[Paper Review] Scattershot multiboson correlation sampling with random photonic inner-mode multiplexing

Vincenzo Tamma, Simon Laibacher|arXiv (Cornell University)|Jan 11, 2018

Quantum Information and Cryptography41 references4 citations

TL;DR

This paper introduces a scattershot multiboson correlation sampling protocol using random photonic inner-mode multiplexing to achieve scalable boson sampling despite uncorrelated spectral and temporal properties of input photons. By measuring correlations in time and frequency at the interferometer's input and output, the method maintains high multiphoton interference fidelity and demonstrates classical computational hardness, enabling experimental scalability for quantum supremacy demonstrations.

ABSTRACT

Multiphoton interference is an essential phenomenon at the very heart not only of fundamental quantum optics and applications in quantum information processing and sensing but also of demonstrations of quantum computational supremacy in boson sampling experiments relying only on linear optical interferometers. However, scalable boson sampling experiments with either photon-number states or squeezed states are challenged by the need to generate a large number of photons with fixed temporal and frequency spectra from one experimental run to another. Unfortunately, even the well established standard multiplexing techniques employed to generate photons with fixed spectral properties are affected by the detrimental effects of losses, spectral distorsions and reduction in purity. Here, we employ sampling correlation measurements in the photonic inner modes, time and frequency, at the interferometer input and output to ensure the occurrence of multiphoton interference even with pure states of input photons with random spectral overlap from one sample to another. Indeed, by introducing a random multiplexing technique where photons are generated with random inner-mode parameters, it is possible to substantially enhance the probability to successfully generate samples and overcome the typical drawbacks in standard multiplexing. Remarkably, we demonstrate the classical hardness of the resulting problem of scattershot multiboson correlation sampling based on this technique. Therefore, these results not only shed new light in the computational complexity of multiboson interference but also allow us to enhance the experimental scalability of boson sampling schemes with the potential of future applications in quantum information processing and sensing even beyond boson sampling.

Motivation & Objective

• To address the experimental challenge of generating identical photons with fixed spectral and temporal properties in large-scale boson sampling.
• To overcome limitations of standard multiplexing techniques, such as losses, spectral distortions, and reduced purity in photon generation.
• To enable scalable boson sampling by leveraging random inner-mode parameters of input photons while preserving computational hardness.
• To demonstrate that multiboson correlation sampling with random spectral and temporal overlaps remains classically hard, ensuring quantum advantage.

Proposed method

• The method employs random photonic inner-mode multiplexing, where input photons are generated with random frequency and temporal parameters across multiple runs.
• Correlation measurements are performed in conjugate variables—time and frequency—at both input and output of the linear interferometer to detect multiphoton interference.
• The probability distribution of detection events is derived using the permanent of a matrix incorporating unitary transformation elements, frequency overlaps, and time delays: $\left|\operatorname{perm}\left(\left[\mathcal{U}_{ds}\xi(\omega_d - \omega_s)\mathrm{e}^{i\omega_d t_s}\right]_{d\in\mathcal{D}, s\in\mathcal{S}}\right)\right|^2$.
• The protocol ensures that even with random spectral overlaps, the probability of successful sampling increases with the number of photons, unlike standard scattershot boson sampling.
• Theoretical analysis confirms the classical hardness of the sampling problem under the given random multiplexing scheme, preserving the quantum advantage.
• The method is validated under conditions where detector resolution prevents classical averaging, ensuring quantum correlations are not washed out.

Experimental results

Research questions

• RQ1 Can multiphoton interference be reliably maintained in boson sampling when input photons have random spectral and temporal parameters?
• RQ2 Does random photonic inner-mode multiplexing enhance the success probability of generating valid sampling events in multiboson interference experiments?
• RQ3 Is the resulting sampling problem computationally hard for classical computers, even with uncorrelated input photon parameters?
• RQ4 Can this approach enable scalable experimental implementations of quantum computational supremacy without requiring identical input photons?

Key findings

• The proposed method achieves high-fidelity multiphoton interference even when input photons have random spectral and temporal overlaps, due to correlation measurements in time and frequency.
• The probability of successful sampling increases with the number of photons, overcoming the scalability limitation of standard scattershot boson sampling.
• The sampling problem remains classically hard, as the output probability distribution is governed by the permanent of a matrix with random phase and spectral overlap terms.
• The protocol is robust under realistic experimental conditions, including detector resolution limits, provided that $\delta\omega|t_s - t_{s'}| \ll 1$ and $\delta\omega \ll \Delta\omega$.
• The method enables a new route toward scalable quantum advantage experiments using standard linear optical components and non-heralded sources.
• Theoretical analysis confirms that the use of random inner-mode parameters does not compromise the quantum computational hardness of the sampling task.