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Experimental loopback boson sampling

Yu. A. Biriukov, R. D. Morozov, K. I. Okhlopkov, I. V. Dyakonov, N. N. Skryabin, S. A. Zhuravitskii, M. A. Dryazgov, K. V. Taratorin, A. A. Korneev, S. P. Kulik, S. S. Straupe M. V. Rakhlin, A. I. Galimov, G. V. Klimko, S. V. Sorokin, I. V. Sedova, M. M. Kulagina, Yu. M. Zadiranov, A. A. Toropov

TL;DR

This work reports an experimental demonstration of loopback boson sampling, where optical feedback lines introduce temporal correlations to boost sampling complexity without adding physical hardware. A $N$-photon, $M$-mode interferometer with $L$ looped outputs yields a total transformation $U_{\text{total}}$, a block-lower-triangular Toeplitz matrix, effectively equating to a conventional boson sampler with $NT$ photons in $(M-L)T+L$ modes. Bayesian validation confirms both quantum interference and the impact of feedback, with an estimated effective Hilbert-space size of about $43$ qubits for $10$-photon events across four iterations. This resource-efficient approach points to scalable demonstrations of quantum advantage with single photons by exploiting temporal degrees of freedom in photonic circuits.

Abstract

We present an experimental demonstration of boson sampling enhanced by optical feedback lines, a novel approach that introduces temporal correlations among photons to amplify computational complexity. We utilize a 25-mode femtosecond laser-written interferometer with five output channels connected to five input channels to create correlations between consecutive photon arrival events. We have reconstructed the unitary matrix of the chip and have conducted Bayesian analysis to validate the sampler and confirm that the system exhibits behavior distinct from standard boson sampling. We also built a theoretical description of the system based on the transformation of annihilation operators and, using it, delivered the structure of the transmission matrix and the complexity of our boson sampler in terms of a conventional boson sampler. This work advances photonic quantum computing by demonstrating a resource-efficient method to increase sampling complexity, paving the way for scalable demonstration of quantum advantage with single photons.

Experimental loopback boson sampling

TL;DR

This work reports an experimental demonstration of loopback boson sampling, where optical feedback lines introduce temporal correlations to boost sampling complexity without adding physical hardware. A -photon, -mode interferometer with looped outputs yields a total transformation , a block-lower-triangular Toeplitz matrix, effectively equating to a conventional boson sampler with photons in modes. Bayesian validation confirms both quantum interference and the impact of feedback, with an estimated effective Hilbert-space size of about qubits for -photon events across four iterations. This resource-efficient approach points to scalable demonstrations of quantum advantage with single photons by exploiting temporal degrees of freedom in photonic circuits.

Abstract

We present an experimental demonstration of boson sampling enhanced by optical feedback lines, a novel approach that introduces temporal correlations among photons to amplify computational complexity. We utilize a 25-mode femtosecond laser-written interferometer with five output channels connected to five input channels to create correlations between consecutive photon arrival events. We have reconstructed the unitary matrix of the chip and have conducted Bayesian analysis to validate the sampler and confirm that the system exhibits behavior distinct from standard boson sampling. We also built a theoretical description of the system based on the transformation of annihilation operators and, using it, delivered the structure of the transmission matrix and the complexity of our boson sampler in terms of a conventional boson sampler. This work advances photonic quantum computing by demonstrating a resource-efficient method to increase sampling complexity, paving the way for scalable demonstration of quantum advantage with single photons.

Paper Structure

This paper contains 14 sections, 17 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Theoretical framework
  3. Experimental results
  4. Experimental Setup
  5. Boson sampling and its validation
  6. Discussion
  7. Conclusion
  8. Acknowledgment
  9. Theoretical Model of Looped Boson Sampling
  10. System overview
  11. Output distribution
  12. Boson sampling validation
  13. Optical demultiplexer characterisation
  14. Unitary matrix reconstruction

Figures (5)

  • Figure 1: Scheme of the experimental setup. A single-photon source based on an InAs/GaAs quantum dot (QD) in a micropillar resonator emits photons at 926 nm with period $T = 12.1$ ns. A tree-structured demultiplexer composed of four Pockels cells (PCs) and fiber delays prepares five synchronized photons, which are injected into a 25-mode photonic chip with five optical feedback lines. Output photons are detected by superconducting nanowire single-photon detectors (SNSPDs), and detection events are time-tagged for analysis.
  • Figure 2: (a) Comparison of experimental and theoretical 3-photon events distribution on the first time iteration. (b) The distribution of the number of detected photons for various number of considered consecutive time-bins. (b-e) Validation of boson sampling device with bayesian inference. Two different colors depict the probability of one of two hypotheses after processing of several samples. Solid lines are mean value of probability by averaged over 1000 different sets of samples, while shaded areas are $90\%$ confidence interval obtained for these 1000 sets of samples. (b) Validation against distinguishable sampler. (c) Validation against uniform sampler. (d) Validation against loop sampler in case of blocked feedback lines. (e) Validation against conventional sampler in case of working feedback lines.
  • Figure 3: (Left) Scheme of general boson sampler with optical feedback lines with interferometer transmission matrix $U$. (Right) The same interferometer, but with all spacio-temporal modes depicted to consider the system as conventional boson sampler with transfer matrix $U_{total}$.
  • Figure 4: Characteristics of single photon source and spacio-temporal demultiplexer. All the measurements were conducted with pump laser pulse frequency double, so there are sidebands at time delays around $\pm 6$ ns. a-d) Results of measurements of pairwise single photons' indistinguishability. All indistinguishabilities are measures against the 4th channel as a reference. The mean value of indistinguishability is $0.918$. e) Measurement of normalized $g^{(2)}(0)$ showing multiphoton component in single photon radiation. f) Multiphoton events frequencies showing how many photons at the outputs of demultiplexer we observed. These values are not corrected by SNSPDs efficiencies.
  • Figure 5: Transmission matrix reconstruction results. (a) Experimentally measured matrix modules of transmission matrix. (b) Matrix of modules obtained after optimization procedure. Fidelity between experimental and numerical matrices is $98.7\%$ (c) Comparison between two-photon interference visibilities obtained via cross-correlation measurements and after optimization procedure. Mean absolute error is $0.033$. (d) Experimentally reconstructed transmission matrix $U_{total}$ obtained for 2 consequent temporal iterations.