arXiv subjects

Dinh-Long Vu

Publications and source records attributed to Dinh-Long Vu.

11 recordsLinked to original sources

arXiv2026

Quantum Weighted Moving Average for Predicting Limit Order Book Trends

Can quantum computers be useful for forecasting multivariate financial time series? In this work, we consider the problem of predicting price trends from limit order book (LOB) data. After identifying key components of classical models, we introduce the quantum weighted moving average (QWMA) model. The two main building blocks are, first, classically preprocessing via normalization of both feature and temporal dimensions and, second, a linear combination of unitaries-based layer for unitarily-embedded classical data. The models are evaluated on the FI-2010 benchmark dataset and a second dataset of China A-share stocks. While we do not present evidence of quantum advantage, the combined classical-quantum model demonstrates performances close to the best classical models. The quantum part of the model is expressive enough to focus on the most predictive parts of the time series. Several specializations of the QWMA model are considered, in particular a variant related to the widely-used exponential moving average (EMA). We give consideration to the limitations of the methods and the datasets.

quant-ph↗

arXiv2026

Quantum Box-Muller Transform

The Box-Muller transform is a widely used method to generate Gaussian samples from uniform samples. Quantum amplitude encoding methods encode the multi-variate normal distribution in the amplitudes of a quantum state. This work presents the Quantum Box-Muller transform which creates a superposition of binary-encoded grid points representing the multi-variate normal distribution. The gate complexity of our method depends on quantum arithmetic operations and, using a specific set of known implementations, the complexity is quadratic in the number of qubits. We apply our method to Monte-Carlo integration, in particular to the estimation of the expectation value of a function of Gaussian random variables. Our method implies that the state preparation circuit used multiple times in amplitude estimation requires only quantum arithmetic circuits for the grid points and the function, in addition to a single controlled rotation. We show how to provide the expectation value estimate with an error that is exponentially small in the number of qubits, similar to the amplitude-encoding setting with error-free encoding.

quant-ph↗

arXiv2025

Quantum Advantage for Multi-option Portfolio Pricing and Valuation Adjustments

A critical problem in the financial world deals with the management of risk, from regulatory risk to portfolio risk. Many such problems involve the analysis of securities modelled by complex dynamics that cannot be captured analytically, and hence rely on numerical techniques that simulate the stochastic nature of the underlying variables. These techniques may be computationally difficult or demanding. Hence, improving these methods offers a variety of opportunities for quantum algorithms. In this work, we study the problem of Credit Valuation Adjustments (CVAs) which has significant importance in the valuation of derivative portfolios. As a variant, we also consider the problem of pricing a portfolio of many different financial options. We propose quantum algorithms that accelerate statistical sampling processes to approximate the price of the multi-option portfolio and the CVA under different measures of dispersion. Technically, our algorithms are based on enhancing the quantum Monte Carlo (QMC) algorithms by Montanaro with an unbiased version of quantum amplitude estimation. We analyse the conditions under which we may employ these techniques and demonstrate the application of QMC techniques on CVA approximation when particular bounds for the variance of CVA are known.

quant-ph↗

arXiv2024

Low depth amplitude estimation without really trying

Standard quantum amplitude estimation algorithms provide quadratic speedup to Monte-Carlo simulations but require a circuit depth that scales as inverse of the estimation error. In view of the shallow depth in near-term devices, the precision achieved by these algorithms would be low. In this paper we bypass this limitation by performing the classical Monte-Carlo method on the quantum algorithm itself, achieving a higher than classical precision using low-depth circuits. We require the quantum algorithm to be weakly biased in order to avoid error accumulation during this process. Our method is parallel and can be as weakly biased as the constituent algorithm in some cases.

quant-ph↗

arXiv2022

Integrable domain walls in ABJM theory

One-point functions of local operators are studied, at weak and strong coupling, for the ABJM theory in the presence of a 1/2 BPS domain wall. In the underlying quantum spin chain the domain wall is represented by a boundary state which we show is integrable yielding a compact determinant formula for one-point functions of generic operators.

