arXiv subjects

Jack Morgan

Publications and source records attributed to Jack Morgan.

6 recordsLinked to original sources

arXiv2025

On the Classical Shadow Nonparametric Bootstrap

Classical shadows are an efficient method for constructing an approximate classical description of a quantum state using very few measurements. In the paper we propose to enhance classical shadow methods using bootstrap resampling methods. We apply nonparametric bootstrapping to assess the variability and accuracy of estimators by repeatedly sampling with replacement from the observed data, i.e. in our case the classical shadow measurements. We show that the bootstrap distributions are very different from the Gaussian approximations. Likewise, the theoretical error bounds are not tight compared to the bootstrap percentiles. Finally, we suggest using resampling tools to make risk assessments.

quant-ph↗

arXiv2025

Improving Quantum Recurrent Neural Networks with Amplitude Encoding

Quantum machine learning holds promise for advancing time series forecasting. The Quantum Recurrent Neural Network (QRNN), inspired by classical RNNs, encodes temporal data into quantum states that are periodically input into a quantum circuit. While prior QRNN work has predominantly used angle encoding, alternative encoding strategies like amplitude encoding remain underexplored due to their high computational complexity. In this paper, we evaluate and improve amplitude-based QRNNs using EnQode, a recently introduced method for approximate amplitude encoding. We propose a simple pre-processing technique that augments amplitude encoded inputs with their pre-normalized magnitudes, leading to improved generalization on two real world data sets. Additionally, we introduce a novel circuit architecture for the QRNN that is mathematically equivalent to the original model but achieves a substantial reduction in circuit depth. Together, these contributions demonstrate practical improvements to QRNN design in both model performance and quantum resource efficiency.

quant-ph↗

arXiv2025

On Quantum and Quantum-Inspired Maximum Likelihood Estimation and Filtering of Stochastic Volatility Models

Stochastic volatility models are the backbone of financial engineering. We study both continuous time diffusions as well as discrete time models. We propose two novel approaches to estimating stochastic volatility diffusions, one using Quantum-Inspired Classical Hidden Markov Models (HMM) and the other using Quantum Hidden Markov Models. In both cases we have approximate likelihood functions and filtering algorithms that are easy to compute. We show that the non-asymptotic bounds for the quantum HMM are tighter compared to those with classical model estimates.

quant-ph↗

arXiv2024

On Quantum Ambiguity and Potential Exponential Computational Speed-Ups to Solving Dynamic Asset Pricing Models

We formulate quantum computing solutions to a large class of dynamic nonlinear asset pricing models using algorithms, in theory exponentially more efficient than classical ones, which leverage the quantum properties of superposition and entanglement. The equilibrium asset pricing solution is a quantum state. We introduce quantum decision-theoretic foundations of ambiguity and model/parameter uncertainty to deal with model selection.

q-fin.PR↗

arXiv2024

An Enhanced Hybrid HHL Algorithm

We present a classical enhancement to improve the accuracy of the Hybrid variant (Hybrid HHL) of the quantum algorithm for solving linear systems of equations proposed by Harrow, Hassidim, and Lloyd (HHL). We achieve this by using higher precision quantum estimates of the eigenvalues relevant to the linear system, and a new classical step to guide the eigenvalue inversion part of Hybrid HHL. We show that eigenvalue estimates with just two extra bits of precision result in tighter error bounds for our Enhanced Hybrid HHL compared to HHL. Our enhancement reduces the error of Hybrid HHL by an average of 57 percent on an ideal quantum processor for a representative sample of 2x2 systems. On IBM Torino and IonQ Aria-1 hardware, we see that the error of Enhanced Hybrid HHL is on average 13 percent and 20 percent (respectively) less than that of HHL for the same set of systems.

quant-ph↗

arXiv2023

Quantum Computational Algorithms for Derivative Pricing and Credit Risk in a Regime Switching Economy

Quantum computers are not yet up to the task of providing computational advantages for practical stochastic diffusion models commonly used by financial analysts. In this paper we introduce a class of stochastic processes that are both realistic in terms of mimicking financial market risks as well as more amenable to potential quantum computational advantages. The type of models we study are based on a regime switching volatility model driven by a Markov chain with observable states. The basic model features a Geometric Brownian Motion with drift and volatility parameters determined by the finite states of a Markov chain. We study algorithms to estimate credit risk and option pricing on a gate-based quantum computer. These models bring us closer to realistic market settings, and therefore quantum computing closer the realm of practical applications.

quant-ph↗