Kelly Betting with Quantum Payoff: a continuous variable approach

• URL: http://arxiv.org/abs/2001.11395v6
• Date: Thu, 16 Sep 2021 13:58:59 GMT
• Title: Kelly Betting with Quantum Payoff: a continuous variable approach
• Authors: Salvatore Tirone, Maddalena Ghio, Giulia Livieri, Vittorio Giovannetti, Stefano Marmi
• Abstract summary: The payoff of the gambler is encoded into the internal degrees of freedom of a quantum memory element. We define the doubling rate of the model and identify the optimal gambling strategy for fixed odds and probabilities of winning.
• Score: 1.3999481573773072
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The main purpose of this study is to introduce a semi-classical model describing betting scenarios in which, at variance with conventional approaches, the payoff of the gambler is encoded into the internal degrees of freedom of a quantum memory element. In our scheme, we assume that the invested capital is explicitly associated with the quantum analog of the free-energy (i.e. ergotropy functional by Allahverdyan, Balian, and Nieuwenhuizen) of a single mode of the electromagnetic radiation which, depending on the outcome of the betting, experiences attenuation or amplification processes which model losses and winning events. The resulting stochastic evolution of the quantum memory resembles the dynamics of random lasing which we characterize within the theoretical setting of Bosonic Gaussian channels. As in the classical Kelly Criterion for optimal betting, we define the asymptotic doubling rate of the model and identify the optimal gambling strategy for fixed odds and probabilities of winning. The performance of the model are hence studied as a function of the input capital state under the assumption that the latter belongs to the set of Gaussian density matrices (i.e. displaced, squeezed thermal Gibbs states) revealing that the best option for the gambler is to devote all her/his initial resources into coherent state amplitude.

Related papers

• Characterizing Trainability of Instantaneous Quantum Polynomial Circuit Born Machines [7.716642023459826]
  Instantaneous quantum quantum circuit Born machines (IQP-QCBMs) have been proposed as quantum generative models.<n>We show that barren plateaus depend on the generator set and the spectrum of the chosen kernel.<n>We identify regimes in which low-weight-biased kernels avoid exponential suppression in structured topologies.
  arXiv  Detail & Related papers  (2026-02-11T17:12:56Z)
• Optimal quantum learning in proximity to universality [0.0]
  boundary between classically simulable and computationally superior quantum systems is fundamental to identifying true quantum advantage.<n>We introduce a tunable $N$-qubit random circuit model, where a fraction $p$ of Clifford gates are probabilistically substituted with nonstabilizing conditional-$hatT$ gates.<n>We establish a direct correspondence between the reservoir's performance on temporal processing tasks and its entanglement spectrum statistics and long-range nonstabilizer resource content.
  arXiv  Detail & Related papers  (2025-10-21T13:27:41Z)
• Closing the Quantum-Classical Scaling Gap in Approximate Optimization [0.0]
  We reassess findings with different classical paradigm -- Simulated Bifurcation Machine (SBM)<n>By leveraging chaotic behavior rather than thermal fluctuations, SBM achieves comparable or superior scaling performance.<n>We conclude that it is unlikely that current generation of quantum annealers, can demonstrate supremacy in discrete approximate optimization.
  arXiv  Detail & Related papers  (2025-05-28T16:02:57Z)
• Variational Quantum Algorithm for Solving the Liouvillian Gap [0.0]
  In open quantum systems, the Liouvillian gap characterizes the relaxation time toward the steady state.<n>We propose a variational quantum algorithm for efficiently estimating the Liouvillian gap.
  arXiv  Detail & Related papers  (2025-05-22T05:59:55Z)
• Quantum Rabi oscillations in the semiclassical limit: backreaction on the cavity field and entanglement [89.99666725996975]
  We show that for a strong atom-field coupling, when the duration of the $pi $pulse is below $100omega -1$, the behaviour of the atomic excitation probability deviates significantly from the textbook. In the rest of this work we study numerically the backreaction of the qubit on the cavity field and the resulting atom-field entanglement.
  arXiv  Detail & Related papers  (2025-04-12T23:24:59Z)
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling [49.1574468325115]
  A key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient. We develop a single- parameter scaling theory for the spectral statistics in this scenario, which embodies exact self-similarity of the spectral correlations along the complete scrambling dynamics. We establish that scaling predictions are matched by a privileged process, and serve as bounds for other dynamical scrambling scenarios, allowing one to quantify inefficient or incomplete scrambling on all timescales.
  arXiv  Detail & Related papers  (2023-10-17T15:41:50Z)
• 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)
• A quantum-classical decomposition of Gaussian quantum environments: a stochastic pseudomode model [0.8258451067861933]
  We show that the effect of a Bosonic environment linearly coupled to a quantum system can be simulated by a Gaussian Lindblad master equation. For a subset of rational spectral densities, all parameters are explicitly specified without the need of any fitting procedure.
  arXiv  Detail & Related papers  (2023-01-18T14:17:17Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• A Quantum Optimal Control Problem with State Constrained Preserving Coherence [68.8204255655161]
  We consider a three-level $Lambda$-type atom subjected to Markovian decoherence characterized by non-unital decoherence channels. We formulate the quantum optimal control problem with state constraints where the decoherence level remains within a pre-defined bound.
  arXiv  Detail & Related papers  (2022-03-24T21:31:34Z)
• High Fidelity Quantum State Transfer by Pontryagin Maximum Principle [68.8204255655161]
  We address the problem of maximizing the fidelity in a quantum state transformation process satisfying the Liouville-von Neumann equation. By introducing fidelity as the performance index, we aim at maximizing the similarity of the final state density operator with the one of the desired target state.
  arXiv  Detail & Related papers  (2022-03-07T13:27:26Z)
• Driven-dissipative criticality within the discrete truncated Wigner approximation [0.0]
  We establish a quantum jump formalism to integrate the quantum master equation describing the dynamics of the system. We apply our method to simulation of the paradigmatic dissipative Ising model, where we are able to capture the critical fluctuations of the system beyond the level of mean-field theory.
  arXiv  Detail & Related papers  (2021-08-16T18:00:01Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Efficient Hamiltonian Simulation for Solving Option Price Dynamics [0.0]
  We present a digital quantum algorithm to solve Black-Scholes equation on a quantum computer by mapping it to the Schr"odinger equation. The algorithm shows a feasible approach for using efficient Hamiltonian simulation techniques as Quantum Signal Processing.
  arXiv  Detail & Related papers  (2021-01-11T16:54:53Z)
• Non-Markovianity of Quantum Brownian Motion [0.0]
  We study quantum non-Markovian dynamics of the Caldeira-Leggett model, a prototypical model for quantum Brownian motion. A comparison of our results with the corresponding results for the spin-boson problem show a remarkable similarity in the structure of non-Markovian behavior of the two paradigmatic models.
  arXiv  Detail & Related papers  (2020-07-06T16:35:09Z)
• Quantum advantage in simulating stochastic processes [0.0]
  We show that quantum memoryless dynamics can simulate classical processes that require memory. We show that the set of classical states accessible via Markovian master equations with quantum controls is larger than the set of those accessible with classical controls.
  arXiv  Detail & Related papers  (2020-05-05T18:00:01Z)

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.