Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Area of Science:

• Quantum Physics
• Quantum Information Science

Background:

• Quantum simulation is a powerful method for studying complex quantum systems.
• Non-Hermitian systems, including PT-symmetric and pseudo-Hermitian systems, present unique challenges and opportunities.
• Investigating anti-parity-time (PT)-pseudo-Hermitian systems is crucial for understanding generalized quantum mechanics.

Purpose of the Study:

• To theoretically investigate the quantum simulation of an anti-PT-pseudo-Hermitian two-level system.
• To determine the minimum Hilbert space dimensions required for simulating such systems.
• To compare the success probabilities of simulations using different dimensional spaces.

Main Methods:

• Theoretical analysis of quantum simulation protocols.
• Exploration of anti-PT-pseudo-Hermitian two-level systems in varying Hilbert space dimensions.
• Investigation of system behavior in arbitrary, anti-PT-symmetric, and Hermitian phases.

Main Results:

• Six dimensions are identified as the minimum required for simulating an anti-PT-pseudo-Hermitian two-level system in an arbitrary phase.
• A six-dimensional simulation exhibits higher success probability compared to an eight-dimensional one.
• Dimensionality can be reduced to four or two dimensions for systems in the anti-PT-symmetric or Hermitian phases, respectively.
• Both qubit-qudit hybrid and pure-qubit systems can realize the simulation.

Conclusions:

• The study provides crucial insights into the dimensionality requirements for quantum simulation of non-Hermitian systems.
• Optimal Hilbert space dimensions are found to be phase-dependent, offering efficiency gains.
• The feasibility of experimental implementation is highlighted, paving the way for future research.