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Multi-photon quantum interference in a multi-port integrated photonic device
Benjamin J. Metcalf, Nicholas Thomas-Peter, Justin B. Spring, Dmytro Kundys, Matthew A. Broome, Peter Humphreys, Xian-Min Jin, Marco Barbieri, W. Steven Kolthammer, James C. Gates, Brian J. Smith, Nathan K. Langford, Peter G. R. Smith, Ian A. Walmsley
TL;DR
Integrated photonic circuits must scale in complexity while remaining verifiably quantum, but photon loss and inaccessible components make this difficult. This work combines classical element-wise characterisation with multiphoton interference tests in a three-interferometer, eight-mode device. The device demonstrates three-photon quantum operation inconsistent with classical and biseparable models, while the authors identify loss reduction as essential for further scaling.
Problem
The paper addresses how integrated photonic devices can reach quantum-processing complexity beyond efficient classical simulation despite photon loss and verification challenges.
Method
The authors classically characterise individual circuit parameters, predict quantum behaviour, and validate operation through two- and three-photon interference measurements.
Results
Three-photon interference across eight output combinations is irreconcilable with classical models and inconsistent with biseparable quantum explanations.
Takeaways & Limitations
The demonstrated multiphoton interference supports integrated implementations of advanced protocols such as teleportation, cluster-state generation, and boson-sampling tests.
Takeaways & Limitations
Further scaling remains constrained by photon loss, requiring improved integrated sources, synchronisation, and detectors.
Abstract
from arXiv · showhide
Increasing the complexity of quantum photonic devices is essential for many optical information processing applications to reach a regime beyond what can be classically simulated, and integrated photonics has emerged as a leading platform for achieving this. Here, we demonstrate three-photon quantum operation of an integrated device containing three coupled interferometers, eight spatial modes and many classical and nonclassical interferences. This represents a critical advance over previous complexities and the first on-chip nonclassical interference with more than two photonic inputs. We introduce a new scheme to verify quantum behaviour, using classically characterised device elements and hierarchies of photon correlation functions. We accurately predict the device's quantum behaviour and show operation inconsistent with both classical and bi-separable quantum models. Such methods for verifying multiphoton quantum behaviour are vital for achieving increased circuit complexity. Our experiment paves the way for the next generation of integrated photonic quantum simulation and computing devices.
RESULTS
The circuit is designed to demonstrate genuinely quantum operation while increasing both photon number and spatial-mode complexity. Classical characterisation and two-photon validation enable tests of three-photon interactions against classical and biseparable explanations.
- RESULTS: Three coupled interferometers distribute three photons across eight modes to test genuinely quantum operation at increased circuit complexity.The experiment targets three-photon interactions relevant to cluster-state generation and teleportation.
- RESULTS: Classical input states provide a loss-tolerant, element-wise characterisation of the circuit without resource-intensive quantum process tomography.The reconstructed device transformation supports calculation of classical bounds and quantum predictions.
- RESULTS: Two-photon interference agrees with quantum predictions but is inconsistent with classical theory, validating the characterisation and photon indistinguishability.This validation precedes the three-photon test.
- RESULTS: Three-photon measurements exclude both classical and biseparable quantum models with high confidence, indicating operation involving the full circuit complexity.The observed interference cannot be explained by a simplified or restricted circuit subsection.
Characterising circuit operation
The integrated circuit is characterised component by component using classical light and loss-insensitive measurements. Beam-splitter reflectivities and interferometer phases are then used to reconstruct and test the device transformation.
- Characterising circuit operation: The circuit contains three coupled Mach–Zehnder interferometers, ten beam splitters, and three thermo-optic phase shifters.Thermo-electric temperature control maintained stable beam-splitting ratios and phase offsets over many weeks.
- Characterising circuit operation: Beam-splitter reflectivities η1 to η10 are measured with continuous-wave laser light using a four-measurement ratiometric analysis independent of coupling and transmission losses.Light is coupled into each accessible input port and power is recorded at the output ports.
- Characterising circuit operation: η8 = 0.55 ± 0.02 is determined from integrated transverse-scatter intensity in the ratiometric analysis.The CCD images the scattered light and integrates a specified output region.
- Characterising circuit operation: Scanning each thermo-optic phase shift gives an effective interferometer reflectivity, while fitting the interference fringe estimates the zero-voltage phase and checks the defining beam-splitter parameters.The phase characterisation uses the four relevant beam splitters for each Mach–Zehnder interferometer.
circuit complexity
Two-photon tests validate the circuit model before three-photon measurements probe the device’s full coupled-interferometer complexity. The observed visibilities agree with quantum predictions and reject classical and biseparable explanations.
