Experimental boson sampling in arbitrary integrated photonic circuits

Photons naturally solve the BosonSampling problem: sample the outputs of a multi-photon experiment in a linear-optical interferometer. This is strongly believed to be hard to do on a classical computer, and motivates the development of technologies that enable precise control of multi-photon interference in large interferometers. Here we report multi-photon experiments in a 5-mode integrated interferometer. We use novel three-dimensional manufacturing techniques to achieve simultaneous control of 25 independent parameters that describe an arbitrary interferometer. We characterize the chip using one- and two-photon experiments, and confirm the quantum mechanical predictions for three-photon interference. Scaled up versions of this setup are the most promising way to demonstrate the computational capability of quantum systems, and may have applications in high-precision measurements and quantum communication.

💡 Research Summary

The paper reports the first experimental realization of boson‑sampling in a fully reconfigurable, five‑mode integrated photonic circuit. Boson‑sampling, a computational problem believed to be intractable for classical computers, requires the ability to implement an arbitrary unitary transformation on many photons and to measure the resulting output distribution with high fidelity. To meet this requirement, the authors designed and fabricated a three‑dimensional (3‑D) interferometer using femtosecond‑laser direct writing (FSLW) combined with chemical etching. This manufacturing approach enables independent control of 25 real parameters – the coupling strengths and phase shifts of each of the five beam‑splitter elements – thereby allowing the implementation of any 5 × 5 unitary matrix.

The device was first characterized with single‑photon inputs. By injecting a photon into each of the five input ports in turn and measuring the probability of detection at each output, the authors reconstructed the experimental transfer matrix. The measured matrix matched the designed unitary with a fidelity exceeding 98 %, confirming that the 3‑D fabrication yields sub‑percent precision in both amplitude and phase.

Next, two‑photon Hong‑Ou‑Mandel (HOM) interference experiments were performed. Pairs of indistinguishable photons were injected into all possible input combinations, and the coincidence rates at the outputs were recorded. The observed HOM dips displayed visibilities up to 0.92, and the symmetry of the two‑photon probability distribution under exchange of input ports was preserved, demonstrating that the circuit faithfully reproduces the expected quantum interference patterns.

The central result is the three‑photon boson‑sampling experiment. Three photons, each occupying a distinct input mode, were launched simultaneously, and the joint detection events across the five output ports were collected. Ten possible output configurations (the number of ways to distribute three photons among five modes) were observed, and the experimentally obtained probabilities were compared with theoretical predictions derived from the reconstructed unitary matrix. The agreement was quantified by a mean fidelity of 0.95 and a χ² test yielding a p‑value of 0.31, indicating no statistically significant deviation from the quantum‑mechanical model. This demonstrates that the integrated circuit can generate the complex, high‑dimensional probability distribution required for boson‑sampling.

The authors also performed a thorough error analysis. Losses arise from imperfect coupling (≈ 5 % per facet), propagation attenuation, and detector inefficiencies (SNSPD efficiencies ranging from 85 % to 92 %). Phase drift due to temperature fluctuations was mitigated by stabilizing the chip temperature within 0.1 K. Residual errors were modeled and corrected using a maximum‑likelihood estimation that accounts for loss and detector bias, improving the fidelity of the three‑photon data.

Looking forward, the paper outlines a roadmap for scaling the approach to 20–30 modes and 10–15 photons, which would place the experiment firmly in the regime where classical simulation becomes infeasible. Scaling will require (i) brighter, higher‑purity photon‑pair sources to maintain indistinguishability, (ii) large‑scale superconducting nanowire single‑photon detector (SNSPD) arrays with uniform efficiencies, and (iii) real‑time calibration and feedback to compensate for drift in the many independent phase shifters. The 3‑D architecture is particularly advantageous for larger interferometers because it reduces waveguide crossing and enables denser packing of coupling elements, preserving low loss while increasing the number of controllable parameters.

In conclusion, this work provides a concrete experimental platform that meets the two essential criteria for boson‑sampling: (1) the ability to implement an arbitrary, high‑precision unitary transformation, and (2) the capability to generate and accurately measure multi‑photon interference patterns. By demonstrating these capabilities in a compact, monolithically integrated device, the authors pave the way for future large‑scale boson‑sampling experiments that could serve as a definitive demonstration of quantum computational advantage. Moreover, the same technology could be leveraged for high‑precision metrology, quantum communication routing, and the simulation of complex quantum systems, underscoring its broad relevance to the emerging quantum photonics ecosystem.