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Quantum Simulation of Pseudo-Hermitian-φ-Symmetric Two-Level Systems.

¹Department of Physics, College of Science, North China University of Technology, Beijing 100144, China.

Entropy (Basel, Switzerland)

|July 27, 2022

Summary

We introduce pseudo-Hermitian-φ-symmetric systems, a complex extension of pseudo-Hermitian systems, broadening the scope of non-Hermitian quantum theory. Quantum simulations using duality quantum computing are proposed for these novel systems.

Keywords:

linear combination of unitaries non-Hermitian pseudo-Hermitian quantum simulation

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Area of Science:

Quantum Physics
Theoretical Physics
Quantum Information Science

Background:

Non-Hermitian (NH) quantum theory is gaining traction for its unique properties and applications in open/dissipative systems.
Existing NH systems include PT-symmetric and pseudo-Hermitian systems.
These systems are crucial for understanding complex quantum phenomena.

Purpose of the Study:

To generalize pseudo-Hermitian systems to a complex framework, termed pseudo-Hermitian-φ-symmetric systems.
To explore the implications of this complex extension on the non-Hermitian class.
To propose quantum simulation methods for these novel systems within a Hermitian framework.

Main Methods:

Generalization of pseudo-Hermitian systems to pseudo-Hermitian-φ-symmetric systems.
Investigation of quantum simulation techniques using linear combination of unitaries.
Application of duality quantum computing schemes.

Main Results:

The introduction of pseudo-Hermitian-φ-symmetric systems expands the class of NH systems.
Conventional pseudo-Hermitian systems are identified as a subgroup of this broader class.
A detailed simulation protocol for a general P-pseudo-Hermitian-φ-symmetric two-level system is presented.

Conclusions:

Pseudo-Hermitian-φ-symmetric systems offer a richer framework for studying non-Hermitian quantum mechanics.
Duality quantum computing provides a viable approach for simulating these complex systems.
Future implementation on quantum devices is anticipated.