Source-linked AI summary
Photonic Boson Sampling in a Tunable Circuit
Matthew A. Broome, Alessandro Fedrizzi, Saleh Rahimi-Keshari, Justin Dove, Scott Aaronson, Timothy Ralph, Andrew G. White
TL;DR
The study asks whether measured linear-optical evolution can predict bosonic scattering amplitudes through submatrix permanents. It measures the circuit unitary and finds close agreement between predicted and observed interference visibility for one configuration.
Problem
The study asks whether measured linear-optical evolution can predict bosonic scattering amplitudes through submatrix permanents.
Method
It measures the circuit’s unitary evolution after runs and uses selected submatrices’ permanents to calculate scattering probabilities.
Results
The predicted non-classical interference visibility was 0.951 versus 0.939 observed for one input/output configuration.
Takeaways & Limitations
The close predicted and observed visibilities support the permanent-based calculation for this configuration.
Takeaways & Limitations
Higher-order photon-emission terms cannot be entirely removed with linear optics alone, though their effect can be reduced.
Abstract
from arXiv · showhide
Quantum computers are unnecessary for exponentially-efficient computation or simulation if the Extended Church-Turing thesis---a foundational tenet of computer science---is correct. The thesis would be directly contradicted by a physical device that efficiently performs a task believed to be intractable for classical computers. Such a task is BosonSampling: obtaining a distribution of n bosons scattered by some linear-optical unitary process. Here we test the central premise of BosonSampling, experimentally verifying that the amplitudes of 3-photon scattering processes are given by the permanents of submatrices generated from a unitary describing a 6-mode integrated optical circuit. We find the protocol to be robust, working even with the unavoidable effects of photon loss, non-ideal sources, and imperfect detection. Strong evidence against the Extended Church-Turing thesis will come from scaling to large numbers of photons, which is a much simpler task than building a universal quantum computer.
I. Four-photon source and BosonSampling circuit
The experiment generates photon pairs by spontaneous parametric downconversion and injects single photons into a six-mode BosonSampling circuit using calcite beam-displacers and waveplates. Operating at 20% maximum pump power, the setup achieves 260 Hz average two-photon coincidences and 185 mHz average four-fold coincidences.
- Photon source: Photon pairs are produced by forward and backward passes through a type-I phase-matched BBO crystal, pumped by frequency-doubled 410 nm light.The laser operates at 76 MHz with 100 fs pulses and ∼3.8 W average output power at 820 nm; frequency doubling yields ∼1.5 W centred at 410 nm.
- Photon injection: Single photons enter the BosonSampling circuit through calcite beam-displacers and waveplates, with the source operated at 20% maximum pump power to reduce higher-order emission.The forward downconversion pass is used for two-photon measurements.
- Detection rates: 64% average input coupling efficiency produces a 260 Hz average two-photon coincidence rate across all circuit modes.This measurement is performed across all modes of the circuit.
- Detection rates: 185 mHz average four-fold coincidence rate is obtained when three photons enter the circuit and the fourth photon serves as a trigger detector.The source again runs at 20% maximum pump power.
II. Measured unitary matrix and calculation of permanents
The section describes measuring the optical network’s unitary evolution, constructing photon-specific submatrices, and using their permanents to predict bosonic scattering probabilities. For one configuration, the predicted visibility was 0.951 versus an observed 0.939, with uncertainty estimated from 10 unitary characterisations.
- Permanent calculation: The constructed submatrices’ permanents were used to calculate probability amplitudes for bosonic scattering events.The section presents this as the procedure for generating photon-specific scattering predictions.
- Measured unitary evolution: The optical network’s evolution Uexp was measured after each experimental run to account for changes in laboratory conditions.This ensured that the generated scattering probabilities represented the circuit used in each run.
- Submatrix construction: For input S=(1, 0, 1, 0, 0, 0) and output T=(0, 1, 0, 0, 1, 0), the submatrix UT was formed by selecting tj copies of each column.The corresponding matrix UST was then formed by selecting si copies of rows from UT.
- Visibility comparison: 0.951 predicted visibility compared with 0.939 observed for the specified input/output configuration.The predicted value was obtained from probabilities for indistinguishable and distinguishable photons.
- Uncertainty estimation: 10 separate unitary characterisations supplied the standard-deviation estimate for predicted-visibility errors.The estimate used the spread of predicted visibilities across those characterisations.
III. Calculation of visibility using coherent-state inputs
The section calculates interference visibility by injecting equal-amplitude coherent states into a linear-optical network and comparing phase-averaged correlations with and without temporal overlap. Zero-delay inputs interfere, whereas delays much longer than the coherence length produce an incoherent output-field sum.
- Coherent-state inputs: Equal-amplitude coherent states with phases θ_i are injected into selected input modes, and the input electric-field vector is transformed by the network unitary U.The input amplitudes are normalized as E_i=e^iθ_i.
- Coherent-state inputs: With zero time delay, overlapping coherent states generate a 2n-order detector correlation described by a phase-averaged cross-correlation function.The correlation is evaluated between detectors at selected output modes.
- Temporal distinguishability: Delays much longer than the coherence lengths eliminate interference, leaving the output cross-correlation as an incoherent sum of input fields.This provides the noninterfering reference for visibility calculations.
- Visibility definition: Interference visibility is defined from the coherent and incoherent correlation cases using a definition analogous to Eq.(3) in the main text.The output electric field for each input mode contributes to the visibility calculation.
IV. Effects of non-ideal photon sources from downconversion
Downconversion is probabilistic, producing photon-pair states with a small per-pulse pair-creation amplitude η. Triggering removes vacuum contributions but cannot eliminate higher-order multiphoton terms, whose effects can be reduced by lowering η and multiplexing sources.
- Non-ideal photon sources: The pair-creation amplitude per pump pulse is η≪1, incorporating nonlinear interaction strength, pump interaction time, and optical coupling efficiency.Triggering on one photon removes the vacuum component, but η^i>0 permits creation of two or more photon pairs.
- Non-ideal photon sources: Higher-order terms cannot be completely removed from downconversion light using linear optics alone.Their detrimental effects can nevertheless be reduced by keeping η at the necessary minimum.
- Non-ideal photon sources: Temporal or spatial multiplexing can maintain a constant single-photon rate while reducing higher-order contamination through smaller η.This uses multiple downconversion sources to offset the lower pair-creation amplitude.