Complexity and multi-functional variants of the Quantum-to-Quantum Bernoulli Factories

• URL: http://arxiv.org/abs/2512.10810v1
• Date: Thu, 11 Dec 2025 16:56:32 GMT
• Title: Complexity and multi-functional variants of the Quantum-to-Quantum Bernoulli Factories
• Authors: Francesco Hoch, Taira Giordani, Gonzalo Carvacho, Nicolò Spagnolo, Fabio Sciarrino,
• Abstract summary: A Bernoulli factory is a model for randomness manipulation.<n> quantum-to-quantum Bernoulli factory schemes encode both the input and output variables using qubit amplitudes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A Bernoulli factory is a model for randomness manipulation that transforms an initial Bernoulli random variable into another Bernoulli variable by applying a predetermined function relating the output bias to the input one. In literature, quantum-to-quantum Bernoulli factory schemes have been proposed, which encode both the input and output variables using qubit amplitudes. This fundamental concept can serve as a subroutine for quantum algorithms that involve Bayesian inference and Monte Carlo methods, or that require data encryption, like in blind quantum computation. In this work, we present a characterisation of the complexity of the quantum-to-quantum Bernoulli factory by providing a lower bound on the required number of qubits needed to implement the protocol, an upper bound on the success probability and the quantum circuit that saturates the bounds. We also formalise and analyse two different variants of the original problem that address the possibility of increasing the number of input biases or the number of functions implemented by the quantum-to-quantum Bernoulli factory. The obtained results can be used as a framework for randomness manipulation via such an approach.

Related papers

• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• A Study of Gate-Based and Boson Sampling Quantum Random Number Generation on IBM and Xanadu Quantum Devices [0.0]
  This paper explores the practicality of generating random numbers from two quantum platforms.<n>We implement simple post-processing methods, including the classic Von Neumann extractor.<n>Results show that, while unbiased bitstreams can be achieved on both platforms, throughput remains low and cost per random bit is high.
  arXiv  Detail & Related papers  (2025-07-04T22:01:55Z)
• Polarization-encoded photonic quantum-to-quantum Bernoulli factory based on a quantum dot source [0.0]
  Recently proposed quantum-to-quantum Bernoulli factory schemes encode both input and output variables in qubit amplitudes. This primitive could be used as a sub-routine for more complex quantum algorithms involving Bayesian inference and Monte Carlo methods.
  arXiv  Detail & Related papers  (2024-10-15T15:21:03Z)
• Efficient Quantum Pseudorandomness from Hamiltonian Phase States [41.94295877935867]
  We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem.<n>We show that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions.<n>We show that our assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives.
  arXiv  Detail & Related papers  (2024-10-10T16:10:10Z)
• Modular Quantum-to-Quantum Bernoulli Factory in an Integrated Photonic Processor [0.0]
  quantum mechanics offers some advantages for generation and manipulation of randomness. Bernoulli factories are protocols capable of changing the bias of Bernoulli random processes in a controlled way. 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 input and output, using a photonic path-encoding approach.
  arXiv  Detail & Related papers  (2024-10-08T17:06:25Z)
• Determining the ability for universal quantum computing: Testing controllability via dimensional expressivity [39.58317527488534]
  Controllability tests can be used in the design of quantum devices to reduce the number of external controls. We devise a hybrid quantum-classical algorithm based on a parametrized quantum circuit.
  arXiv  Detail & Related papers  (2023-08-01T15:33:41Z)
• Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning [47.991114317813555]
  Quantum models implement implicit probabilistic predictors that produce multiple random decisions for each input through measurement shots. This paper proposes to leverage such randomness to define prediction sets for both classification and regression that provably capture the uncertainty of the model.
  arXiv  Detail & Related papers  (2023-04-06T22:05:21Z)
• On Quantum Circuits for Discrete Graphical Models [1.0965065178451106]
  We provide the first method that allows one to provably generate unbiased and independent samples from general discrete factor models. Our method is compatible with multi-body interactions and its success probability does not depend on the number of variables. Experiments with quantum simulation as well as actual quantum hardware show that our method can carry out sampling and parameter learning on quantum computers.
  arXiv  Detail & Related papers  (2022-06-01T11:03:51Z)
• Interactive Protocols for Classically-Verifiable Quantum Advantage [46.093185827838035]
  "Interactions" between a prover and a verifier can bridge the gap between verifiability and implementation. We demonstrate the first implementation of an interactive quantum advantage protocol, using an ion trap quantum computer.
  arXiv  Detail & Related papers  (2021-12-09T19:00:00Z)
• Stochastic emulation of quantum algorithms [0.0]
  We introduce higher-order partial derivatives of a probability distribution of particle positions as a new object that shares basic properties of quantum mechanical states needed for a quantum algorithm. We prove that the propagation via the map built from those universal maps reproduces up to a prefactor exactly the evolution of the quantum mechanical state. We implement several well-known quantum algorithms, analyse the scaling of the needed number of realizations with the number of qubits, and highlight the role of destructive interference for the cost of emulation.
  arXiv  Detail & Related papers  (2021-09-16T07:54:31Z)
• Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
  We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems. Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
  arXiv  Detail & Related papers  (2021-08-30T23:50:05Z)
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond [46.39654665163597]
  We report on experimental tests of topological defect formation via the one-dimensional transverse-field Ising model. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system.
  arXiv  Detail & Related papers  (2020-01-31T02:55:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.