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Experimental Scattershot Boson Sampling
Marco Bentivegna, Nicolò Spagnolo, Chiara Vitelli, Fulvio Flamini, Niko Viggianiello, Ludovico Latmiral, Paolo Mataloni, Daniel J. Brod, Ernesto F. Galvão, Andrea Crespi, Roberta Ramponi, Roberto Osellame, Fabio Sciarrino
TL;DR
Boson Sampling needs experimentally scalable photon sources for a task believed hard to simulate classically. This paper implements Scattershot Boson Sampling with multiple heralded PDC sources on integrated photonic chips, reports a measured event-rate increase, and validates the device statistically; its discussion retains explicit operating assumptions.
Problem
Scaling Boson Sampling is limited by the difficulty of reliably generating many indistinguishable photons, while existing PDC implementations had remained proof-of-principle demonstrations with three photons.
Method
The experiment connects up to six heralded PDC sources to random interferometer inputs and uses integrated chips, photon detection, and statistical validation tests.
Results
4.5 (3.4) increase in event rate was observed versus standard Boson Sampling using a source of average (best) brightness, compared with an expected value of 5.
Takeaways & Limitations
The experiments demonstrate the feasibility of non-trivial Scattershot Boson Sampling realizations and support its use for larger experiments targeting the quantum supremacy regime.
Takeaways & Limitations
In the regime of N = 2000 events, the analysis assumes with high probability that each recorded event comes from a different input state.
Abstract
from arXiv · showhide
Boson Sampling is a computational task strongly believed to be hard for classical computers, but efficiently solvable by orchestrated bosonic interference in a specialised quantum computer. Current experimental schemes, however, are still insufficient for a convincing demonstration of the advantage of quantum over classical computation. A new variation of this task, Scattershot Boson Sampling, leads to an exponential increase in speed of the quantum device, using a larger number of photon sources based on parametric downconversion. This is achieved by having multiple heralded single photons being sent, shot by shot, into different random input ports of the interferometer. Here we report the first Scattershot Boson Sampling experiments, where six different photon-pair sources are coupled to integrated photonic circuits. We employ recently proposed statistical tools to analyse our experimental data, providing strong evidence that our photonic quantum simulator works as expected. This approach represents an important leap toward a convincing experimental demonstration of the quantum computational supremacy.
Experimental Scattershot Boson Sampling
The paper is authored by Marco Bentivegna, Nicolò Spagnolo, Chiara Vitelli, and collaborators.
- Marco Bentivegna, Nicolò Spagnolo, Chiara Vitelli, and Fulvio Flamini are listed among the authors.
- Niko Viggianiello, Ludovico Latmiral, and Paolo Mataloni are also listed as authors.
- Daniel J. Brod, Ernesto F. Galvão, Andrea Crespi, Roberta Ramponi, Roberto Osellame, and Fabio Sciarrino complete the listed author group.
Introduction
Boson Sampling targets output distributions believed difficult to reproduce classically, while Scattershot Boson Sampling uses random heralded inputs from multiple PDC sources to increase event-generation rates. The paper reports integrated-chip experiments using six sources and statistical validation of the device.
- Boson Sampling samples output distributions generated by indistinguishable photons undergoing an interferometer’s unitary transformation.Output probabilities involve matrix permanents, motivating the task’s classical computational difficulty.
- Reliable sources of many indistinguishable photons remain a central scaling difficulty, while PDC sources are nondeterministic and require limited pump power.These constraints had restricted PDC demonstrations to proof-of-principle experiments with three photons.
- Scattershot Boson Sampling connects k > n heralded PDC sources to different interferometer inputs, producing random but heralded input sets.If each source emits with probability ϵ, the n-photon event rate scales as ϵ^n, yielding an exponential improvement for k ≫ n over fixed-input sampling.
- The experiments use a 13-mode integrated photonic chip and up to six PDC sources for 2- and 3-photon interference.The study also presents certified results from a separate 9-mode chip.
- Recently proposed statistical tests are used to validate the functioning of the photonic device and analyze Scattershot data.The paper also uses numerical calculations to discuss simulation and certification complexity.
Scattershot Boson Sampling experiment
The experiment combines multiple heralded PDC sources, synchronization, integrated interferometers, and photon-counting detection to implement Scattershot Boson Sampling. Six sources support 2- and 3-photon interference, including a proof-of-principle demonstration using photons generated by different pump pulses.
- A Scattershot experiment generates n indistinguishable photons from k > n heralded PDC sources in random input modes before interferometric detection.The workflow requires input-state preparation, synchronization, nfold coincidence detection, and analysis across input states.
- Six sources S1–S6 are created from three BBO crystals using two polarization combinations per crystal.Source S2 is exceptional because both of its outputs are injected into the chip.
- The 13-mode setup uses multiple sources and a photon switcher to vary input states, while the 9-mode device changes input fibers manually.
