Quantum simulation of τ-anti-pseudo-Hermitian two-level systems

doi:10.1088/1674-1056/ac8738

摘要/Abstract

摘要： Different from the Hermitian case, non-Hermitian (NH) systems have novel properties and strongly relate to open and dissipative quantum systems. In this work, we investigate how to simulate τ-anti-pseudo-Hermitian systems in a Hermitian quantum device using linear combinations of unitaries and duality quantum algorithm. Specifying the τ to time-reversal (T) and parity-time-reversal (PT) operators, we construct the two NH two-level systems, design quantum circuits including three qubits, and decide the quantum gates explicitly in detail. We also calculate the success probabilities of the simulation. Experimental implementation can be expected in small quantum simulator.

关键词: quantum simulation, linear combination of unitaries, non-Hermitian, anti-pseudo-Hermitian

Abstract: Different from the Hermitian case, non-Hermitian (NH) systems have novel properties and strongly relate to open and dissipative quantum systems. In this work, we investigate how to simulate τ-anti-pseudo-Hermitian systems in a Hermitian quantum device using linear combinations of unitaries and duality quantum algorithm. Specifying the τ to time-reversal (T) and parity-time-reversal (PT) operators, we construct the two NH two-level systems, design quantum circuits including three qubits, and decide the quantum gates explicitly in detail. We also calculate the success probabilities of the simulation. Experimental implementation can be expected in small quantum simulator.

Key words: quantum simulation, linear combination of unitaries, non-Hermitian, anti-pseudo-Hermitian

中图分类号: (Quantum algorithms, protocols, and simulations)

03.67.Ac

03.65.Yz (Decoherence; open systems; quantum statistical methods) 03.65.Aa (Quantum systems with finite Hilbert space) 11.30.Er (Charge conjugation, parity, time reversal, and other discrete symmetries)

Chao Zheng(郑超). Quantum simulation of τ-anti-pseudo-Hermitian two-level systems[J]. 中国物理B, 2022, 31(10): 100301-100301.

Chao Zheng(郑超). Quantum simulation of τ-anti-pseudo-Hermitian two-level systems[J]. Chin. Phys. B, 2022, 31(10): 100301-100301.

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