Standards & Compliance
February 10, 2026
Introduction
Photons serve as excellent carriers of quantum information. They have long coherence times at room temperature and are the inescapable choice for broadcasting quantum information over long distances, either in free space or through the optical fiber network. Quantum state initialization is a particularly important task for photonic qubits, since adjusting entanglement after emission is nontrivial. Initialization strategies depend on the degree of freedom used to encode quantum information, and the most common choice for quantum communication over optical channels is time-bin encoding1. Here, the two-qubit levels consist of the photon being in one of the two-time windows, generally separated by a few nanoseconds. Time-bin encoding is extremely resilient to phase fluctuations resulting from thermal noise in optical fibers, with qubits maintaining their coherence even over hundreds of kilometers2,3. However, the control of the state in which time-bin-entangled photons are generated is challenging and impractical in emerging nano-photonic platforms. For on-chip manipulation of qubit states, dual-rail encoding, in which the two states of a qubit correspond to the photon propagating in one of two optical waveguides, is a superior strategy4,5 and is thus a common choice for quantum computing and quantum simulation in integrated platforms. Yet this approach is not easily compatible with long-distance transmission links using either optical fibers or free space channels.
Recently, frequency-bin encoding has been proposed, and experimentally demonstrated, as an appealing strategy that can combine the best characteristics of time-bin and dual-rail encodings6,7,8,9,10,11. In this approach, quantum information is encoded by the photon being in a superposition of different frequency bands. Frequency bins can be manipulated using phase modulators, and are resistant to phase noise in long-distance propagation. Pioneering studies have investigated the generation and manipulation of frequency-bin-entangled photons in integrated resonators. They have considered quantum state tomography of entangled photon pairs12, qudit encoding13, and multi-photon entangled states14. The experimental results have all been achievable thanks to the recent development of high-Q integrated resonators in the silicon nitride and silicon oxynitride platforms.
Despite all this progress, some obstacles must be overcome to exploit the full advantage of photonic integration. In frequency-bin encoding today, the generation of photon pairs occurs via spontaneous four-wave mixing in a single-ring resonator, with the desired state obtained outside the chip, using electro-optical modulators and/or pulse shapers. And since commercial modulators have limited bandwidth, the frequency span separating the photons cannot exceed a few tens of gigahertz, which sets a limit to the maximum free spectral range of the resonator. Finally, because spontaneous four-wave mixing efficiency scales quadratically with the resonator-free spectral range15, there is also a significant trade-off between the generation rate and the number of accessible frequency bins.
In this work, we show that these limitations can be overcome by utilizing the flexibility of light manipulation in a nano-photonic platform and the dense optical integration possible in silicon photonics. Our approach is based on constructing the desired state by direct, on-chip control of the interference of biphoton amplitudes generated in multiple ring resonators that are coherently pumped. States can thus be constructed “piece-by-piece” in a programmable way, by selecting the relative phase of each source. In addition, since the frequency-bin spacing is no longer related to the ring radius, one can work with very high-finesse resonators, reaching megahertz generation rates. These two breakthroughs, namely high emission rates in combination with high values of the free spectral range, together with output state control using on-chip components, are only possible using multiple rings: they would not be feasible were the frequency bins encoded on the azimuthal modes of a single resonator.
We demonstrate that with the very same device, one can generate all superpositions of the |00⟩|00⟩ and |11⟩|11⟩ states or, in another configuration with different frequency-bin spacing, all superpositions of the |01⟩|01⟩ and |10⟩|10⟩ states. One needs only to drive the on-chip phase shifter and set the pump configuration appropriately. This means that all four fully-separable states of the computational basis and all four maximally entangled Bell states (∣∣Φ±⟩=(|00⟩±|11⟩)/2–√|Φ±⟩=(|00⟩±|11⟩)/2 and ∣∣Ψ±⟩=(|01⟩±|10⟩)/2–√|Ψ±⟩=(|01⟩±|10⟩)/2) are accessible. Our high generation rate allows us to perform quantum state tomography of all these states, reaching fidelities up to 97.5% with purities close to 100%.
