An Analytical Approach to Design Space Exploration for Cavity-Mediated Quantum State Transfer in Multi-core Architectures

Abstract: In multi-core quantum computing architectures, waveguide-mediated interconnects are essential for facilitating fast, high-fidelity quantum state transfer between qubits located in different chips. However, optimizing these systems typically relies on computationally expensive numerical simulations that offer limited physical insight. In this work, we derive exact analytical expressions for the state transfer dynamics of a two-qubit system coupled via a waveguide, modeled through a Jaynes-Cummings Hamiltonian and the Lindblad master equation. We apply the Monte Carlo wave-function method and obtain a closed-form solution for qubit occupation probabilities that accounts for both detuning and dissipative losses. Our analytical framework provides a significant computational speedup compared to standard numerical solvers, enabling large-scale parameter sweeps while maintaining high precision in both fidelity and latency predictions. Furthermore, the model reveals and explains systematic low-fidelity regions arising from destructive interference between internal oscillations and detuning-induced envelopes, which are phenomena that are difficult to characterize through numerical means alone. Finally, we propose a simplified latency model and an efficiency-based function to enable rapid identification of optimal operating points. This analytical approach provides a robust foundation for the design and optimization of interconnects in multi-core quantum processors.

• The paper derives closed-form expressions for qubit excitation and fidelity, linking system parameters directly to performance metrics.
• It employs the Monte Carlo wave-function method with an effective non-Hermitian Hamiltonian, achieving a 100× computational speedup over traditional simulations.
• The analytical model reveals low-fidelity regimes and latency trade-offs, offering actionable insights for optimizing modular quantum processor design.

Analytical Modeling of Cavity-Mediated Quantum State Transfer in Multi-Core Quantum Architectures

Context and Motivation

The proliferation of modular architectures in quantum computing has led to an increased demand for high-fidelity, low-latency quantum state transfer across chip-to-chip links. Waveguide-mediated interconnects (waveguide QED channels) constitute a promising solution, balancing the speed of direct coupling with the distance scalability of optical networks. However, optimizing such channels is hampered by the dependence on numerically expensive simulations, which are not conducive to large-scale parameter sweeps or transparent physical insight.

System Formalism and Analytical Framework

This work formulates the dynamics of a two-qubit state transfer system, each qubit located in a separate chip and coupled via a single-mode waveguide. The interaction is modeled by a Jaynes-Cummings Hamiltonian under the Rotating Wave Approximation, capturing energy-conserving photon–qubit exchanges. Environmental noise and dissipative losses are integrated through a Lindblad master equation.

The authors derive closed-form analytical expressions for the time-dependent probability of qubit excitation at the receiving chip (qubit B) using the Monte Carlo wave-function method. Notably, this approach neglects quantum jumps for the chosen system, simplifying the evolution to an effective non-Hermitian Hamiltonian treatment. Both lossless and lossy scenarios are considered, allowing explicit incorporation of detuning (Δω), coupling strength ($g$), qubit decay ($\gamma$), and waveguide loss ($\kappa$). The resulting formulas expose the precise dependency of fidelity and latency metrics on system parameters, facilitating direct optimization.

Computational Efficiency and Validation

Comparison of analytical predictions with full numerical QuTiP simulations demonstrates excellent agreement, both for excitation probabilities and fidelity-latency heatmaps. Empirically, the analytical method achieves a computational speedup of two orders of magnitude relative to QuTiP, maintaining precision with an average fidelity difference of $4.5 \times 10^{-6}$ and an average latency difference of $3\,\text{ps}$. As a result, exhaustive parameter sweeps (e.g., $200^2$ grid) and real-time design automation scenarios are rendered tractable.

Parameter Space Analysis: Loss-Induced Phenomena

The analytical model reveals parameter regimes historically difficult to characterize through numerical means. Specifically, systematic low-fidelity regions emerge due to destructive interference between internal and envelope oscillations created by detuning. These effects are traced to the ratio of oscillation frequencies ($\theta/\delta$), with odd fractional values marking persistent low-fidelity “diagonals” in parameter space. Under strong waveguide losses, detuning improves fidelity (contradicting on-chip intuition), while high qubit decay suppresses fidelity irrespective of detuning. This nuanced interplay has direct implications on quantum processor architecture, guiding the avoidance of deleterious regimes.

Latency Modeling and Efficiency Function

The authors introduce a simplified latency predictor, leveraging the analytical model for small-loss systems. By identifying phase-matching conditions between envelope and internal waves, latency is resolved as a multiple of internal half-periods. The proposed efficiency function $J(n,t)$ balances fidelity and latency, allowing designers to prioritize either metric during optimization sweeps. This model accurately predicts optimal transmission times, further reducing the need for explicit time-dependent simulations.

Practical and Theoretical Implications

The analytical approach substantiates a robust foundation for automated optimization of waveguide QED links in modular quantum processors. Practically, real-time sensitivity analyses and large-scale parameter space exploration become feasible, supporting rapid iteration in hardware design and EDA workflows. Theoretically, the explicit expressions reveal critical fidelity boundaries, characterize the impact of loss and detuning quantitatively, and expose architectural constraints intrinsic to cavity-mediated quantum information transfer.

The results also suggest that extending the model to multi-mode waveguides or larger excitation subspaces is tractable, potentially generalizing to higher-dimensional modular systems or alternative physical platforms.

Conclusion

This work significantly advances design space exploration for waveguide-mediated quantum state transfer. By achieving exact analytical solutions for both lossless and lossy systems, computational acceleration, and transparent parameter dependency, it enables robust optimization of modular quantum architectures. The characterization of low-fidelity regions and latency-fidelity trade-offs has immediate relevance for the practical scaling of quantum processors, and the modeling framework is extensible to complex physical scenarios.

Future developments may involve analytical treatments of multi-mode channels, integration into quantum circuit compilers, and the inclusion of more sophisticated environmental noise models. The formalism here serves not only to accelerate simulation but also to deepen physical understanding of quantum interconnects (2604.27664).