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Quantum circuits with many photons on a programmable nanophotonic chip

J. M. Arrazola, V. Bergholm, K. Brádler, T. R. Bromley, M. J. Collins, I. Dhand, A. Fumagalli, T. Gerrits, A. Goussev, L. G. Helt, J. Hundal, T. Isacsson, R. B. Israel, J. Izaac, S. Jahangiri, R. Janik, N. Killoran, S. P. Kumar, J. Lavoie, A. E. Lita, D. H. Mahler, M. Menotti, B. Morrison, S. W. Nam, L. Neuhaus, H. Y. Qi, N. Quesada, A. Repingon, K. K. Sabapathy, M. Schuld, D. Su, J. Swinarton, A. Száva, K. Tan, P. Tan, V. D. Vaidya, Z. Vernon, Z. Zabaneh, Y. Zhang

arXiv:2103.02109v1quant-ph

TL;DR

Existing photonic machines lacked a single platform combining dynamic programmability, scalability, and access to classically hard-to-simulate circuits. This paper presents a programmable nanophotonic system that verifies non-classical output and demonstrates Gaussian boson sampling, vibronic spectra, and graph similarity.

  • Problem

    No photonic machine had simultaneously demonstrated dynamic programmability, scalability to hundreds of modes and photons, and access to circuits beyond efficient classical simulation.

  • Method

    The authors build a programmable nanophotonic chip with squeezed-light initialization, a user-programmable SU(4) interferometer, and automated control and readout.

  • Results

    The device demonstrates record capabilities including high sampling rates, large on-chip squeezing, strong photon detection, verified non-classicality, and three proof-of-principle quantum algorithms.

  • Takeaways & Limitations

    The platform provides a remotely configurable nanophotonic system for cloud-accessible demonstrations of several quantum algorithms.

  • Takeaways & Limitations

    Scaling toward quantum advantage remains constrained by the challenge of maintaining acceptably low losses in the interferometer.

Abstract

from arXiv · show

Growing interest in quantum computing for practical applications has led to a surge in the availability of programmable machines for executing quantum algorithms. Present day photonic quantum computers have been limited either to non-deterministic operation, low photon numbers and rates, or fixed random gate sequences. Here we introduce a full-stack hardware-software system for executing many-photon quantum circuits using integrated nanophotonics: a programmable chip, operating at room temperature and interfaced with a fully automated control system. It enables remote users to execute quantum algorithms requiring up to eight modes of strongly squeezed vacuum initialized as two-mode squeezed states in single temporal modes, a fully general and programmable four-mode interferometer, and genuine photon number-resolving readout on all outputs. Multi-photon detection events with photon numbers and rates exceeding any previous quantum optical demonstration on a programmable device are made possible by strong squeezing and high sampling rates. We verify the non-classicality of the device output, and use the platform to carry out proof-of-principle demonstrations of three quantum algorithms: Gaussian boson sampling, molecular vibronic spectra, and graph similarity.

Introduction

Quantum computing has advanced through programmable, remotely accessible machines, but photonic systems still face limitations in scalability, determinism, and classical simulability. This work introduces a programmable nanophotonic chip designed to combine dynamic programmability, scalability to many modes and photons, and access to classically difficult quantum circuits.

  • Quantum-computing progress: Programmable quantum machines now provide automation, stability, repeatability, and remote high-level algorithm access across multiple physical platforms.An 11-qubit trapped-ion system was rigorously benchmarked, while a 53-qubit superconducting system generated samples at rates exceeding reasonably achievable classical hardware.
  • Photonic opportunity: Photonic hardware is emerging as a promising platform for large-scale bosonic quantum algorithms alongside advances in photonic chip fabrication.Recent demonstrations include two-dimensional cluster states with tens of thousands of entangled nodes.
  • Photonic limitations: Existing photonic systems remain limited by efficiently simulable all-Gaussian processing or non-deterministic state preparation and gate implementation.Large cluster-state demonstrations used all-Gaussian states, gates, and measurements, while integrated single-photon experiments suffered from non-deterministic preparation and gates.
  • This work: The reported nanophotonic chip combines dynamic programmability, scalability to hundreds of modes and photons, and access to circuits not efficiently simulable classically at scale.The device is presented as a single scalable and unified machine addressing all three capabilities simultaneously.

