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Modular Photonic Implementation of a Quantum-to-Quantum Bernoulli Factory with Polarization Encoding

Giovanni Rodari, Francesco Hoch, Alessia Suprano, Taira Giordani, Elena Negro, Gonzalo Carvacho, Nicolò Spagnolo, Ernesto F. Galvão, Fabio Sciarrino

Published Jan 1, 2025• 0 citations
Publisher

Abstract

We experimentally implement a polarization-encoded photonic Quantum-to-Quantum Bernoulli Factory. Leveraging a high-brightness Quantum-Dot photon source and bulk optics interferometric setups, our modular and bias-oblivious implementation enables arbitrary functions of the input states to be obtained.
DOI
10.1364/cleo_fs.2025.ff117_2

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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.
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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.
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.
There has been a concerted effort to identify problems computable with quantum technology, which are intractable with classical technology or require far fewer resources to compute. Recently, randomness processing in a Bernoulli factory has been identified as one such task. Here, we report two quantum photonic implementations of a Bernoulli factory, one using quantum coherence and single-qubit measurements and the other one using quantum coherence and entangling measurements of two qubits. We show that the former consumes three orders of magnitude fewer resources than the best-known classical method, while entanglement offers a further fivefold reduction. These concepts may provide a means for quantum-enhanced performance in the simulation of stochastic processes and sampling tasks.