- Output photons are collected with a multimode fiber array and detected by avalanche photodiodes coordinated by an electronic acquisition system.The analysis covers 2- and 3-photon interference in both chips.
- The data include 1680 input-output combinations for the 9-mode chip and 2288 for the 13-mode Scattershot experiment.Two-photon results are shown for input states (9,11) and (11,13).
- Time-multiplexing increases n-photon generation with fixed PDC sources, and the 13-mode experiment demonstrates interference between photons from different pump pulses.Sources S5 and S6 are generated by a different pump pulse and synchronized with the others using delays.
Validation of experimental Boson Sampling data
The experiments use statistical tests to partially certify Scattershot Boson Sampling against uniform and distinguishable-photon alternatives. These tests compare observed data with efficiently testable hypotheses about the device’s sampling behavior.
- Statistical tests provide partial certification against sensible hypotheses about how a Boson Sampling device may fail.
- The Aaronson–Arkhipov test uses an efficiently calculable discriminator that weakly correlates with Boson Sampling probabilities.The test was extended from fixed-input experiments to the Scattershot scenario.
- The experiments applied the Aaronson–Arkhipov test against a Uniform Sampler on both 9-mode and 13-mode chips.The 9-mode experiments included 1680 input-output combinations, while the 13-mode experiments included 2288.
- A likelihood-ratio test compared the experimental data with the distribution expected from distinguishable photons.
- The validation protocol’s success rate was evaluated as a function of the data-set size for both chip configurations.Figure 4 reports success-probability trends for the two alternative distributions.
Discussion
The discussion presents Scattershot Boson Sampling as an experimentally demonstrated route toward higher sampling rates and potentially scalable validation. Simulations indicate that certification can remain feasible while classical calculation of the required distributions becomes costly, subject to experimental imperfections and possible future classical algorithms.
- Discussion: The experiment used 6 PDC sources and increased the event rate by a factor 4.5, or 3.4 compared with standard Boson Sampling using average, or best, source brightness.The expected improvement for this comparison was 5.
- Discussion: When the number of input states is much larger than the number of recorded events, each event is likely to come from a different input state.This discussion assumes one PDC source per input mode.
- Discussion: More efficient classical sampling algorithms may exist for uniformly random interferometers, although none had yet been reported.
- Discussion: For n = 4 and m = 100, the corresponding Scattershot experiment with k = 100 PDC sources has an estimated quantum runtime of ∼50 seconds.
- Discussion: Validation remains feasible into the quantum-supremacy regime because the number of event probabilities requiring classical calculation is low and nearly independent of photon and mode counts.The authors expect this to hold for experiments with up to about 30 photons.
- Discussion: The simulations did not include partial photon distinguishability or other experimental imperfections.The discussion gives incorrectly heralded photons as an example of a larger-device complication.
Fabrication of integrated optics devices
The integrated interferometers were fabricated in glass using femtosecond laser direct writing, which creates buried waveguides through localized refractive-index changes.
- Multimode integrated interferometers were fabricated in Eagle2000 alumino-borosilicate glass by femtosecond laser direct writing.
- Focused ultrashort pulses induce permanent refractive-index changes in the focal volume through nonlinear absorption.
- Buried waveguides are drawn through the glass by translating the sample relative to the writing beam.The technique allows rapid fabrication of custom integrated optical circuits with large dimensions.
Experimental details
The experiment generated single photons from six PDC sources and used integrated chips with manually varied or complete Scattershot input configurations.
- Single photons were generated in six equal parametric downconversion sources implemented in three crystals.
- The 9-mode chip used a 3-photon input state in which one of four emitted photons served as a trigger.
- For the 9-mode chip, input states were manually changed by connecting a fiber array to 20 different input-mode sets.
- The 13-mode chip implemented the complete Scattershot version of the Boson Sampling experiment.
Validation of the experimental data
The experiment validates its data against uniform and distinguishable-photon hypotheses using scalable statistical tests, with high success probabilities after modest data-set sizes.
- The validation tests compare experimental outcomes with uniform sampling and with sampling from distinguishable photons.For each outcome, the certifier computes probabilities for indistinguishable and distinguishable photons, then evaluates the data against both hypotheses.
- The distinguishability test uses a counter D whose sign indicates whether indistinguishable or distinguishable photons are more likely.D increases when the indistinguishable-photon probability exceeds the distinguishable-photon probability and decreases in the opposite case.
- The probabilities are calculated with permanent formulas that incorporate partial photon distinguishability and the chip’s theoretical design parameters.
- Psuccess > 95% is achieved with Nset ∼150 against the uniform distribution and Nset ∼50 against distinguishable photons.For the 9-mode interferometer, input states were manually varied and the resulting events were uniformly mixed before validation; the same procedure was applied to 2-photon data.