Hardware

The hardware is a room-temperature integrated nanophotonic system that prepares up to eight squeezed modes, applies programmable four-mode linear optics, and performs photon-number-resolving readout. Component measurements and modeling verify single-temporal-mode squeezing, multi-photon interference, and non-classical output.

  • Chip architecture: Programmable interferometer circuits use beam splitters, phase shifters, and SU(4) transformations to implement user-programmable four-mode rotations.The full apparatus integrates pump distribution, squeezing, filtering, programmable linear-optical transformations, and autonomous control.
  • Chip architecture: The 10 mm × 4 mm silicon-nitride chip generates squeezed light in up to eight modes, initialized as four independent two-mode squeezed-vacuum states.Four integrated microring squeezers generate bichromatic two-mode squeezed states in nearly single temporal modes.
  • Sources and detection: Squeezers operate at r ≈ 1 with mean photon number n ≈ 1.4 at the sources, while transition-edge sensors provide true photon-number resolution.These capabilities enable quantum algorithms involving strong multi-photon contributions.
  • Component characterization: The average second-order correlation across eight measured modes is g(2) = 1.81(4), indicating operation close to single-temporal-mode squeezing.Each squeezer’s marginal statistics satisfy S(I),i = 2, as expected for a single-mode thermal state.
  • Non-classicality verification: The device passes the non-classicality test, with ϵ0 ≈ 0.20 representing the minimal distance between its noisy Gaussian output and classical Gaussian states.The model gives 2.5 × 10^-3 for the inequality’s right-hand side and 1.0 × 10^-2 for its left-hand side, so the inequality is not satisfied.

Demonstrations

The chip demonstrates programmable photonic implementations of Gaussian boson sampling, molecular vibronic spectra, and graph similarity. These proof-of-principle algorithms use device samples to infer properties of their target distributions, molecules, or graphs.

  • Gaussian boson sampling: The platform demonstrates Gaussian boson sampling using programmable interferometers and photon-number-resolving samples to characterize the device’s non-classical output distribution.Three Haar-random interferometers generated 1.2 × 10^6 samples each, alongside an identity-interferometer benchmark.
  • Gaussian boson sampling: Strong on-chip squeezing enables generation of many photons, with photon-number-specific sampling rates estimated relative to a raw rate of 10^5 events/s.The photon-number distribution was measured with all squeezers on and the interferometer set to identity.
  • Molecular vibronic spectra: The vibronic-spectrum demonstration is proof-of-principle because the programmed profiles omit molecular displacements and use squeezing only in the first mode.The interferometer encodes Duschinsky matrices representing mixing between four normal coordinates in the two molecules.
  • Molecular vibronic spectra: The chip reconstructs Franck–Condon profiles for ethylene and (E)-phenylvinylacetylene, producing 1.2 × 10^6 samples for each molecule.Histogram bars and Lorentzian broadenings are compared with theoretical distributions whose peaks should coincide with experiment.
  • Graph similarity: The graph-similarity algorithm encodes bipartite graphs on eight vertices and distinguishes four graphs through separate feature vectors estimated from 20 million samples each.The feature vectors are built from permutationally invariant photon-pattern orbits.

Discussion

The device establishes a programmable nanophotonic platform with several record capabilities and remote configurability. Scaling toward quantum advantage will require controlling interferometer losses, potentially through improved integrated components and fabrication.

  • Capabilities: The nanophotonic device combines high sampling rates, large on-chip squeezing, nearly ideal second-order correlations, and record detected-photon counts.The hardware is programmable and remotely configurable through a custom application.
  • Scaling: As the first device of its generation, it represents an initial step toward scaling nanophotonic chips to more modes.
  • Scaling: Reaching quantum advantage requires scaling until classical simulation becomes intractable, with interferometer loss identified as the greatest challenge.New integrated beamsplitter and phase-shifter designs could improve loss per interferometer layer by an order of magnitude using currently available fabrication tools.

Methods · Apparatus details · Pump system

The platform combines a programmable eight-mode photonic chip with automated control, stabilized pumping, filtering, and eight-detector photon-number-resolving readout. Its pump system uses a tunable 1554.9 nm laser and modulated 1.5 ns pulses at 100 kHz.

