Random-number-generation-using-boson-sampling---ORCA-Computing

Womanium Quantum Hackathon 2022

Team: 5-qubits

team memebers:

-Víctor Hernán Torres Bruaer, email: [email protected], Dscord ID: Víctor Brauer #2630. -Bakhao Dioum, email: [email protected],DIscord ID : Bakhao#0792. -Arkan Mahmood Hassan, Email: [email protected], Discord ID: Arkan Hassan#2099. -Luis Felipe Morales Bultron,email: [email protected], Dicord ID: Luis Felipe Morales Bultron#0562. -Áulide Martínez Tapia, mail: [email protected], Discor ID: aulide#9284.

Pitch presenter:

Challenge: Random-number-generation-using-boson-sampling---ORCA-Computing.

In this notebook, a short background and introduction about the challenge problem is precented. Later, the links to the other part of our project will be listed inorder.

Introduction

Since Aaronson and Arkhipov (AA) proved that applying a passive linear interferometer with input Fock states cannot be efficiently simulated by a classical computer because it's a problem of computing the permanent of large complex valued matrices which is of complexity class P-Complete, the search for concrete application for the boson sampling problem emerged. Despite being a non universal quantum computer, photonic quantum computers which implement boson sampling have been proven to be far less experimentally demanding when compared to other standard photonic quantum computers with full implementation of linear optics. This is so since it only requires passive optical elements (beamsplitters, phase_shifts and photodetector). Despite all of the above, boson sampling still struggles to find practical use because of the randomness of the boson sampling results. We therefore want to exploit that randomness as a source of a quantum random number generator QRNG). Despite the boson sampling problem not being able to be simulated with classical computer without exponential ressources, the output of a boson sampler doesn't necessary generate a completely random output. We therefore require post processing using The Von Neumann correction method.

How to build a boson sampler using optical hardware

Single photon sources: single photons are generated using nonlinear crystals through Spontaneous Parametric down conversion (SPDC) or Spontaneous Four Wave Mixing (SPFWM) in a probabilistic process (non-deterministic). In the case for example of the SPDC, with a strong coherent pump, a pair of photons is generated (signal and idler photon). A photodetector is put on the signal where a photon detection will ensure we know there is a photon in the idler due to quantum correlations. The idler photon will be rooted to one of the input of the boson samplers. And that is an example of how an input single photon mode is generated.

Linear interferometers can be decomposed into single mode phase shifts and a set of beam splitters(BS) that can be experimentally achieved using linear optical elements. The most common applications for the network of linear optical elements are Reck design and Clements design. Clements optical netwrok design is proven to be more robust against photon losses and offers an optimal linear optical network arrangement.

Detection: photodetectors are used to build a multiplexed photon counting detector.

At last, the hardware required to build a boson sampling requires very few optical elements.

Applications

QNRG can be used on the generation of crypto-keys. Given that a boson sampler can generate states sampled from "almost" uniform probability distributions, one expects more random string of numbers (after post-processing) than those generated by classical pseudo-random number generators. This in turn offers stronger an hard to break protocols when creating crypto-keys, say for example those needed by finacial transactions.

Another possible uses of QNRG are in physical simulations. Boson samplers could be used to generate truly random numbers and this can then be used in classical computers or other quantum computers to simulate physical situations more accurately.

Content of the work

In the fisrt notebook we study the Boson sampling formalism and create data simulating a Fock Boson Sampling.

1._Boson_sampling_for_data_generation_final 

In this notebook we were also able to generate data simulating a Gaussian Boson Sampling.

1.5_Gaussian_boson_sampling_for_data_generation_final  

In the second part of the wokr we analyze the data, to get a better understanding of the unbiased distribution.

2._Analysis_of_the_BS_data_final  

Finally in the third part of the work we are able to prest a random number generator based on the simulations of Fock Boson Sampling. 3._Random_number_generator_final  

Conclusion

We make hard research in the Boson Sampling being able to simulate data from Fock Boson Sampling and Gaussian Boson Sampling. Also, we study the generated data to understand the unbiased probability distribution of the random numbers generated in terms of the length of the string produced.

With these tools, we were able to create a Random Number Generator that takes in-time data from BS simulations. This will be easily applicable to a real Boson Sampler.

Perspectives: What's next?

The next steps are:

$1.$ Use a real interferometer to create a RN generator that uses in-time data from a real Boson Sampling experiment.

$2.$ Get a better understanding of the parameters of the interferometer and the initial state to get better random numbers.

$3.$ Apply some randomness tests in order to check out the possible applications.