- Two-photon interference: Pairwise tests of input modes cf, cd, and df agree with quantum predictions and indicate good fidelity among the three photon states.Each photon is tested individually against the other two.
- Two-photon interference: The two-photon data are consistent with quantum predictions, with reduced chi-squared χ2_r = 0.9 and P(χ2_r ≥23) < 10^-16 for the quantum residuals.The ultimate classical visibility limit of 1/2 is exceeded for output combinations de, cd, and dg.
- Three-photon interference: Three-photon interference arises with all three coupled interferometers operating simultaneously, using photons injected into modes c, d, and f.Heralded four-fold detection distinguishes the desired |111⟩cdf events from unwanted |022⟩cdf noise events.
- Three-photon interference: Three-photon visibilities agree with quantum predictions and are completely inconsistent with equivalent classical predictions.The predictions use the individually characterised circuit elements.
- Three-photon interference: Biseparable quantum models predict P < 10^-8 for the observed three-photon interference signature.These models treat one photon as completely distinguishable from the other two at all temporal delays.
DISCUSSION
The experiment demonstrates multipartite quantum operation in an eight-mode integrated circuit and introduces practical verification methods for scaling its complexity.
- The device simultaneously accesses three coupled interferometers, classical interference at three nodes, and nonclassical interference at five nodes.
- The experiment is the first chip-based multipartite nonclassical interference demonstration relying on more than two individual photonic inputs.
- Three-photon interferences across eight output combinations are irreconcilable with classical models.
- A loss-independent classical characterisation technique and two-photon interference enable verification of successful device operation against simulations.
- Minimising losses remains critical for scaling integrated circuits toward regimes that cannot be simulated using classical processors.
- The demonstrated multiphoton interference supports nontrivial boson-sampling tests and integrated implementations of teleportation and cluster-state generation.
Device fabrication
The circuit was fabricated on silica-on-silicon using UV-direct-write technology to create compact waveguide components.
- UV-direct writing formed waveguides by focusing a 244 nm continuous-wave UV laser onto a silica-on-silicon substrate.
- Computer-controlled two-dimensional motion positioned the substrate transversely during waveguide fabrication.
- Beam splitters were created by crossing waveguides at different angles using the UV-writing process.
High-brightness multiphoton states on-chip
The experiment used a spectrally factorable down-conversion source and optimized coupling and filtering to generate bright, high-fidelity multiphoton states on chip.
- An 80 MHz Ti:Sapphire oscillator generated 415 nm pump light for two type-II KDP parametric down-conversion crystals.
- Spectral factorability and 3 nm interference filters improved heralding efficiency by matching daughter-photon bandwidths.
- The source achieved a four-photon coincidence rate of 20 Hz, with two-photon fidelities of 0.99 and 0.96 for narrowband-narrowband and narrowband-broadband pairs.
- Three photons were launched through polarization-maintaining fibers and a six-axis piezo-controlled array for simultaneous coupling into the chip.
Predicted visibilities
Predicted quantum and classical visibilities were obtained from characterized circuit behavior by comparing zero-delay and infinite-delay output correlations.
- The complete quantum output state was simulated using the characterized circuit unitary before calculating interference visibilities.
- Quantum visibility is calculated from intensity cross-correlation functions at zero and infinite temporal delay.
- At zero delay, output-mode intensity cross-correlations are evaluated for photons launched into selected input modes.
- Delaying one input photon produces a classical mixture used to calculate the infinite-delay reference correlation.
- The classical bound is estimated with three equal-amplitude coherent states having mutually randomized phases.
- The classical model uses incoherent sums between delayed and non-delayed photons for the infinite-delay cross-correlation.
Chi-squared test
The analysis constructs a probability model for measured interference visibilities using uncertainties in both observations and characterized circuit parameters. A transformed basis makes the visibilities statistically independent, enabling a chi-squared test.
- The probability density estimates the likelihood of observing a set of m interference visibilities v.
- Each calculated visibility depends on circuit parameters, with separate standard deviations for measured visibilities and characterized parameters.
- A basis transformation makes the visibility variables statistically independent and factorizes the resulting probability function.
- Assuming uncorrelated simulation uncertainties lowers the calculated chi-squared by approximately 0.3 relative to the quantum analysis.
ACKNOWLEGEMENTS
The work acknowledges support from multiple research councils, European projects, foundations, and fellowships, with additional individual funding for several authors.
- The work was supported by EPSRC, the EC project Q-ESSENCE, the Royal Society, and AFOSR EOARD.
- XMJ acknowledges support from NSFC and CPSF.
- NKL and MB were supported by EC Marie Curie fellowships.
- The passage identifies equal contributions by some authors and begins a reference to Politi and colleagues.