  • Pump system: 100 kHz repetition rate and 1.5 ns duration define the regular rectangular pulse train produced by the custom modulated pump laser.The pulse train is generated by a 10 GHz bandwidth fiber-integrated intensity modulator.
  • Methods: The apparatus integrates a programmable eight-mode Gaussian-state chip with photon-number-resolving-compatible temporal modes.The chip is electrically and optically packaged for operation within the full apparatus.
  • Apparatus details: A locking system aligns and stabilizes the resonance wavelengths of the on-chip squeezer resonators.This stabilization supports operation of the integrated squeezing elements.
  • Apparatus details: Digital-to-analog converter arrays program the chip’s phase-shifter voltages.The DACs provide the electrical control needed to configure the programmable interferometric circuit.
  • Apparatus details: Low-loss off-chip wavelength filters suppress unwanted light while passing wavelengths close to the signal and idler for detection.The filters are positioned before the detection system.
  • Apparatus details: Eight transition-edge sensor detectors provide photon-number-resolving readout, with auxiliary equipment for operation and data acquisition.The detection system is an array of eight TES detectors.
  • Apparatus details: A server-based master controller runs custom software to coordinate continuous automated subsystem operation and process remotely submitted jobs.The controller also receives and processes jobs sent to the machine.
  • Pump system: 1554.9 nm is the wavelength of the compact continuous-wave tunable pump laser assembly.The laser output is sent to the intensity modulator to form the regular optical pulses.

Integrated components

The integrated chip distributes pump light across four spatial modes, uses microring squeezers and pump-rejection filters, and implements a programmable interferometer with thermo-optic control. Packaging and temperature stabilization support stable electrical and optical operation.

  • Pump distribution and squeezing: A binary tree of 50/50 MMI beam splitters equally distributes the pump light among four spatial modes, each coupled to a separate squeezer.Pump light enters through a single waveguide input.
  • Pump distribution and squeezing: Microring resonators use strongly pumped spontaneous four-wave mixing to generate bichromatic two-mode squeezing.The ring waveguide cross-section is 1500 nm x 800 nm, and the radius is 113 µm, corresponding to an FSR of 200 GHz.
  • Noise and stabilization: No excess noise from unwanted processes in the rings was measured, while Raman scattering in fiber pump components remains the dominant photon-noise source.Better pump filtering before the squeezers is identified as a way to manage this noise in future versions.
  • Filtering and locking: Each resonator output passes through an AMZI pump-rejection filter that suppresses nonlinear light generation and provides rejected pump light for resonance locking.The rejected pump is collected as a signal for locking ring resonances to the pump laser wavelength.
  • Programmable interferometer: The interferometer combines MMIs and phase shifters in a rectangular network whose thermo-optic controls enable arbitrary programmability.The MMI splitting ratio remains constant to within 1% over the wavelengths used, with control provided by a multi-channel DAC system.
  • Noise and stabilization: The chip is electrically and optically packaged with a copper sub-mount, thermo-electric cooler, connectorized PCBs, and wire bonds to support stable operation.Cables carry electronic signals for programming the unitary transformation and locking the system.

Operating procedure · Chip calibration

Users submit Strawberry Fields programs as jobs that are compiled into hardware instructions, executed through a monitored calibration-and-acquisition sequence, and followed by chip re-initialization. Chip calibration establishes phase-to-voltage control for thermo-optic shifters and uses two-squeezer interference to extract relevant input-phase relationships.

  • Operating procedure: Users write quantum programs with the Strawberry Fields Python library, which are sent as jobs specifying squeezing parameters and interferometer phases.The master controller compiles each job into hardware instructions.
  • Operating procedure: The control sequence sets interferometer voltages for the requested unitary operation and allows the chip to thermally equilibrate.These steps precede squeezer calibration and state verification.
  • Operating procedure: Ring resonance wavelengths are swept to calibrate squeezer control circuitry, after which the rings are locked to the pump wavelength.The sequence then checks that the interferometer and squeezers are in the desired state.
  • Operating procedure: The requested samples are acquired from the detectors, followed by checks that the interferometer and squeezers have not drifted during data acquisition.The post-acquisition checks verify that the chip remains in its specified state.
  • Operating procedure: Sample and job data are returned to the user, and the chip is re-initialized to its default state.These steps complete the operating procedure.
  • Chip calibration: Thermo-optic phase shifters are calibrated to determine each shifter’s voltage-to-phase relationship before setting the interferometer to a user-specified state.The thermal nature of the phase shifters implies, and tests confirm, that phase and voltage are related with high accuracy.
  • Chip calibration: Calibration determines φ0 and α, enabling the phase-to-voltage relationship to be inverted for requested phases using classical light injected into one interferometer mode at a time.Pump light enters the second input of each mode’s filter AMZI, while a telecom fiber switch selects the calibration-light mode.
  • Chip calibration: Two-squeezer interference calibrates the three relevant input phases by sweeping phase shifters in modes 0, 1, and 2 while monitoring the NRF between interfering modes.Mode 3 has no input phase shifter because only the relative phase between inputs is physically relevant; the phase-to-voltage relationship is then extracted.

