arXiv subjects

Mohammad Abedi

Publications and source records attributed to Mohammad Abedi.

8 recordsLinked to original sources

arXiv2026

Geometric inflation of deviations challenges neural quantum states in dynamics of quantum Ising models

Neural quantum states (NQS) have emerged as a powerful framework for simulating non-equilibrium dynamics in strongly correlated quantum systems, offering scalable variational representations of highly entangled states. Yet, accurate NQS simulations have been found to be surprisingly challenging in some physical regimes of limited complexity. Here, we address paradigmatic quench dynamics of a one-dimensional quantum Ising model as a controlled benchmark. Through supervised state reconstruction we establish substantially tighter empirical upper bounds on the required parameter count than previous estimates, ruling out representational limitations as the key obstruction. Instead, we uncover a geometric inflation of small deviations as a hitherto overlooked challenge for accurate solutions of the infinitesimal time-dependent variational principle (TDVP): the dynamical rotation of the kernel of the quantum geometric tensor (QGT) can suddenly lend physical significance to previously irrelevant parameter deviations. The stability of matrix product state solutions of the same TDVP suggests that the non-linearity of the neural network ansatz is the origin of the sensitivity. These results identify QGT-null-space rotation as a geometric diagnostic of sensitive NQS dynamics and as a concrete target for improving TDVP algorithms

quant-ph↗

arXiv2026

Entropic Dynamics of Jump-Diffusion Option Pricing

Standard models of stock price dynamics and option valuation usually begin by postulating stochastic processes. This paper develops an entropic inference framework that derives these processes from information constraints. The key symmetry is that markets reward returns rather than price levels, which selects log price as the dynamical variable. Price changes are represented by two channels. The continuous channel carries constraints of continuity and directionality. The jump channel carries the arrival rate and the first two moments of jump size. Since these constraints apply to disjoint parts of the microstate, the channels factorize. The resulting dynamics is the Merton jump diffusion, with Geometric Brownian Motion as the no jump limit. The log price density satisfies the Kolmogorov Feller equation, whose no jump limit is the Fokker Planck equation. The same inferential principle, with no arbitrage imposed through the mean log return, selects the Esscher transform from the many martingale measures available in an incomplete market. The option price then satisfies Mertons partial integro differential equation, and the risk neutral mixture of lognormal distributions generates the implied volatility smile. The Black Scholes results are recovered when jumps vanish. What changes from one model to another is not the inference, but the information supplied to it.

q-fin.PR↗

arXiv2025

Reinforcement learning entangling operations on spin qubits

High-fidelity control of one- and two-qubit gates past the error correction threshold is an essential ingredient for scalable quantum computing. We present a reinforcement learning (RL) approach to find entangling protocols for semiconductor-based singlet-triplet qubits in a double quantum dot. Despite the presence of realistically modelled experimental constraints, such as various noise contributions and finite rise-time effects, we demonstrate that an RL agent can yield performative protocols, while avoiding the model-biases of traditional gradient-based methods. We optimise our RL approach for different regimes and tasks, including training from simulated process tomography reconstruction of unitary gates, and investigate the nuances of RL agent design.

quant-ph↗

arXiv2019

Entropic Dynamics of Exchange Rates and Options

An Entropic Dynamics of exchange rates is laid down to model the dynamics of foreign exchange rates, FX, and European Options on FX. The main objective is to represent an alternative framework to model dynamics. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. Entropic Dynamics is an application of entropic inference, which is equipped with the entropic notion of time to model dynamics. The scale invariance is a symmetry of the dynamics of exchange rates, which is manifested in our formalism. To make the formalism manifestly invariant under this symmetry, we arrive at choosing the logarithm of the exchange rate as the proper variable to model. By taking into account the relevant information about the exchange rates, we derive the Geometric Brownian Motion, GBM, of the exchange rate, which is manifestly invariant under the scale transformation. Securities should be valued such that there is no arbitrage opportunity. To this end, we derive a risk-neutral measure to value European Options on FX. The resulting model is the celebrated Garman-Kohlhagen model.

q-fin.PR↗

arXiv2019

Entropic Dynamics of Stocks and European Options

We develop an entropic framework to model the dynamics of stocks and European Options. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. The objective of the paper is to lay down an alternative framework for modeling dynamics. An important information about the dynamics of a stock's price is scale invariance. By imposing the scale invariant symmetry, we arrive at choosing the logarithm of the stock's price as the proper variable to model. The dynamics of stock log price is derived using two pieces of information, the continuity of motion and the directionality constraint. The resulting model is the same as the Geometric Brownian Motion, GBM, of the stock price which is manifestly scale invariant. Furthermore, we come up with the dynamics of probability density function, which is a Fokker--Planck equation. Next, we extend the model to value the European Options on a stock. Derivative securities ought to be prices such that there is no arbitrage. To ensure the no-arbitrage pricing, we derive the risk-neutral measure by incorporating the risk-neutral information. Consequently, the Black--Scholes model and the Black--Scholes-Merton differential equation are derived.

q-fin.PR↗

arXiv2019

Entropic Dynamics: Reconstructing Quantum Field Theory in Curved Space-time

The Entropic Dynamics reconstruction of quantum mechanics is extended to quantum field theory in curved space-time. The Entropic Dynamics framework, which derives quantum theory as an application of the method of maximum entropy, is combined with the covariant methods of Dirac, Hojman, Kuchař, and Teitelboim, which they used to develop a framework for classical covariant Hamiltonian theories. The goal is to formulate an information-based alternative to current approaches based on algebraic quantum field theory. One key ingredient is the adoption of a local notion of entropic time in which instants are defined on curved three-dimensional surfaces and time evolution consists of the accumulation of changes induced by local deformations of these surfaces. The resulting dynamics is a non-dissipative diffusion that is constrained by the requirements of foliation invariance and incorporates the necessary local quantum potentials. As applications of the formalism we derive the Ehrenfest relations for fields in curved-spacetime and briefly discuss the nature of divergences in quantum field theory.

gr-qc↗

arXiv2018

A Covariant Approach to Entropic Dynamics

Entropic Dynamics (ED) is a framework for constructing dynamical theories of inference using the tools of inductive reasoning. A central feature of the ED framework is the special focus placed on time. In previous work a global entropic time was used to derive a quantum theory of relativistic scalar fields. This theory, however, suffered from a lack of explicit or manifest Lorentz symmetry. In this paper we explore an alternative formulation in which the relativistic aspects of the theory are manifest. The approach we pursue here is inspired by the works of Dirac, Kuchar, and Teitelboim in their development of covariant Hamiltonian methods. The key ingredient here is the adoption of a local notion of time, which we call entropic time. This construction allows the expression of arbitrary notion of simultaneity, in accord with relativity. In order to ensure, however, that this local time dynamics is compatible with the background spacetime we must impose a set of Poisson bracket constraints; these constraints themselves result from requiring the dynamcics to be path independent, in the sense of Teitelboim and Kuchar.

gr-qc↗

arXiv2016

Entropic Dynamics on Curved Spaces

Entropic dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. Entropic dynamics on flat spaces has been extensively studied. The objective of this paper is to extend the entropic dynamics of $N$ particles to curved spaces. The important new feature is that the displacement of a particle does not transform like a vector because fluctuations can be large enough to feel the effects of curvature. The final result is a modified Schrödinger equation in which the usual Laplacian is replaced by the Laplace-Beltrami operator.

quant-ph↗