Emulation of Self-Consistent Non-Hermitian Quantum Formalisms

TL;DR

This paper introduces operator dilation schemes enabling the physical simulation of self-consistent non-Hermitian quantum mechanics, demonstrated through digital quantum simulators with experimental evidence in a qubit.

Contribution

It proposes novel operator dilation methods to realize non-Hermitian quantum formalism in physical systems, bridging theory and experimental implementation.

Findings

First experimental evidence of dynamical metric in a qubit

Demonstration of non-Hermitian formalism via quantum simulation

New paradigm for simulating non-Hermitian quantum systems

Abstract

Standard quantum mechanics predicts the non-conservation of state norms and probability when the fundamental requirement of the Hermiticity of the Hamiltonian is relaxed. Biorthogonal quantum mechanics, or the more general metric formalism, provides a rigorous formulation of non-Hermitian quantum mechanics wherein norms and probabilities are conserved. The key feature is that the Hilbert space is endowed with a non-trivial dynamical metric. Beyond theoretical considerations, the physical implementation of the metric formalism remains unaddressed. In this work, we propose novel operator dilation schemes, which show that the self-consistent non-Hermitian quantum mechanics can be accessed in physical platforms via an embedding in closed Hermitian systems. Using digital quantum simulators, we present a proof of principle and the first experimental evidence for the dynamical metric engendered by non-Hermiticity in a qubit. Our work ushers in a new paradigm in the quantum simulation of non-Hermitian systems.