Abstract
The recently theoretical and experimental researches on {mathcal{PT}}-symmetric system have attracted unprecedented attention because of the various interesting features and potential applications in extending canonical quantum mechanics. However, as the counterpart of {mathcal{PT}}-symmetry, there are few experimental researches on the anti-{mathcal{PT}}-symmetric quantum system because of the challenges in simulating anti-{mathcal{PT}}-symmetry in experiment. Here, we propose an algorithm for simulating the generalized anti-{mathcal{PT}}-symmetric system in the quantum circuit model. Utilizing the algorithm, we demonstrated the quantum simulation of anti-{mathcal{PT}} system experimentally, and an oscillation of information flow is observed in a nuclear magnetic resonance quantum simulator. The experiment showed that the information could recover from the environment completely when the anti-{mathcal{PT}}-symmetry is broken, whereas no information can be retrieved in the symmetry-unbroken phase. Our work opens the gate for the practical quantum simulation and experimental investigation of universal anti-{mathcal{PT}}-symmetric system in a quantum computer.
Highlights
The limitation on the Hermiticity of Hamiltonian can ensure the reality in the spectrum of energy eigenvalues and the unitarity of the resulting time evolution
We experimentally show that the information flow oscillates back and forth between the environments and system in broken phase and the phenomenon of information backflow occurs, which indicates information flows from the environment back to the system and this does not happen in traditional Hermitian quantum mechanics[37,38]
To present the information retrieval in anti-PT -symmetric system, we identify the information flow by trace distance to measure the distinguishability between two quantum states
Summary
The limitation on the Hermiticity of Hamiltonian can ensure the reality in the spectrum of energy eigenvalues and the unitarity of the resulting time evolution. This work has inspired numerous theoretical and experimental studies[5,6,7,8,9,10,11,12,13,14,15,16,17] of the non-hermitian systems, including demonstrating novel properties of quantum systems[14,15] and extending fundamental quantum mechanics[16,17] Another important counterpart anti-PT -symmetry, which means the system Hamiltonian is anti-commutative with the joint PT operator fH; PT g 1⁄4 0, has attracted much research interest. We propose an algorithm for the simulation of generalized anti-PT -symmetric evolution with a circuit-based quantum computing system using a three-qubit scheme and the simulation scheme is based on decomposing the non-Hermitian
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