gqsp-hermitian-embedding-pricing

name	gqsp-hermitian-embedding-pricing
description	Generalised Quantum Signal Processing with Hermitian block embedding for solving 2D Black Scholes equation. Based on arXiv:2606.00458 — quantum linear algebra for option pricing.
category	quantum
trigger_words	quantum signal processing, GQSP, hermitian block embedding, Black Scholes, option pricing, non-Hermitian operator
arxiv_id	2606.00458v1

GQSP with Hermitian Block Embedding for Financial PDEs

Overview

Methodology for applying Generalised Quantum Signal Processing (GQSP) to non-Hermitian matrix problems via Hermitian block embedding, demonstrated on the 2D Black Scholes equation for financial derivatives pricing.

Problem

• Black Scholes equation → finite difference discretisation → non-Hermitian time step matrix
• GQSP requires Hermitian or unitary form for polynomial transformations
• Direct application to non-Hermitian operators impossible

Solution: Hermitian Block Embedding

• Embed non-Hermitian matrix into larger Hermitian block structure
• Enables GQSP polynomial transformations on the embedded form
• Matrix inverse (for pricing) computed via polynomial approximation

Results

• Two-asset European call options pricing
• Close agreement with classical backward Euler finite difference
• Accurately captures dynamics of original non-Hermitian operator

Workflow

1. Discretise PDE → obtain non-Hermitian matrix A
2. Construct Hermitian block embedding H of A
3. Apply GQSP polynomial transformation to H
4. Extract solution from embedded result
5. Validate against classical methods

When to Use

• Quantum algorithms for financial PDEs
• Non-Hermitian operator processing via GQSP
• Multi-asset option pricing
• Matrix function evaluation for non-normal matrices