Benchmarking Gaussian and non-Gaussian input states with a hybrid sampling platform

Abstract

The original boson sampling paradigm-consisting of multiple single-photon input states, a large interferometer, and multi-channel click detection-was originally proposed as a photonic route to quantum computational advantage. Its non-Gaussian resources, essential for outperforming any classical system, are provided by single-photon inputs and click detection. Yet the drive toward larger experiments has led to the replacement of experimentally demanding single-photon sources with Gaussian states, thereby diminishing the available non-Gaussianity-a critical quantum resource. As the community broadens its focus from the initial sampling task to possible real-world applications, it becomes crucial to quantify the performance cost associated with reducing non-Gaussian resources and to benchmark sampling platforms that employ different input states. To address this need, we introduce the Paderborn Quantum Sampler (PaQS), a hybrid platform capable of performing sampling experiments with eight Gaussian or non-Gaussian input states in a 12-mode interferometer within a single experimental run. This architecture enables direct, side-by-side benchmarking of distinct sampling regimes under otherwise identical conditions. By employing a semi-device-independent framework, offering certification that does not rely on prior knowledge of the interferometer or the input states, we verify that the observed data cannot be reproduced by any classical model-a prerequisite for demonstrating quantum advantage. Applying this framework, we observe clear performance gains arising from non-Gaussian input states.

Figures (4)

• Figure 1: Conceptual implementations for various sampling configurations. In all cases, the input fields enter from the bottom of the setup and are detected with PNR detectors upon exiting the interferometer at the top. The input states of the interferometer can be either eight SMSV states, heralded Fock states, or thermal states, corresponding to implementing GBS, SBS, and thermal boson sampling (TBS), respectively. To implement SBS, the second mode of each TMSV input state is detected with PNR detectors to herald the number of photons entering each interferometer port. To realize sampling with thermal states - thermal boson sampling (TBS) - the second mode of each TMSV state is discarded, i.e., traced out.
• Figure 2: Schematic of the PaQS sampling system. The subsystems are separated to highlight the modular design. EOM — electro-optic modulator; PBS — polarizing beam splitter; SLM — spatial light modulator; GR — grating; PDC — parametric down-conversion source; F — filtering stage; CC — (temporal) compensation crystal; PLCU — path-length compensation unit.
• Figure 3: System verification measurements.a, Measured Klyshko efficiencies for each interferometer output mode. Average value of 8.7%$\pm$1.5% is indicated by the dashed line b, Measured second‑order correlation function from one arm of a TMSV state as the mean photon number is varied. The asymptote at approximately 1.95 is indicated by the dashed line. c, Normalized coincidence counts between the heralding and signal detections as the EOM2 driving voltage is tuned. The minima correspond to GBS and the maxima to SBS. d, Coincidence counts (corrected for multiphoton events and normalized to the sinusoidal fit) between selected output detectors as the fiber temperature of one mode is varied, demonstrating HOM interference. All uncertainties arise from Poisson counting statistics.
• Figure 4: Quantumness analysis.a, Recorded minimum eigenvalues during a full measurement run at a mean photon number of 0.569, together with GBS data at 2.152 for comparison. Each data point corresponds to a 1 s integration window; the grey band denotes the uncertainty. b, Highest and lowest observed minimum eigenvalues for generated GBS, SBS, and TBS data across all measured mean photon numbers. Shaded regions represent uncertainties of reported values and have been connected to guide the eye. Uncertainties are estimated from counting errors.