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arXiv:2410.06204 · Nature Photonics

Modular quantum-to-quantum Bernoulli factory in an integrated photonic processor

Francesco Hoch, Taira Giordani, Luca Castello, Gonzalo Carvacho, Nicolò Spagnolo, Francesco Ceccarelli, Ciro Pentangelo, Simone Piacentini, Andrea Crespi, Roberto Osellame, Ernesto F. Galvão, Fabio Sciarrino

Published Oct 3, 2024• 12 citations

Abstract

Generation and manipulation of randomness is a relevant task for several applications of information technology. It has been shown that quantum mechanics offers some advantages for this type of task. A promising model for randomness manipulation is provided by Bernoulli factories—protocols capable of changing the bias of Bernoulli random processes in a controlled way. At first, this framework was proposed and investigated in a fully classical regime. Recent extensions of this model to the quantum case showed the possibility of implementing a wider class of randomness manipulation functions. We propose a Bernoulli factory scheme with quantum states as the input and output, using a photonic-path-encoding approach. Our scheme is modular and universal and its functioning is truly oblivious of the input bias—characteristics that were missing in earlier work. We report on experimental implementations using an integrated and fully programmable photonic platform, thereby demonstrating the viability of our approach. These results open new paths for randomness manipulation with integrated quantum technologies. A quantum-to-quantum Bernoulli factory is demonstrated by using a reconfigurable Clements’s squared unitary circuit in an integrated quantum photonic platform. Three interferometer designs are proposed for the basic operations of a field on qubit states.

DOI: 10.1038/s41566-024-01526-8

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A Bernoulli factory is a randomness manipulation routine that takes as input a Bernoulli random variable, outputting another Bernoulli variable whose bias is a function of the input bias. Recently proposed quantum-to-quantum Bernoulli factory schemes encode both input and output variables in qubit amplitudes. This primitive could be used as a subroutine for more complex quantum algorithms involving Bayesian inference and Monte Carlo methods. Here, we report an experimental implementation of a polarization-encoded photonic quantum-to-quantum Bernoulli factory. We present and test three interferometric setups implementing the basic operations of an algebraic field (inversion, multiplication, and addition), which, chained together, allow for the implementation of a generic quantum-to-quantum Bernoulli factory. These in-bulk schemes are validated using a quantum dot-based single-photon source featuring high brightness and indistinguishability, paired with a time-to-spatial demultiplexing setup to prepare input resources of up to three single-photon states.

A Bernoulli factory is a model of randomness processing. Recently, the quantum generalization of a Bernoulli factory with a quantum input and classical output offers a clear advantage over classical means in simulating classical randomness. A more ``quantum'' version of a Bernoulli factory with a quantum input and quantum output has been proposed and shows applications in simulating quantum randomness using quantum resources, the so-called quantum-to-quantum Bernoulli factory, which simulates probability amplitudes rather than probability. In this paper, we report an experimental implementation of a quantum-to-quantum Bernoulli factory with linear optics. We implement three elements of a quantum-to-quantum Bernoulli factory, including inversion, multiplication, and addition, and demonstrate how to compare quantum states via a quantum-to-quantum Bernoulli factory. Our results provide a thorough understanding of the Bernoulli factory problem in the quantum world and will stimulate the quantum advantages in simulating a wider range of classically infeasible random processes.

Randomness processing in the Bernoulli factory framework provides a concrete setting in which quantum resources can outperform classical ones. We experimentally demonstrate quantum randomness processing based on Bell-basis measurements of two identical input quoins prepared on IBM superconducting hardware. Using only the measurement outcomes (and no external classical randomness source), we realize the classically inconstructible Bernoulli doubling primitive

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and, as intermediate outputs from the same Bell-measurement statistics, an exact fair coin

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and the classically inconstructible function

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. We benchmark the measured output biases against ideal predictions and discuss the impact of device noise. Our results establish a simple resource-efficient experimental primitive for quantum-to-classical randomness processing and support the viability of quantum Bernoulli factories for quantum-enhanced stochastic simulation and sampling tasks.

Integrated quantum photonics has emerged as one of the leading platforms for scaling quantum information processing, offering compact, stable, and low-loss hardware with precise phase and mode control. Advances in integrated photonics architectures and active programmability now enable complex, high-dimensional transformations essential for quantum advantage tasks. We introduce an integrated, reconfigurable 3D photonic device with 128 modes for manipulation of single-photon quantum states (Qolossus 3D). Leveraging a continuously coupled architecture and thermo-optic programmability, the platform implements reconfigurable unitary transformations at unprecedented scale for integrated quantum optics. Exploiting indistinguishable single photons demultiplexed from a quantum dot source, we perform Boson Sampling across the large-dimensional chip and analyse the resulting output distributions for up to 4 photons. We then exploit it to demonstrate randomness generation via Boson Sampling. Agreement with theoretical predictions validates both the device's reconfigurable operation and the generation of random numbers. Our results highlight the scalability, stability, and precise control of integrated photonics for quantum information processing.