jaynes-Cummings model and can have practical implications for quantum metrology with hybrid quantum systems.
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.
Today Quantum Computers have a wide range of applications, one of the prominent is quantum simulation. Simulations are used for many industrial and research purposes. Here we understand how can we simulate three atoms heisenberg model interaction on three qubits using real NISQ(Noisy Intermediate-Scale Quantum Computing) device 'ibmq_jakarta' first we perform simulation by classical method after that we will go on quantum approach,for 3 qubit simulation its represented by 8×8 matrix. This is because there are 2³ = 8 states in the N =3(N represents number of qubits used) system, if the simulation were 50 particles(N=50) then it would be approx 10¹⁵×10¹⁵! Well beyond the capacity of today's classical computers, but for quantum computers this task will require only 15 qubits.
This work presents a digital quantum simulation of a three-level atomic system interacting with a single-mode electromagnetic field based on the Jaynes-Cummings model, implemented on IBM Quantum superconducting processors. A qutrit is encoded using two physical qubits to represent the atomic states, while an additional qubit encodes the truncated field mode, enabling the realization of effective Λ -type atomic dynamics. The continuous-time light-matter interaction is implemented in a digital form by discretizing the evolution using Suzuki-Trotter decomposition. In contrast to an analog realization, the digital simulation replaces the continuous evolution with a sequence of quantum gates whose parameters are explicitly controlled. Phase evolution arising from the interaction Hamiltonian is digitally encoded using calibrated R Z gates, whose rotation angles are fixed by the physically relevant coupling scale and the chosen Trotter time step. State preparation is achieved using Hadamard and parametrized rotation gates, while the interaction dynamics are implemented through controlled operations. A comparative analysis between first- and second-order Trotter implementations reveals a trade-off between digital accuracy and hardware-induced noise. Overall, the results demonstrate that calibrated gate operations and noise-aware circuit design enable reliable digital simulation of multilevel light-matter interactions on noisy intermediate-scale quantum platforms.
This work presents a digital quantum simulation of a three-level atomic system interacting with a single-mode electromagnetic field based on the Jaynes-Cummings model, implemented on IBM Quantum superconducting processors. A qutrit is encoded using two physical qubits to represent the atomic states, while an additional qubit encodes the truncated field mode, enabling the realization of effective ΛΛΛ-type atomic dynamics.The continuous-time light-matter interaction is implemented in a digital form by discretizing the evolution using Suzuki-Trotter decomposition. In contrast to an analog realization, the digital simulation replaces the continuous evolution with a sequence of quantum gates whose parameters are explicitly controlled. Phase evolution arising from the interaction Hamiltonian is digitally encoded using calibrated RZR_ZRZ​ gates, whose rotation angles are fixed by the physically relevant coupling scale and the chosen Trotter time step.State preparation is achieved using Hadamard and parametrized rotation gates, while the interaction dynamics are implemented through controlled operations. A comparative analysis between first- and second-order Trotter implementations reveals a trade-off between digital accuracy and hardware-induced noise. Overall, the results demonstrate that calibrated gate operations and noise-aware circuit design enable reliable digital simulation of multi-level light-matter interactions on noisy intermediate-scale quantum platforms.