Holonomic gates in pseudo-Hermitian quantum systems

Tian

et al. 2020

Entropy

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.

Section: Introductionmentioning

confidence: 99%

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

Tian

et al. 2020

Entropy

“…E.g., abnormal energy-difference conserving dynamics 63 , a breakdown of adiabaticity 68 , the information flow changing the direction when passing the EPs 18 , etc. Quantum simulations of anti-symmetric counterparts are also investigated 16 , 17 , 19 .…”

Section: Introductionmentioning

confidence: 99%

Distinguish between typical non-Hermitian quantum systems by entropy dynamics

2022

Sci Rep

Non-Hermitian (NH) quantum systems attract research interest increasingly in recent years, among which the PT-symmetric, P-pseudo-Hermitian and their anti-symmetric counterpart systems are focused much more. In this work, we extend the usage of entropy to distinguish time-evolutions of different classes and phases of typical NH-systems. In detail, we investigate the entropy dynamics of two-level NH-systems after quantum decoherence induced by single-qubit projective measurements, finding that it depends on both the initial states and the selection of the computational bases of the measurements. In a general case, we show how to distinguish all the eight phases of the above NH-systems step by step, in which process three different initial states are necessary if the basis of measurement is fixed. We propose how the distinguishing process is realized in quantum simulation, in which quantum tomography is not needed. Our investigations can be applied to judge phase transitions of non-Hermitian systems.

“…P-pseudo-Hermiticitian Hamiltonians were found to have real spectra in some conditions [ 29 , 30 , 31 , 32 , 33 , 34 ], while a necessary and sufficient condition is given for the reality of the spectrum of NH Hamiltonians admitting a complete set of biorthonormal eigenvectors in [ 31 ]. Properties of pseudo-Hermitian systems and their relationships with PT-symmetric systems are often investigated and discussed [ 35 , 36 , 37 , 38 , 39 , 40 , 41 ]. In this work, we extend pseudo-Hermitian Hamiltonians to the complex domain for the first time by introducing a phase factor

.…”

Section: Introductionmentioning

confidence: 99%

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

2022

Entropy

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.