Krein space quantization and New Quantum Algorithms

TL;DR

This paper explores the use of Krein space quantization and ambient space formalism to develop new quantum algorithms for complex quantum systems, aiming to improve computational methods for ill-conditioned problems and non-unitary dynamics.

Contribution

It introduces a novel approach extending Krein space quantization to create quantum algorithms for challenging quantum systems, surpassing existing techniques.

Findings

Proposes a new quantum algorithm framework based on Krein space quantization.

Addresses underdetermined and ill-conditioned linear systems in quantum computation.

Potential to unify various quantum algorithms within a single framework.

Abstract

Krein space quantization and the ambient space formalism have been successfully applied to address challenges in quantum geometry (e.g., quantum gravity) and the axiomatic formulation of quantum Yang-Mills theory, including phenomena such as color confinement and the mass gap. Building on these advancements, we aim to extend these methods to develop novel quantum algorithms for quantum computation, particularly targeting underdetermined or ill-conditioned linear systems of equations, as well as quantum systems characterized by non-unitary evolution and open quantum dynamics. This approach represents a significant step beyond commonly used techniques, such as Quantum Singular Value Decomposition, Sz.-Nagy dilation, and Unitary Operator Decomposition. The proposed algorithm has the potential to establish a unified framework for quantum algorithms.