A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Quantum computer method for pricing lookback options with jumps.
Characterizes optimal-speed quantum state evolution Hamiltonians.
Quantum field theory uses Lorentzian bordisms to describe time evolution.
Abstract reviews symmetry and reduction in dynamical systems.
Quantum walks model financial returns with flexibility and asymmetry.
Develops an analytic theory for quantum imaginary time evolution.
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum s…
Model financial markets using open quantum systems to understand market imperfections.
Quantum methods model uncertain volatility in financial markets.
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is governed via (a kind of) a parallel transport in this bundle. Some problems concernin…
This work presents a novel fundamental algorithm for for defining and training Neural Networks in Quantum Information based on time evolution and the Hamiltonian. Classical Neural Network algorithms (ANN) are computationally expensive. For example, in image classification, representing an image pixel by pixel using cla…
We show how to train a quantum network of pairwise interacting qubits such that its evolution implements a target quantum algorithm into a given network subset. Our strategy is inspired by supervised learning and is designed to help the physical construction of a quantum computer which operates with minimal external cl…
Quantum method prices options by evolving a state in imaginary time.
Quantum neural networks generalize better due to flatter parameter space.
Study on quantum particle evolution on Grushin cylinder, embedding in R^3.
Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using subsampling methods from randomized numerical linear algebra. We derive a simulation tech…
Quantum crypto-economics models price risks in blockchain technology.
UKM framework optimizes VQCs, showing QCL performance is bounded.
This version withdrawn by arXiv administrators because the submitter did not have the right to agree to our license at the time of submission.
A quantum walk-based method for generating precise probability distributions efficiently.
We analyze the relationships between game theory and quantum mechanics and the extensions to statistical physics and information theory. We use certain quantization relationships to assign quantum states to the strategies of a player. These quantum states are contained in a density operator which describes the new quan…
Quantum control is valuable for various quantum technologies such as high-fidelity gates for universal quantum computing, adaptive quantum-enhanced metrology, and ultra-cold atom manipulation. Although supervised machine learning and reinforcement learning are widely used for optimizing control parameters in classical …
Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned topological models ha…
In this second part of the `essay on the completion of quantum theory' we define the {\em unitary setting of completed quantum mechanics}, by adding as intrinsic data to those from Part I (arXiv:1711.08643) the choice of a north pole N and south pole S in the geometric space. Then we explain that, in the unitary settin…
We propose a new cognitive framework for option price modelling, using quantum neural computation formalism. Briefly, when we apply a classical nonlinear neural-network learning to a linear quantum Schrödinger equation, as a result we get a nonlinear Schrödinger equation (NLS), performing as a quantum stochastic filter…
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum mechanical observables. In particular, previous studies constructed quantum grav…
Paper explores solving HJB equations using neural networks.
In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to define a dynamic-dependent metric tensor on the principal manifold, such that the…
The paper studies distributions and controllability in quantum mechanical systems.
Quantum Gaussian processes enable scalable quantum learning.
We present a broad agenda for meaningful banking regulation reform aiming the creation of evolutive competitive environment to maximize the effectiveness of international financial system through the introduction of fair competition process among the banks in free market capitalism. We assume that the international fin…
We introduce a differential geometric framework for describing families of quantum error-correcting codes and for understanding quantum fault tolerance. This work unifies the notion of topological fault tolerance with fault tolerance in other kinds of quantum error-correcting codes. In particular, we use fibre bundles …
In their activity, the traders approximate the rate of return by integer multiples of a minimal one. Therefore, it can be regarded as a quantized variable. On the other hand, there is the impossibility of observing the rate of return and its instantaneous forward time derivative, even if we consider it as a continuous …
Evolutionary strategy optimizes quantum circuit design and parameters.
Quantum UCB algorithm reduces reinforcement learning regret exponentially.
Quantum-enhanced metrology aims to estimate an unknown parameter such that the precision scales better than the shot-noise bound. Single-shot adaptive quantum-enhanced metrology (AQEM) is a promising approach that uses feedback to tweak the quantum process according to previous measurement outcomes. Techniques and form…
We present a finite-dimensional version of the quantum model for the stock market proposed in [C. Zhang and L. Huang, A quantum model for the stock market, Physica A 389(2010) 5769]. Our approach is an attempt to make this model consistent with the discrete nature of the stock price and is based on the mathematical for…
Quantum computing exploits basic quantum phenomena such as state superposition and entanglement to perform computations. The Quantum Approximate Optimization Algorithm (QAOA) is arguably one of the leading quantum algorithms that can outperform classical state-of-the-art methods in the near term. QAOA is a hybrid quant…
Optimizes trading trajectories for large portfolios quickly.
New algorithm improves efficiency of quantum system modeling.
We introduce a new tool for predicting the evolution of an option for the cases where at some specific time, there is a high-degree of uncertainty for identifying its price. We work over the special case where we can predict the evolution of the system by joining a single price for the Option, defined at some specific …
We use the theory of Berezin-Toeplitz operators of Ma and Marinescu to study the quantum Hamiltonian dynamics associated with classical Hamiltonian flows over closed prequantized symplectic manifolds in the context of geometric quantization of Kostant and Souriau. We express the associated evolution operators via paral…
This paper bridges Kahler geometry and quantum mechanics in lognormal statistical models.
New method combines Monte Carlo and tensor networks for solving complex equations.
Quantum MC simulations generate financial risk distributions efficiently.
Quantum theory is used to model secondary financial markets. Contrary to stochastic descriptions, the formalism emphasizes the importance of trading in determining the value of a security. All possible realizations of investors holding securities and cash is taken as the basis of the Hilbert space of market states. The…
Adaptive wave model for financial option pricing is proposed, as a high-complexity alternative to the standard Black--Scholes model. The new option-pricing model, representing a controlled Brownian motion, includes two wave-type approaches: nonlinear and quantum, both based on (adaptive form of) the Schrödinger equatio…
Quantum models generate financial time series with desired properties.