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First- and second-order digital quantum simulation of three-level Jaynes-Cummings dynamics on superconducting quantum processors

Anonymous

Published Jun 1, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.26187/deakin.32970095

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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.
Quantum simulation of many-body systems offers a powerful approach to exploring collective quantum dynamics beyond classical computational reach. Although spin and fermionic models have been extensively simulated on digital quantum computers, the simulation of bosonic systems on programmable quantum processors is often hindered by the intrinsically large Hilbert space of bosonic modes. In this work, we study the digital quantum simulation of bosonic modes using the Holstein-Primakoff (HP) transformation and implement this protocol on a cloud-based superconducting quantum processor. Two representative models are realized on quantum hardware: (i) the driven harmonic oscillator and (ii) the Jaynes-Cummings model. Using data obtained from the quantum simulations, we systematically examine the interplay between algorithmic and hardware-induced errors to identify optimal simulation parameters. The dominant algorithmic errors arise from the finite number of qubits used in the HP mapping and the finite number of Trotter steps in the time evolution, while hardware errors mainly originate from gate infidelity, decoherence, and readout errors. This study advances the digital quantum simulation of many-body systems involving bosonic degrees of freedom on currently available cloud quantum processors and provides a framework that can be extended to more complex spin-boson and multimode cavity models.
ABSTRACT We present a fully digital approach for simulating single‐mode squeezed states using an enhanced bosonic encoding strategy on a circuit model, and demonstrate it on a superconducting quantum processor through a cloud platform. By mapping up to photonic Fock states onto qubits, our framework leverages Gray‐code‐based encodings to reduce gate overhead compared to conventional one‐hot or binary mappings. We further optimize resource usage by restricting the simulation to Fock states with even numbers of photons only, effectively doubling the range of photon numbers that can be represented for a given number of qubits. To overcome noise and finite coherence in current hardware, we employ a variational quantum simulation protocol, which adapts shallow, parameterized circuits through iterative optimization. Implemented on the Zuchongzhi‐2 superconducting platform, our method demonstrates squeezed‐state dynamics via a parameter sweep from vacuum state preparation () to squeezing levels that extend beyond the conventional truncation bound of encoded Fock space (). Results of our demonstration, corroborated by quantum state tomography and Wigner‐function analysis, confirm high‐fidelity state preparation and demonstrate the potential of Gray‐code‐inspired techniques for realizing continuous‐variable physics on near‐term, qubit‐based quantum processors.
Matter under extreme conditions behaves as a non-equilibrium, strongly-interacting quantum system. Such systems are in the non-perturbative regime of quantum chromodynamics (QCD), where their time evolution is classically intractable. Quantum computing offers a promising alternative, but present-day devices are limited in qubit count and circuit depth, so efficient formulations and algorithms are key to scaling toward experimentally relevant QCD simulations. A scalable framework is established for simulating energy loss and hadronization in 1+1-dimensional SU(2) lattice gauge theory, in which a heavy quark traverses a lattice of light quarks. Classical lattice QCD methods are translated into physics-informed circuits to prepare the interacting ground state. The evolution is run on IBM's quantum processor ibm_pittsburgh, where the charge distribution and energy loss are measured. A further study develops the quantum simulation of the fully gauge-fixed SU(2) Hamiltonian in a mixed basis, a formulation that is expected to remain efficient at all gauge couplings. Digitizing the continuous gauge fields with as few as three qubits per plaquette reproduces low-energy observables with 10−310^{-3}10−3 precision. Scaling to larger systems is limited by resource overhead, which motivates truncations that preserve the relevant observables. Sequency Hierarchy Truncation (SeqHT) exploits the hierarchy in basis-operator contributions. Demonstrated on the adiabatic preparation of the λφ4λφ^4λφ4 ground state on ibm_sherbrooke, SeqHT reduces circuit depth by ~30%, suppressing hardware noise in the extracted observables. All simulations in this dissertation are validated on quantum hardware against classical benchmarks. These studies advance quantum simulations of real-time QCD dynamics.
In recent years, there has been a significant progress in the development of digital quantum processors. The state-of-the-art quantum devices are imperfect, and fully algorithmic fault-tolerant quantum computing is a matter of future. Until technology develops to the state with practical error correction, computational approaches other than the standard digital one can be used to avoid execution of the most noisy quantum operations. We demonstrate how a hybrid digital-analog approach allows simulating dynamics of a transverse-field Ising model without standard two-qubit gates, which are currently one of the most problematic building blocks of quantum circuits. We use qubit-qubit crosstalks (couplings) of IBM superconducting quantum processors to simulate Trotterized dynamics of spin clusters and then we compare the obtained results with the results of conventional digital computation based on two-qubit gates from the universal set. The comparison shows that digital-analog approach significantly outperforms standard digital approach for this simulation problem, despite of the fact that crosstalks in IBM quantum processors are small. We argue that the efficiency of digital-analog quantum computing can be improved with the help of more specialized processors, so that they can be used to efficiently implement other quantum algorithms. This indicates the prospect of a digital-to-analog strategy for near-term noisy intermediate-scale quantum computers.
A higher-order Suzuki-Trotter decomposition or Trotterization can be exploited to mitigate the Trotter error in digital quantum simulation. This work revisits the second-order symmetric Trotterization in terms of the Trotter error, where quantum many-body spin dynamics of the transverse-field Ising model is simulated. While the work presents a pedagogical way to exploit a real quantum computer, the effectiveness of the symmetric Trotterization is evaluated in a prototype superconducting quantum device on IBM Quantum Experience. It turns out that the symmetric Trotterization does not provide higher accuracy than the first-order Trotterization in the testbed using the transverse-field Ising model. The result indicates that apart from the quantum errors, such as logical gate error and readout error, the use of a higher-order Trotterization should be circumspect, and the Trotter error would play an insignificant role in particular applications in an early stage of realized noisy intermediate-scale quantum (NISQ) devices.