Photon detection system

The photon-detection system uses high-efficiency TES detectors whose photon-number-dependent voltage traces are digitized and assigned photon numbers through detector-specific calibration. This calibration enables real-time classification, avoiding the global-data dependence of PCA-based trace matching.

  • Detector operation: Each TES detector has quantum efficiency above 95% and produces an analog voltage pulse every 10 µs, with pulse shape depending on incident photon number.The signals are digitized into voltage traces, and photon detection requires associating each trace with a photon number n.
  • Calibration motivation: Global PCA-based trace comparison cannot assign photon numbers to individual traces in real time because it depends on all traces from the experimental run.This dependence limits the speed of trace-to-photon-number assignment in a complex system.
  • Calibration procedure: Detector-specific calibration assigns each subsequent voltage trace immediately to a photon number in real time, up to the calibration-determined nmax.Calibration comprises identifying a standard trace for overlap calculations and determining photon-number bin edges.
  • Calibration procedure: The standard trace is the average of identified two-photon traces, balancing detector-nonlinearity capture against obtaining enough representative events.Higher photon-number trace sets could extend nmax, but calibration from one arm of a two-mode squeezed vacuum favors more n-photon than (n + 1)-photon events.

Noise reduction factor

The noise reduction factor quantifies photon-number correlations between signal and idler modes in each two-mode squeezed vacuum source. Ideal correlations give NRF = 0, coherent states give NRF = 1, and loss is the dominant imperfection degrading correlations.

  • Definition: NRF measures the variance of the photon-number difference between signal and idler observables for each individual squeezer.The observables are n_s and n_i, and NRF is defined using ∆2(n_s − n_i).
  • Interpretation: NRF = 0 corresponds to perfect signal-idler photon-number correlations in an ideal two-mode squeezed vacuum source.The signal and idler photon numbers are perfectly correlated in this ideal case.
  • Interpretation: NRF = 1 is the expected value for a pair of coherent states.This provides the contrasting reference for uncorrelated coherent-state behavior.
  • Imperfections: Loss is the dominant imperfection degrading signal-idler photon-number correlations in the system.The passage identifies total photon transmission loss as the principal source of correlation degradation.
  • Measurement protocol: 8×10^5 samples were collected per NRF measurement, divided into eight batches of 1 × 10^5 samples.The interferometer was set to identity, one squeezer was activated at a time, and batch means and standard deviations produced the reported data points and ±1σ uncertainties.

Second-order correlation

The section uses unheralded second-order correlation, g(2), to assess whether each squeezer predominantly occupies one temporal mode. It establishes ideal and non-ideal reference values and explains that noise makes the reported measurements lower bounds.

  • Measurement: Unheralded g(2) was measured for the signal and idler of each squeezer to verify significant population of only one temporal mode.The statistic is defined for an output channel using its photon number operator n.
  • Interpretation: g(2) provides a loss-insensitive measure of temporal-mode structure and is related to the Schmidt number K in the absence of noise.
  • Reference values: 2 is the ideal g(2) value for a single-temporal-mode two-mode squeezed vacuum source, while coherent states or highly multi-mode squeezed light yield 1.
  • Measurement: 8×105 samples were collected per squeezer with the interferometer set to identity and only one squeezer activated, then divided into eight batches.The mean and standard deviation across batches provided the reported data points and ±1σ uncertainties.
  • Limitations: The reported g(2) values are raw, noise-uncorrected lower bounds because unwanted Raman scattering dominates noise and lowers g(2) toward unity.

