Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Advanced Materials Letters

Brief Review: Simulation of Novel Systems Using Duality Quantum Algorithm

Chao Zheng

Published Sep 1, 2019• 1 citation
Publisher

Abstract

In this article, we review the recent works of quantum simulation of novel systems briefly, the parity-time-reversal-symmetric (PT-symmetric) quantum system and the Yang-Baxter-equation (YBE) system, using duality quantum algorithm. Duality quantum algorithm studies the linear combinations of unitary operators, making it possible to simulate non-unitary evolutions of novel quantum systems. A PT-symmetric quantum system is a typical non-Hermitian system of which the evolution is not unitary and cannot be simulated directly by a conventional quantum computer. A recent work by C. Zheng has established a theory to simulate a general PT-symmetric two level system by duality quantum computing. The other typical example is the YBE quantum systems, of which the evolutions can be both unitary and non-unitary. C. Zheng and S. J. Wei described a theory that the two hand sides of the YBE can be simulated efficiently by the duality quantum algorithm in their recent research. Perspectives of future applications are expected at last. Copyright © VBRI Press.

DOI
10.5185/amlett.2019.9908

Related papers

Duality quantum simulation of a general parity-time-symmetric two-level system

Chao Zheng

\n\nThe evolution of a two-level quantum system with a general parity-time-reversal-invariant Hamiltonian is reinterpreted as a subsystem in a four-dimensional Hilbert space, which makes it possible to simulate any two-level parity-time-symmetric (PT-symmetric) quantum system using a conventional quantum mechanics system. We studied the ability to simulate and investigate novel quantum systems and phenomena using a nowadays-available Hermitian quantum computer or a duality quantum computer. The quantum circuits are given for a qubit and two qudit systems, and they would be useful for experimental implementation and applications in the future.\n

Europhysics Letters (EPL)•Sep 17, 2018•32 citations

Quantum simulation of PT-arbitrary-phase–symmetric systems

Chao Zheng

Abstract Parity-time-reversal (PT) symmetric quantum mechanics promotes the increasing research interest of non-Hermitian (NH) systems for the theoretical value, novel properties, and links to open and dissipative systems in various areas. Recently, anti-PT–symmetric systems and their featured properties have started to be investigated. In this work, we develop the PT and anti-PT symmetry to PT-arbitrary-phase symmetry (or PT- φ symmetry) for the first time, being analogous to bosons, fermions and anyons. It can also be seen as a complex extension of the PT symmetry, unifying the PT and anti-PT symmetries and having intermediate properties between them. Many of the established concepts and mathematics in the PT-symmetric system are still compatible. We mainly investigate quantum simulation of this novel NH system in two dimensions in detail and discuss for higher-dimensional cases in general using the linear combinations of unitaries in the scheme of duality quantum computing, enabling implementations and experimental investigations of novel properties on both small quantum devices and near-term quantum computers.

Europhysics Letters (EPL)•Nov 1, 2021•17 citations

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

Chao Zheng

Non-Hermitian (NH) quantum theory has been attracting increased research interest due to its featured properties, novel phenomena, and links to open and dissipative systems. Typical NH systems include PT-symmetric systems, pseudo-Hermitian systems, and their anti-symmetric counterparts. In this work, we generalize the pseudo-Hermitian systems to their complex counterparts, which we call pseudo-Hermitian-φ-symmetric systems. This complex extension adds an extra degree of freedom to the original symmetry. On the one hand, it enlarges the non-Hermitian class relevant to pseudo-Hermiticity. On the other hand, the conventional pseudo-Hermitian systems can be understood better as a subgroup of this wider class. The well-defined inner product and pseudo-inner product are still valid. Since quantum simulation provides a strong method to investigate NH systems, we mainly investigate how to simulate this novel system in a Hermitian system using the linear combination of unitaries in the scheme of duality quantum computing. We illustrate in detail how to simulate a general P-pseudo-Hermitian-φ-symmetric two-level system. Duality quantum algorithms have been recently successfully applied to similar types of simulations, so we look forward to the implementation of available quantum devices.

Entropy•Jun 24, 2022•8 citations

Duality quantum simulation of a generalized anti-PT-symmetric two-level system

Chao Zheng

\n\nIn this work, quantum simulation of the evolution of a two-level quantum system with a generalized anti-PT(APT)-symmetric Hamiltonian in arbitrary phase is investigated theoretically. The evolution is reinterpreted as a subsystem in a Hilbert space of higher dimensions, enabling it to construct any two-dimensional APT-symmetric Hamiltonian in a Hermitian quantum system. In some special phases, a two-qubit quantum computer is able to achieve the quantum simulation. However, a minimum six-dimensional Hilbert space is necessary for a general case, indicating that a qutrit is needed as an ancillary. We show how to realize the simulation process in a qubit-qutrit hybrid system using the duality quantum algorithm. We also give the flow chart and quantum circuit for a quantum computer of three qubits to realize the quantum simulation. Therefore, experimental realizations and applications can be expected in the future.\n

Europhysics Letters (EPL)•Jun 18, 2019•19 citations

A Qubit Algorithm for Simulating the Nonlinear Schroedinger Equation

Connor Simpson

Recent work in mathematical physics and nonlinear optics has shown that Hamiltonians that are non-Hermitian but still symmetric under parity and time reversal can describe eigenstates of a system with real eigenvalues. Other research has also showed that the nonlinear Schrodinger equation can be generalized to describe PT-symmetric systems, which generates novel solutions not described by its Hermitian equivalent. The Hermitian form of the nonlinear Schroedinger equation can also be extended to describe a particular case of the general PT-symmetric NLS, suggesting a connection between the two. I attempted to generate a unitary operator that will be useful for unitary quantum algorithms describing a coupled set of nonlinear Schroedinger equations and the PT-symmetric version of the NLS.

