Brief Review: Simulation of Novel Systems Using Duality Quantum Algorithm

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