Two-squeezer interference

The section models two-squeezer interference in Gaussian states with identical squeezing and homogeneous loss, deriving phase-dependent noise reduction factors. Measurements across interferometer phase settings are compared with the model, while fitted parameters quantify interference visibility under partial distinguishability.

  • Model assumptions: Identical two-mode squeezed states undergoing a beam splitter with homogeneous transmission loss yield equal mode variances and mean photon numbers.The model assumes identical squeezing in both sources and Gaussian operations characterized by unitary U and transmission efficiency η.
  • Analytical result: NRF_a1,b2 = NRF_a2,b1 = 1 + n −(η + n) sin2(θ) sin2(φ) gives the cross-pair noise reduction factors.The interferometer is parametrized by angles θ and φ.
  • Experimental procedure: 4 × 10^5 photon-number samples were acquired for each of 40 phase settings spanning φ from 0 to 2π.The two selected squeezers were activated, θ was set to π/2 for effective 50/50 interference, and four NRF combinations were fitted to the model.
  • Distinguishability limit: Completely distinguishable temporal modes would produce zero interference visibility and no oscillating phase dependence with amplitude n + η.The interferometer cannot interfere modes populated by substantially different temporal profiles.
  • Fit parameters: n = 0.18(4) and η = 0.11(1) were obtained by averaging the extracted fit parameters over all traces.These fitted values partially quantify distinguishability and loss effects in the observed interference curves.

Scalability

Scaling toward quantum advantage is framed around a 100-mode target with no more than 3 dB of interferometer loss. The main obstacles are current optical loss and the power and thermal demands of larger thermo-optic interferometers, though design improvements and thermal management offer routes forward.

  • Scalability: 100 modes with no more than 3 dB of interferometer loss is the stated scalability target for potential quantum advantage.The loss criterion is demanding because interferometer loss scales with the number of modes.
  • Scalability: Approximately 8 dB of total system loss currently includes about 3 dB from the four-spatial-mode interferometer.Loss is dominated by MMI-based beam splitters at 0.2 to 0.4 dB per layer and bent waveguide-coil segments at 0.35 to 0.55 dB per layer.
  • Scalability: Directional couplers could reduce beam-splitter loss to about 0.008 dB per layer by contributing approximately 200µm of length per layer.This improvement depends on moving to a fabrication line with more precise lithography.
  • Scalability: A 50-spatial-mode interferometer would require 2,450 phase shifters and dissipate about 120 W across approximately 21 cm2.The current interferometer dissipates approximately 1 W for a typical unitary setting in a chip area of 0.4 cm2.

Supplemental Information

The supplemental information details theoretical modeling and analysis methods for the chip, including parameter estimation, non-classicality benchmarking, Gaussian boson sampling probabilities, and algorithm-specific constructions. It also states limitations involving loss, classical simulation, and approximation quality.

  • Theoretical device model: The chip distribution is benchmarked by fitting two-dimensional photon-number histograms to a two-mode squeezed-vacuum model with two Schmidt modes and detector noise.Parameters are retrieved from measured histograms using a Levenberg–Marquardt inverse-problem solver.
  • Non-classicality benchmark: The non-classicality analysis generalizes an existing threshold-detector criterion to non-uniform squeezing and losses, while coarse-graining the output distribution to a single-Schmidt-mode model.The analysis relates efficient classical simulation to closeness between the mixed input states and classical Gaussian states, quantified through quantum fidelity.
  • Gaussian boson sampling: For Gaussian states generated by squeezing and linear interferometry, output probabilities are computed from hafnians of photon-pattern-dependent submatrices.Rows and columns are deleted for unoccupied modes and repeated according to detected photon numbers.
  • Molecular vibronic spectra: Molecular vibronic spectra are constructed from the Duschinsky transformation, displacement vector, and singular-value decomposition of the transformed normal-mode matrix.The supplemental discussion notes that no efficient classical algorithm is known, although approximate methods such as ezSpectrum exist and may be challenging for large molecules.
  • Graph similarity: Graph-similarity features encode compatible bipartite graphs on eight vertices and estimate orbit probabilities from photon click patterns.The approach remains uncertain as a source of quantum advantage because loss tolerance has not been studied and classical methods have outperformed exact GBS feature-vector computations on some tasks.
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