# Researchers achieve quantum breakthrough with novel quantum-to-quantum Bernoulli factory design

July 29, 2024

Unlike classical computers, which use bits to process information as either 0s or 1s, quantum computers use quantum bits, also known as qubits, which can represent and process both 0 and 1 simultaneously thanks to a quantum property called superposition. This fundamental difference gives quantum computers the potential to solve some complex problems much more efficiently than classical computers.

INL researcher Ernesto Galvão, in collaboration with Sapienza Università di Roma (Rome) and Istituto di Fotonica e Nanotecnologie (Milan), recently published a groundbreaking study in the journal Science Advances, where they describe a new set-up for a quantum-to-quantum Bernoulli factory.

A Bernoulli factory is a method to manipulate randomness, using as inputs random coin flips with a certain probability distribution, and outputting coin flips with a different, desired distribution.

Let us imagine we have a coin that lands on heads with some unknown probability. Now, we want to create a new coin that lands on heads with a different probability, possibly described by a function of the initial probability. The Bernoulli factory is an ingenious way to flip our original coin multiple times and use the different outcomes to simulate the new coin with the desired probability.

Ernesto Galvão adds “This kind of randomness manipulation is a subroutine in various probabilistic computations, for example numerical integral calculations and so-called Monte Carlo methods for simulation of physical systems. The quantum-to-quantum version of these protocols are similar, except the distributions are encoded both at the input and output as quantum states. This means such a factory can be used in a coherent way as a subroutine in a larger quantum computation.”

We asked Ernesto Galvão a few questions to help us understand the latest quantum breakthrough:

**Why are Bernoulli factories being studied?**

**EFG: **This type of randomness manipulating protocol has applications as a subroutine in numerical integration and simulation of different systems. Recently, it has been shown that for some specific transformations on the randomness distributions, quantum computers can offer an advantage over classical protocols. This motivated our collaboration to devise a way to implement Bernoulli factories using linear optics and photodetectors to manipulate the polarization of single photons.

**Why do you use an interferometer in this study?**

**EFG:** An interferometer is the simplest type of photonic quantum information processor, where the dynamics is completely driven by the settings of linear-optical elements, capable of changing the path and polarization degrees of freedom of the photons. Given the bosonic statistics that photons obey, they evolve in such multimode interferometers in a way that is computationally hard for classical computers to simulate. We proposed a way to encode and manipulate information for these applications, using the polarization of light.

**What is the main outcome?**

**EFG: **We showed that all the necessary dynamical steps required to implement arbitrary quantum Bernoulli factories could be implemented using only photonic polarization, gadgets to manipulate it, and photodetectors. Our design also enabled the concatenation of these building blocks. This required devising ways to implement each of the building blocks, manipulating special states of single photons. We managed to implement the building blocks, and also to show that they worked well together, as we envisaged in the theoretical side of the work. In principle, we can implement any such protocol that is theoretically allowed by quantum mechanics. We also showed that the input states themselves can be used as a quantum program that changes the device’s functioning. The downside is that our simple interferometer-based machine becomes less and less efficient as we concatenate multiple building blocks, because of the need for selecting only a fraction of the runs where we know, by design, that the protocol was successful. Even so, this is the first time such a machine is implemented in a way capable in principle to do any possible randomness manipulation protocol.

**Can you comment on the relevance of the study?**

**EFG:** This is a step in the exploration of the information processing capabilities of quantum light. Since Bernoulli factories were identified as a promising set-up where quantum machines have an advantage over classical machines, this is an interesting demonstration of quantum-enhanced information processing. This work was done as part of the QU-BOSS project, coordinated by Rome and with the participation of project partner INL.

We have submitted a patent protecting the intellectual property describing our designs for quantum-to-quantum Bernoulli factories. We call them “quantum-to-quantum” because both the input and the output are quantum states. This means in the future we can use these Bernoulli factories as a subroutine of a larger photonic quantum computation – I hope we can interest some company to take up this idea and develop it further.

This work is supported by ERC grant QU-BOSS, Grant agreement ID: 884676.

*Text by Catarina Moura, Science Communication Officer*