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arXiv:2607.23036

Parameter Calibration for Reduced-Bandwidth Two-Photon Waveguide-QED Simulations

Romain Piron, Akihito Soeda

quant-phSubmitted Jul 25, 2026• Announced Jul 28, 2026• 0 citations
arXivHTMLPDF

Abstract

Waveguide-QED platforms represent one potential approach to scalable quantum technologies, but their simulation remains computationally demanding due to the large number of frequency modes required to describe traveling photons. In practice, increasing the simulated bandwidth rapidly raises the numerical cost, leading to a trade-off between accuracy and tractability. The existing approaches formulated in time-domain indirectly control this trade-off through the choice of time step, which obscures the connection between discretization parameters and the represented spectral window. In this work, we introduce an end-to-end framework to explicitly control the effective bandwidth in waveguide-QED simulations of two-photon scattering. We show that truncating the frequency domain requires consistent shifts of the model parameters, and derive a systematic calibration procedure that preserves the physical accuracy of the reduced model. This enables tuning the central frequency and the bandwidth of the numerical spectrum, leading to a several-fold reduction in the Hilbert space dimension while maintaining physical accuracy. We discuss the limitations of this calibration and relate the finite-bandwidth viewpoint to time-domain discretizations.

Comments
11 pages, 10 figures

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Waveguide-QED platforms represent one potential approach to scalable quantum technologies, but their simulation remains computationally demanding due to the large number of frequency modes required to describe traveling photons. In practice, increasing the simulated bandwidth rapidly raises the numerical cost, leading to a trade-off between accuracy and tractability. The existing approaches formulated in time-domain indirectly control this trade-off through the choice of time step, which obscures the connection between discretization parameters and the represented spectral window. In this work, we introduce an end-to-end framework to explicitly control the effective bandwidth in waveguide-QED simulations of two-photon scattering. We show that truncating the frequency domain requires consistent shifts of the model parameters, and derive a systematic calibration procedure that preserves the physical accuracy of the reduced model. This enables tuning the central frequency and the bandwidth of the numerical spectrum, leading to a several-fold reduction in the Hilbert space dimension while maintaining physical accuracy. We discuss the limitations of this calibration and relate the finite-bandwidth viewpoint to time-domain discretizations.
Simulations of quantum dynamics of traveling photons interacting with matter can be used to model and design photonic quantum-network components. Such simulations require selecting a finite set of photonic modes, where smaller sets are more desirable for computational efficiency. In this work, however, we show that opting for smaller subsets alters simulation results, if done naively. We therefore provide a consistency condition that can be used to calibrate the simulation input parameters to increase efficiency while preserving accuracy, simultaneously. This condition is then used to derive a simple prescription that reduces the propagation cost by two order of magnitude in a waveguide benchmark. Finally, we extend the same calibration principle to a two-dimensional atomic array, demonstrating the simultaneous benefits beyond analytically solvable waveguide models.
The exchange of quantum information among nodes in a quantum network is one of the main challenges in modern technologies. Superconducting waveguide QED networks hold great potential for realizing distributed quantum computation, where distinct nodes communicate via itinerant single photons. Yet, different frequencies among the nodes restrict their applicability and limit scalability. Here we derive the controls required to shape single photons arbitrarily detuned with respect to their natural frequency, allowing thus for an on-demand and deterministic exchange of quantum information among frequency detuned nodes. We provide a theoretical framework, analyzing the properties of the controls for typical photon shapes, identifying operation regimes amenable for experimental realization. We then show how these controls enable frequency-selective quantum state transfer among non-resonant and distant nodes of a realistic network. In addition, we also provide a simple extension for remote entanglement generation between these nodes. The suitability and high-fidelity of these protocols is supported by numerical simulations, highlighting the novel networking possibilities unlocked when shaping frequency-tunable single photons.
