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arXiv:2609.26429

Photonic CZ gates based on few-photon scattering from emitter-cavity systems

Mateusz Duda, Pieter Kok

quant-phSubmitted Sep 22, 2026• Announced Sep 23, 2026• 0 citations
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Abstract

In this paper we analyze the performance of photonic CZ gates based on N waveguide-coupled cavities containing two-level emitters. We derive single- and two-photon scattering matrices for one cavity using the input-output formalism of quantum optics and for N>1 cavities using the SLH formalism, allowing us to compute the CZ gate fidelity. We consider two input Gaussian wave packets that are centered on a two-photon transition of the emitter-cavity system, and find a trade-off between optimizing the single-photon and two-photon wave packet shape. While the single-photon wave packet is preserved for large emitter-cavity coupling rates, where there is little overlap with the single-photon transitions, the two-photon wave packet acquires the necessary $π$ phase shift for smaller coupling rates, comparable to the cavity decay rate multiplied by the number of cavities. We find that this trade-off limits the CZ gate fidelity to approximately 60% when averaging over all input states.

Comments
30 pages, 9 figures

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In this paper we analyze the performance of photonic CZ gates based on N waveguide-coupled cavities containing two-level emitters. We derive single- and two-photon scattering matrices for one cavity using the input-output formalism of quantum optics and for N>1 cavities using the SLH formalism, allowing us to compute the CZ gate fidelity. We consider two input Gaussian wave packets that are centered on a two-photon transition of the emitter-cavity system, and find a trade-off between optimizing the single-photon and two-photon wave packet shape. While the single-photon wave packet is preserved for large emitter-cavity coupling rates, where there is little overlap with the single-photon transitions, the two-photon wave packet acquires the necessary πππ phase shift for smaller coupling rates, comparable to the cavity decay rate multiplied by the number of cavities. We find that this trade-off limits the CZ gate fidelity to approximately 60% when averaging over all input states.
We demonstrate theoretically that waveguide-coupled cavities with embedded two-level emitters can act as a highly efficient, high-fidelity single-photon switch. The photon switch is an optical router triggered by a classical signal—the propagation direction of single input photons in the waveguide is controlled by changing the emitter-cavity coupling parameters , for example, using applied fields. The switch reflects photons in the weak emitter-cavity coupling regime and transmits photons in the strong coupling regime. By calculating transmission and reflection spectra using the input-output formalism of quantum optics and the transfer matrix approach, we obtain the fidelity and efficiency of the switch with a single-photon input in both regimes. We find that a single waveguide-coupled cavity can route input photon wave packets with near-unity efficiency and fidelity if the wave packet width is smaller than the cavity mode linewidth. We also find that using multiple waveguide-coupled cavities increases the switching bandwidth, allowing wider wave packets to be routed with high efficiency and fidelity. For example, an array of three waveguide-coupled cavities can reflect an input Gaussian wave packet with a full width at half-maximum of 1 nm (corresponding to a few-picosecond pulse) with an efficiency E r = 96.4 % and a fidelity F r = 97.7 % , or transmit the wave packet with an efficiency E t = 99.7 % and a fidelity F t = 99.8 % . Such efficient, high-fidelity single-photon routing is essential for scalable photonic quantum technologies. Published by the American Physical Society 2024
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Engineering deterministic photonic gates with simple resources is one of the long-standing challenges in photonic quantum computing. Here, we design a passive conditional gate between copropagating photons using an array of only two-level emitters. The key resource is to harness the effective photon-photon interaction induced by the chiral coupling of the emitter array to two waveguide modes with different resonant momenta at the emitter’s transition frequency. By studying the system’s multiphoton scattering response, we demonstrate that, in certain limits, this configuration induces a nonlinear π -phase shift between the polariton eigenstates of the system without distorting spectrally the wave packets. Then, we show how to harness this nonlinear phase shift to engineer a conditional, deterministic photonic gate in different qubit encodings, with a fidelity arbitrarily close to 1 in the limit of large number of emitters and coupling efficiency. Our configuration can be implemented in topological photonic setups with multiple chiral-edge modes, opening their use for quantum information processing, or in other setups where such chiral light-matter couplings can be effectively obtained, such as optical fibers or photonic-crystal optical and microwave waveguides.
Abstract We propose an architecture for achieving high-fidelity deterministic quantum logic gates on dual-rail encoded photonic qubits by letting photons interact with a two-level emitter (TLE) inside an optical cavity. The photon wave packets that define the qubit are preserved after the interaction due to a quantum control process that actively loads and unloads the photons from the cavity and dynamically alters their effective coupling to the TLE. The controls rely on nonlinear wave mixing between cavity modes enhanced by strong externally modulated electromagnetic fields or on AC Stark shifts of the TLE transition energy. We numerically investigate the effect of imperfections in terms of loss and dephasing of the TLE as well as control field miscalibration. Our results suggest that III-V quantum dots in GaAs membranes is a promising platform for photonic quantum information processing.
Abstract We present a theoretical study of controlled single-photon routing in a cavity-quantum electrodynamics system coupled to dual waveguides, where each cavity embedding with a two-level atom mediates photon transport between two channels. The proposed system achieves enhanced routing performance through tailored phase-dependent cavity–waveguide couplings that generate optimized quantum interference patterns. Using a real-space formalism, we derive analytical expressions for single-photon scattering amplitudes and identify optimal conditions for maximum routing efficiency. Our analysis shows that targeted routing with near-unity efficiency can be realized by precisely manipulating both the accumulated phase and differential phase shift, while the atom–cavity coupling strength enables frequency-selective tunability. Furthermore, we demonstrate engineered nonreciprocal transmission and chiral scattering, enabling deterministic control over photonic propagation direction. This phase-tunable protocol establishes a scalable platform for quantum network implementation and enables novel functionalities in photonic quantum information processing.
We propose a scheme for realizing a deterministic two-photon controlled-ZZZ (cz) gate based on variants of the two-photon quantum Rabi model, which is feasible within the framework of circuit QED. We begin by utilizing the two-photon interaction to implement the nonlinear sign gate and subsequently we construct the cz gate following the Knill-Laflamme-Milburn scheme [Nature (London) 409, 46 (2001)]. We consider three different regimes: the strong-coupling regime, the perturbative ultrastrong-coupling regime, and the large-detuning regime. Our results indicate that the cz gate operates fast with high fidelity. We also show that the photonic state in the waveguide can be input into the circuit QED system through a variable coupler and released after interaction with almost the same waveform except for a $\ensuremath{\pi}$-phase shift. Our scheme offers a suitable approach for achieving fast and deterministic two-photon quantum gates via light-matter interactions.