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

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.

💡 Research Summary

The paper investigates photon‑mediated two‑qubit gates, focusing on state‑transfer fidelity between two qubits coupled through a single‑mode cavity. By mapping the Tavis‑Cummings Hamiltonian onto a three‑qubit “qubitized” Hamiltonian, the authors reduce the infinite‑dimensional bosonic problem to a tractable eight‑dimensional Hilbert space. The mapping relies on restricting the total excitation number to one, which is justified within the rotating‑wave approximation (RWA) regime.

Time evolution is performed using a first‑order Suzuki‑Trotter decomposition: the Hamiltonian is split into a free part (qubit frequencies) and an interaction part (qubit‑cavity couplings). The authors derive an analytical bound for the Trotter error, ϵ ≈ δt²(g₁Δ₁ + g₂Δ₂ + g₁g₂), and select a time step δt that guarantees a total fidelity loss below 10⁻³. In the resonant case (Δ₁ = Δ₂ = 0, g₁ = g₂ = g) the optimal transfer time is T = π/(√2 g); the required δt is about 0.015 g⁻¹.

The quantum circuit is implemented in Qiskit. Three qubits represent Qubit 1, the cavity, and Qubit 2. The initial state |e₁,0_c,g₂⟩ is prepared, and the Trotterized unitary U_ST = e^{-iH₀δt}e^{-iH_intδt} is applied repeatedly. After each step the overlap with the target state |g₁,0_c,Φ₂⟩ yields the fidelity F(t). Dissipation is modeled by coupling the cavity to a sink with rate κ, effectively adding a Lindblad term to the dynamics.

Key findings include:

1. Equal couplings (g₁ = g₂) and large detunings – Even when both qubits are far off‑resonant from the cavity, high‑fidelity transfer (F > 0.9) can be achieved by appropriately choosing g and κ. This opens a pathway for heterogeneous platforms where qubits have disparate transition frequencies.

2. Asymmetric couplings (g₁ ≠ g₂) – Transfer efficiency drops sharply, but the directionality of excitation flow can be controlled: the more strongly coupled qubit tends to act as the source, the weaker as the sink.

3. Cavity damping (κ) – When κ ≪ g, the transfer proceeds almost losslessly, preserving the resonant transfer time. For κ ≈ g or larger, photon loss dominates, causing rapid fidelity degradation. Hence high‑Q cavities are essential for practical implementations.

4. Validity of RWA – Simulations show that non‑energy‑conserving processes (e.g., simultaneous two‑photon absorption/emission) are negligible under the single‑excitation constraint and the chosen δt, confirming that the method remains accurate beyond the strict RWA regime.

5. Scalability – While the three‑qubit problem can be solved by exact diagonalization on a classical computer, the presented quantum algorithm scales naturally to multi‑mode cavities and larger qubit registers, where classical resources become prohibitive.

The authors benchmark their quantum‑circuit results against analytical solutions (available for special parameter sets) and against classical exact diagonalization, finding excellent agreement within the error bounds set by the Trotter step. They also provide a systematic procedure for estimating the required δt given a target total error, which can be adapted to more complex models.

In conclusion, the work demonstrates that NISQ‑compatible quantum simulations can reliably map out the performance landscape of cavity‑mediated two‑qubit gates across a broad parameter space, identifying under‑explored regimes (far‑detuned, asymmetric coupling, low‑damping) where high‑fidelity operations are possible. The methodology offers a practical tool for designing and optimizing photon‑mediated interactions in heterogeneous quantum architectures and paves the way for future studies of multi‑qubit, multi‑mode light‑matter systems that are intractable with conventional analytical or classical numerical techniques.