Light-matter interaction at the single-quantum level is the heart of many regimes of high fundamental importance to modern quantum technologies. Strong interaction of a qubit with a single photon of an electromagnetic field mode is described by the cavity/circuit electrodynamics (QED) regime which is one of the most advanced platforms for quantum computing. The opposite regime of the waveguide QED, where qubits interact with a continuum of modes in an infinite one-dimensional space, is also at the focus of recent research revealing novel quantum phenomena. Despite the demonstration of several key features of waveguide QED, the transition from an experimentally realizable finite-size system to the theoretically assumed infinite device size is neither rigorously justified nor fully understood. In this paper, we formulate a unifying theory which under a minimal set of standard approximations accounts for physical boundaries of a system in all parameter domains. Considering two qubits in a rectangular waveguide which naturally exhibits a low frequency cutoff we are able to account for infinite number of modes and obtain an accurate description of the waveguide transmission, a life-time of a qubit-photon bound state and the exchange interaction between two qubit-photon bounds states. For verification, we compare our theory to experimental data obtained for two superconducting qubits in a rectangular waveguide demonstrating how the infinite size limit of waveguide QED emerges in a finite-size system. Our theory can be straightforwardly extended to other waveguides such as the photonic crystal and coupled cavity arrays.
QwaveMPS is an open-source Python library for simulating one-dimensional quantum many-body waveguide systems using matrix product states (MPS). It provides a user-friendly interface for constructing, evolving, and analyzing quantum states and operators, facilitating studies in quantum physics and quantum information with waveguide-QED systems. This approach enables efficient, scalable simulations by focusing computational resources on the most relevant parts of the quantum system. Thus, one can study a wide range of complex dynamical interactions, including time-delayed feedback effects in the non-Markovian regime and deeply nonlinear systems, at a highly reduced computational cost compared to full Hilbert space approaches, making it both practical and convenient to model a variety of open waveguide-QED systems (in Markovian and non-Markovian regimes), treating quantized atoms and quantized photons on an equal footing. The QwaveMPS package automates the waveguide-QED-specific tensor-network operations, including construction of the time-bin evolution operator from physical parameters, the swap network required for delayed interactions, orthogonality-center and truncation management, the matrix-product factorization of NNN-photon Fock-state inputs, and the evaluation of single-time and two-time field observables (such as the second-order quantum correlation function) at chosen points along the waveguide.
In this article, we consider a realistic waveguide implementation of a quantum network that serves as a testbed to show how to maximize the storage and manipulation of quantum information in QED setups. We analyze two approaches using wavepacket engineering and quantum state transfer protocols. First, we propose and design a family of orthogonal photons in the time domain. These photons allow for a selective interaction with distinct targeted qubits. Yet, mode multiplexing employing resonant nodes is largely spoiled by cross-talk effects. This motivates the second approach, namely, frequency multiplexing. Here we explore the limits of frequency multiplexing through the waveguide, analyzing its capabilities to host and faithfully transmit photons of different frequencies within a given bandwidth. We perform detailed one- and two-photon simulations and provide theoretical bounds for the fidelity of coherent quantum state transfer protocols under realistic conditions. Our results show that state-of-the-art experiments can employ dozens of multiplexed photons with global fidelities fulfilling the requirements imposed by fault-tolerant quantum computing. This is with the caveat that the conditions for single-photon fidelity are met. Published by the American Physical Society 2024
Time-frequency entangled photons constitute an important resource for a plethora of applications across the diverse quantum technology landscape. Thus, efficient and tunable setups for the generation of entangled photons are requisite for modern quantum technologies. In this work, we propose a generic cavity QED setup designed for on-demand generation of time-frequency entangled photon pairs, with each photon propagating in a separate waveguide. We outline a potential incarnation of this setup in the microwave superconducting circuit QED architecture. We derive and numerically solve the set of equations of motion governing the evolution of the quantum state of the system, allowing us to examine the photon emission dynamics. Using the Schmidt decomposition of the joint spectral amplitude of the emitted photon pair, we compute the entanglement entropy analyzing its dependence on the system parameters. We outline the potential extension of the proposed scheme for the generation of multiphoton time-frequency entangled states.