•Jan 1, 2019•0 citations

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

Chao Zheng

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.

Chinese Physics B•Aug 5, 2022•5 citations
In this article, we review the recent works of quantum simulation of novel systems briefly, the parity-time-reversal-symmetric (PT-symmetric) quantum system and the Yang-Baxter-equation (YBE) system, using duality quantum algorithm. Duality quantum algorithm studies the linear combinations of unitary operators, making it possible to simulate non-unitary evolutions of novel quantum systems. A PT-symmetric quantum system is a typical non-Hermitian system of which the evolution is not unitary and cannot be simulated directly by a conventional quantum computer. A recent work by C. Zheng has established a theory to simulate a general PT-symmetric two level system by duality quantum computing. The other typical example is the YBE quantum systems, of which the evolutions can be both unitary and non-unitary. C. Zheng and S. J. Wei described a theory that the two hand sides of the YBE can be simulated efficiently by the duality quantum algorithm in their recent research. Perspectives of future applications are expected at last. Copyright © VBRI Press.
\n\nThe evolution of a two-level quantum system with a general parity-time-reversal-invariant Hamiltonian is reinterpreted as a subsystem in a four-dimensional Hilbert space, which makes it possible to simulate any two-level parity-time-symmetric (PT-symmetric) quantum system using a conventional quantum mechanics system. We studied the ability to simulate and investigate novel quantum systems and phenomena using a nowadays-available Hermitian quantum computer or a duality quantum computer. The quantum circuits are given for a qubit and two qudit systems, and they would be useful for experimental implementation and applications in the future.\n
Abstract Parity-time-reversal (PT) symmetric quantum mechanics promotes the increasing research interest of non-Hermitian (NH) systems for the theoretical value, novel properties, and links to open and dissipative systems in various areas. Recently, anti-PT–symmetric systems and their featured properties have started to be investigated. In this work, we develop the PT and anti-PT symmetry to PT-arbitrary-phase symmetry (or PT- φ symmetry) for the first time, being analogous to bosons, fermions and anyons. It can also be seen as a complex extension of the PT symmetry, unifying the PT and anti-PT symmetries and having intermediate properties between them. Many of the established concepts and mathematics in the PT-symmetric system are still compatible. We mainly investigate quantum simulation of this novel NH system in two dimensions in detail and discuss for higher-dimensional cases in general using the linear combinations of unitaries in the scheme of duality quantum computing, enabling implementations and experimental investigations of novel properties on both small quantum devices and near-term quantum computers.
Non-Hermitian (NH) quantum theory has been attracting increased research interest due to its featured properties, novel phenomena, and links to open and dissipative systems. Typical NH systems include PT-symmetric systems, pseudo-Hermitian systems, and their anti-symmetric counterparts. In this work, we generalize the pseudo-Hermitian systems to their complex counterparts, which we call pseudo-Hermitian-φ-symmetric systems. This complex extension adds an extra degree of freedom to the original symmetry. On the one hand, it enlarges the non-Hermitian class relevant to pseudo-Hermiticity. On the other hand, the conventional pseudo-Hermitian systems can be understood better as a subgroup of this wider class. The well-defined inner product and pseudo-inner product are still valid. Since quantum simulation provides a strong method to investigate NH systems, we mainly investigate how to simulate this novel system in a Hermitian system using the linear combination of unitaries in the scheme of duality quantum computing. We illustrate in detail how to simulate a general P-pseudo-Hermitian-φ-symmetric two-level system. Duality quantum algorithms have been recently successfully applied to similar types of simulations, so we look forward to the implementation of available quantum devices.
\n\nIn this work, quantum simulation of the evolution of a two-level quantum system with a generalized anti-PT(APT)-symmetric Hamiltonian in arbitrary phase is investigated theoretically. The evolution is reinterpreted as a subsystem in a Hilbert space of higher dimensions, enabling it to construct any two-dimensional APT-symmetric Hamiltonian in a Hermitian quantum system. In some special phases, a two-qubit quantum computer is able to achieve the quantum simulation. However, a minimum six-dimensional Hilbert space is necessary for a general case, indicating that a qutrit is needed as an ancillary. We show how to realize the simulation process in a qubit-qutrit hybrid system using the duality quantum algorithm. We also give the flow chart and quantum circuit for a quantum computer of three qubits to realize the quantum simulation. Therefore, experimental realizations and applications can be expected in the future.\n
Recent work in mathematical physics and nonlinear optics has shown that Hamiltonians that are non-Hermitian but still symmetric under parity and time reversal can describe eigenstates of a system with real eigenvalues. Other research has also showed that the nonlinear Schrodinger equation can be generalized to describe PT-symmetric systems, which generates novel solutions not described by its Hermitian equivalent. The Hermitian form of the nonlinear Schroedinger equation can also be extended to describe a particular case of the general PT-symmetric NLS, suggesting a connection between the two. I attempted to generate a unitary operator that will be useful for unitary quantum algorithms describing a coupled set of nonlinear Schroedinger equations and the PT-symmetric version of the NLS.
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.