Cavity Mediated Two-Qubit Gate: Tuning to Optimal Performance with NISQ Era Quantum Simulations

TL;DR

This work presents a quantum-circuit framework to simulate cavity-mediated two-qubit gates in the Tavis–Cummings model, enabling state-transfer fidelity analysis across detunings, couplings, and cavity damping on NISQ devices. By qubitizing the Hamiltonian and applying Suzuki–Trotter time evolution, the authors benchmark the full non-RWA dynamics against the rotating-wave approximation, derive dispersive-regime transfer times, and explore damped-cavity effects. They reveal regimes where high-fidelity transfer occurs even for far-detuned qubits and show how unequal couplings degrade transfer unless detunings are judiciously chosen to balance Rabi frequencies. The approach directly maps to scalable simulations and can be extended to more complex photon-mediated operations and larger cavity networks, offering practical routes to optimize light-mmatter interfaces in quantum information processing.

Abstract

A variety of photon-mediated operations are critical to the realization of scalable quantum information processing platforms and their accurate characterization is essential for the identification of optimal regimes and their experimental realizations. Such light-matter interactions are often studied with a broad variety of analytical and computational methods that are constrained by approximation techniques or by computational scaling. Quantum processors present a new avenue to address these challenges. We consider the case of cavity mediated two-qubit gates. To investigate quantum state transfer between the qubits, we implement simulations with quantum circuits that are able to reliably track the dynamics of the system. Our quantum algorithm, compatible with NISQ (Noisy Intermediate Scale Quantum) era systems, allows us to map out the fidelity of the state transfer operation between qubits as a function of a broad range of system parameters including the respective detunings between the qubits and the cavity, the damping factor of the cavity, and the respective couplings between the qubits and the cavity. The algorithm provides a robust and intuitive solution, alongside a satisfactory agreement with analytical solutions or classical simulation algorithms in their respective regimes of validity. It allows us to identify under-explored regimes of optimal performance, relevant for heterogeneous quantum platforms, where the two-qubit gate can be rather effective between far-detuned qubits that are neither resonant with each other nor with the cavity. Besides its present application, the method introduced in the current paper can be efficiently used in otherwise untractable variations of the model and in various efforts to simulate and optimize photon-mediated two-qubit gates and other relevant operations in quantum information processing.

Figures (14)

• Figure 1: Schematic description of a system of two qubits coupled through a cavity. Qubit 1 and Qubit 2 operate at frequencies $\omega_1 = \omega_c + \Delta_1$ and $\omega_2 = \omega_c + \Delta_2$ respectively and are coupled to the cavity with respective coupling strengths $g_1$ and $g_2$. $\Delta_1$ and $\Delta_2$ are the detunings of Qubit 1 and Qubit 2 respectively with the cavity that has a damping factor $\kappa$ and is at frequency $\omega_c$. The damping process is represented by the coupling of the cavity with a sink.
• Figure 2: Illustration of the approach to solve the problem through the implementation of a quantum circuit. The left-hand side depicts the analytical procedure of "qubitizing" the Hamiltonian, i.e. mapping the Tavis-Cummings Hamiltonian on to a Hamiltonian with only qubits. This analytical component also includes the Suzuki-Trotter decomposition. The right-hand side highlights the steps of the quantum simulation to evolve the quantum state either on a quantum simulator or on a quantum processor.
• Figure 3: Quantum circuit for the time evolution of the initial state of a two-qubit system in a cavity under the Tavis-Cumings Hamiltonian. The circuit includes 3 qubits. The second qubit in the circuit represents the cavity while the first and the third represent Qubit 1 and Qubit 2 respectively, in our Tavis-Cummings Hamiltonian.
• Figure 4: Illustration of the systematic error in the time evolution due to the Suzuki-Trotter decomposition. (a): Difference with ideal fidelity, $1-F_{max}$, for the transfer of the polarized state from Qubit 1 to Qubit 2 as a function of the Trotter time step $\delta t$. The dashed line represents the target of $1-F_{max}$$\le 0.001$. (b): Evolution of the total energy in the system as a function of time for $\delta t = 0.01 \mathrm{g^{-1}}$, $\delta t = 0.05 \mathrm{g^{-1}}$ and $\delta t = 0.08 \mathrm{g^{-1}}$.
• Figure 5: Evolution of the occupation of the qubits and the cavity excited states as a function of time. The system is initially in the state with Qubit 1 in its excited state and Qubit 2 and the cavity in their ground states. Panels (a), (b) and (c) show short time dynamics up to the time for first resonant state transfer $t_{f}$. Panels (d), (e) and (f) show long time dynamics up to the time for the first dispersive state transfer $t_{f}^{'}(\Delta=5g)$.