Boson Sampling with 20 Input Photons and a 60-Mode Interferometer in a $1{0}^{14}$-Dimensional Hilbert Space

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Boson Sampling with 20 Input Photons and a 60-Mode Interferometer in a $1 0^{14}$ -Dimensional Hilbert Space

Hui Wang, Jian Qin, Xing Ding, Ming-Cheng Chen, Si Chen, Xiang You, Yu-Ming He, Xiao Jiang, L. You, Z. Wang, C. Schneider, Jelmer J. Renema, Sven Höfling, Chao-Yang Lu, and Jian-Wei Pan

Phys. Rev. Lett. 123, 250503 – Published 18 December 2019

See Synopsis: Quantum Computers Approach Milestone for Boson Sampling

Abstract

Quantum computing experiments are moving into a new realm of increasing size and complexity, with the short-term goal of demonstrating an advantage over classical computers. Boson sampling is a promising platform for such a goal; however, the number of detected single photons is up to five so far, limiting these small-scale implementations to a proof-of-principle stage. Here, we develop solid-state sources of highly efficient, pure, and indistinguishable single photons and 3D integration of ultralow-loss optical circuits. We perform experiments with 20 pure single photons fed into a 60-mode interferometer. In the output, we detect up to 14 photons and sample over Hilbert spaces with a size up to $3.7 \times 10^{14}$ , over 10 orders of magnitude larger than all previous experiments, which for the first time enters into a genuine sampling regime where it becomes impossible to exhaust all possible output combinations. The results are validated against distinguishable samplers and uniform samplers with a confidence level of 99.9%.

Received 31 October 2019
Revised 19 November 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.250503

Physics Subject Headings (PhySH)

Boson sampling Quantum computation Quantum optics Quantum simulation

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Synopsis

Quantum Computers Approach Milestone for Boson Sampling

Published 18 December 2019

Experiments show that when enough photons travel through a complex optical network, only a quantum computer can efficiently sample the range of possible outcomes.

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Authors & Affiliations

Hui Wang^1,2, Jian Qin^1,2, Xing Ding^1,2, Ming-Cheng Chen^1,2, Si Chen^1,2, Xiang You^1,2, Yu-Ming He^1,2, Xiao Jiang^1,2, L. You³, Z. Wang³, C. Schneider⁴, Jelmer J. Renema⁵, Sven Höfling^4,6,1, Chao-Yang Lu ^1,2, and Jian-Wei Pan^1,2

¹Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, People’s Republic of China
²Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, People’s Republic of China
³State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology (SIMIT), Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050, China
⁴Technische Physik, Physikalisches Instität and Wilhelm Conrad Röntgen-Center for Complex Material Systems, Universitat Würzburg, Am Hubland, D-97074 Würzburg, Germany
⁵Adaptive Quantum Optics Group, Mesa+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, Netherlands
⁶SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, United Kingdom

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Vol. 123, Iss. 25 — 20 December 2019

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Images

Figure 1
Experimental setup of boson sampling. A single $InAs / GaAs$ quantum dot, resonantly coupled to a microcavity yielding a Purcell factor of $\sim 18$ , is used to create pulsed resonance fluorescence single photons. For demultiplexing, 19 pairs of Pockels cells (PCs) and polarized beam splitters (PBSs) are used to actively translate a stream of photon pulses into 20 spatial modes. Optical fibers with different lengths are used to compensate time delays. The 20 input single photons are injected into a 3D integrated, 60-mode ultralow-loss photonic circuit (see Fig. 3 for more details), which consists of 396 beam splitters and 108 mirrors. Finally, the output single photons are detected by 60 superconducting nanowire single-photon detectors with efficiencies ranging from 0.6 to 0.82. All coincidence are recorded by a 64-channel coincidence count unit (not shown).
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Figure 2
Characterization of the single-photon source. (a) By varying the amplitude of the pumping laser field, a Rabi oscillation up to 4 is observed. At $π$ pulse, $\sim 16.3 million$ single photons per second are recorded by a superconducting nanowire single-photon detector. (b) Characterization of single-photon purity using the second-order correlation function. The strongly antibunched peak at zero-time delay reveals $g^{2} (0) = 0.025 (1)$ (c) Measurement of photon indistinguishability by Hong-Ou-Mandel interference between two photons with different emission time separations. The extracted photon indistinguishabilities are 0.954(1), 0.948(1), 0.933(1), 0.929(1), 0.922(1), and 0.923(1) at emission time separations of 13 ns, 39 ns, 210 ns, 395 ns, $1.8 μ s$ , and $6.5 μ s$ , respectively. The data are fitted by a model considering Markov noise.
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Figure 3
Construction and characterization of the 60-mode photonic network. (a) The 60-mode interferometer consists of one rectangular piece and two triangular pieces. The rectangular is fabricated by bonding (through intermolecular force) six trapezoidal pieces with a size of $28.28 \times 28.28 \times 4.00 {mm}^{3}$ . The triangular is constructed in a similar way, with a size of $24.00 \times 24.00 \times 20.00 {mm}^{3}$ . The bonding interfaces are coated with random polarization-dependent beam-splitting ratio. The trapezoidal pieces are cut and bounded with a dimension tolerance of $< 5 μ m$ and parallel precision better than 5”. The design ensures that any possible spatial mismatch is much smaller than the coherence length of the quantum-dot single photons ( $\sim 30 mm$ ). (b) Illustration of light propagation inside the 3D photonic circuit. The rectangular piece has six horizontal ten-mode layers, while the two triangular ones have ten vertical six-mode layers. In the rectangular piece, only the photons in the same horizontal layer can interfere with each other but not with vertically different layers. After that, ten vertical layers are incorporated, which are to make the photons from different horizontal layers interfere with each other. Therefore, the interferometer is fully connected. (c) The measured 1200 elements of amplitude. These values are determined by the recorded counts of the 60 single-photon detectors when we inject photons in every input port one by one. (d) The measured 1200 elements of amplitude. These elements are measured using Mach-Zehnder-type interference with a narrow-band laser. (e) Unitarity test of the reconstructed matrix. All output probabilities are normalized to unity, corresponding to 20 diagonal elements. The average of all off-diagonal elements is as small as 0.01(1), confirming that the matrix is well reconstructed. (f) Statistical histogram of 1200 elements of amplitude. (g) Statistical histogram of 1200 elements of phase. The phase is uniformly distributed from $- π$ to $π$ .
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Figure 4
(a) Summary of distance (purple) and fidelity (orange) of all 190 possible two-photon boson sampling tests. The averaged distance and distance are 0.043(7) and 0.996(1), respectively. (b) Reconstructed three-photon distribution for an input combination (2,10,12). (c) Reconstructed four-photon distribution for an input combination (1,2,4,7). (d) Boson sampling rates with different settings of input photons and lost photons. (e) Summary of the dimensions of output Hilbert space of all previous work and this experiment (red dots).
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Figure 5
Validation of the boson sampling results. (a) Bayesian analysis of typical 11- to 14-photon boson sampling results. The solid points are from Bayesian analysis by updating every experimental data, which reach a level of 99.9% with only $\sim 50$ samples. The open dots are from Bayesian analysis by updating simulated data of distinguishable bosons, which quickly converge to 0. These results confirm that the experimental events are from a genuine boson sampler, rather than a distinguishable sampler. (b) Designed row-norm estimator to discriminate experimental data from a uniform sampler. The solid dots are updated by the experimental data, while the open dots are from a simulated uniform sampler. The increasing differences between them can exclude the uniform sampling hypothesis. For clarity, in each panel, the four different datasets are displayed with an offset in the $x$ axis.
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