Quantum simulation of a general PT-symmetric two-level system

Miloslav Znojil

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

Chao Zheng, Tian Jin, Daili Li +3 more

Besides Hermitian systems, quantum simulation has become a strong tool to investigate non-Hermitian systems, such as PT-symmetric, anti-PT-symmetric, and pseudo-Hermitian systems. In this work, we theoretically investigate quantum simulation of an anti-P-pseudo-Hermitian two-level system in different dimensional Hilbert spaces. In an arbitrary phase, we find that six dimensions are the minimum to construct the anti-P-pseudo-Hermitian two-level subsystem, and it has a higher success probability than using eight dimensions. We find that the dimensions can be reduced further to four or two when the system is in the anti-PT-symmetric or Hermitian phase, respectively. Both qubit-qudit hybrid and pure-qubit systems are able to realize the simulation, enabling experimental implementations in the near future.

Minyi Huang, Asutosh Kumar, Junde Wu

Chao Zheng

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.

M. Kira, S. W. Koch