hep-th↗

arXiv2020

A diagrammatic approach towards the thermodynamics of integrable systems

We propose an exact summation method to compute thermodynamic observables in integrable quantum field theories. The key idea is to use the matrix-tree theorem to write the Gaudin determinants that appear in the cluster expansion as a sum over graphs. For theories with a diagonal S-matrix, this method is more powerful than the standard Thermodynamic Bethe Ansatz (TBA) technique as it is exact to all orders of powers in inverse volume. We have obtained using this method the TBA equation, the excited state energies in finite volume, the Leclair-Mussardo formula for one point functions, the finite-temperature boundary entropy and cumulants of conserved charges in Generalized Gibbs Ensembles. Moreover, the graph expansion can also be regarded as an alternative to algebraic manipulations involving Gaudin determinants. We have applied this idea to derive the equations of state and other transport properties in Generalized Hydrodynamics. For theories with a non-diagonal S-matrix, the description of a complete set of states is more involved and it is not known how a cluster expansion can be implemented. It is nevertheless possible to apply the direct summation method in reverse and interpret known TBA equations with complex strings in terms of diagrams.

hep-th↗

arXiv2019

Cumulants of conserved charges in GGE and cumulants of total transport in GHD: exact summation of matrix elements?

We obtain the cumulants of conserved charges in Generalized Gibbs Ensemble (GGE) by a direct summation of their finite-particle matrix elements. The Gaudin determinant that describes the norm of Bethe states is written as a sum over forests by virtue of the matrix-tree theorem. The aforementioned cumulants are then given by a sum over tree-diagrams whose Feynman rules involve simple Thermodynamic Bethe Ansatz (TBA) quantities. The internal vertices of these diagrams have the interpretation of virtual particles that carry anomalous corrections to bare charges. Our derivation follows closely the spirit of recent works [1,2]. We also conjecture that the cumulants of total transport in Generalized Hydrodynamics (GHD) are given by the same diagrams up to minor modifications. These cumulants play a central role in large deviation theory and were obtained in [3] using linear fluctuating hydrodynamics at Euler scale. We match our conjecture with the result of [3] up to the fourth cumulant. This highly non-trivial matching provides a strong support for our conjecture.

cond-mat.stat-mech↗

arXiv2019

Boundary TBA, trees and loops

We derive a graph expansion for the thermal partition function of solvable two-dimensional models with boundaries. This expansion of the integration measure over the virtual particles winding around the time cycle is obtained with the help of the matrix-tree theorem. The free energy is a sum over all connected graphs, which can be either trees or trees with one loop. The generating function for the connected trees satisfies a non-linear integral equation, which is equivalent to the TBA equation. The sum over connected graphs gives the bulk free energy as well as the exact g-functions for the two boundaries. We reproduced the integral formula conjectured by Dorey, Fioravanti, Rim and Tateo, and proved subsequently by Pozsgay. The method is easily extended to the case of non-diagonal bulk scattering and diagonal reflection matrices. Our method can be extended to the case of non-diagonal bulk scattering and diagonal reflection matrices with proper regularization.

hep-th↗

arXiv2019

Boundary entropy of integrable perturbed $SU(2)_k$ WZNW

We apply the recently developped analytical methods for computing the boundary entropy, or the g-function, in integrable theories with non-diagonal scattering. We consider the particular case of the current-perturbed $SU(2)_k$ WZNW model with boundary and compute the boundary entropy for a specific boundary condition. The main problem we encounter is that in case of non-diagonal scattering the boundary entropy is infinite. We show that this infinity can be cured by a subtraction. The difference of the boundary entropies in the UV and in the IR limits is finite, and matches the known g-functions for the unperturbed $SU(2)_k$ WZNW model for even values of the level.

hep-th↗

arXiv2019

Equations of state in generalized hydrodynamics

We, for the first time, report a first-principle proof of the equations of state used in the hydrodynamic theory for integrable systems, termed generalized hydrodynamics (GHD). The proof makes full use of the graph theoretic approach to Thermodynamic Bethe ansatz (TBA) that was proposed recently. This approach is purely combinatorial and relies only on common structures shared among Bethe solvable models, suggesting universal applicability of the method. To illustrate the idea of the proof, we focus on relativistic integrable quantum field theories with diagonal scatterings and without bound states such as strings.

cond-mat.stat-mech↗

arXiv2018

TBA and tree expansion

We propose an alternative, statistical, derivation of the Thermodynamic Bethe Ansatz based on the tree expansion of the Gaudin determinant. We illustrate the method on the simplest example of a theory with diagonal scattering and no bound states. We reproduce the expression for the free energy density and the finite size corrections to the energy of an excited state as well as the LeClair-Mussardo series for the one-point function for local operators.

hep-th↗