Quantum simulation of the pseudo-Hermitian Landau-Zener-Stückelberg-Majorana effect

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While the Hamiltonians used in standard quantum mechanics are Hermitian, it is also possible to extend the theory to non-Hermitian Hamiltonians. Particularly interesting are non-Hermitian Hamiltonians satisfying parity-time (PT) symmetry, or more generally pseudo-Hermiticity, since such non-Hermitian Hamiltonians can still exhibit real eigenvalues. In this article, we present a quantum simulation of the time-dependent non-Hermitian non-PT-symmetric Hamiltonian used in a pseudo-Hermitian extension of the Landau-Zener-Stückelberg-Majorana (LZSM) model. The simulation is implemented on a superconducting processor by using Naimark dilation to transform a non-Hermitian Hamiltonian for one qubit into a Hermitian Hamiltonian for a qubit and an ancilla; postselection on the ancilla state ensures that the qubit undergoes nonunitary time evolution corresponding to the original non-Hermitian Hamiltonian. We observe properties such as the dependence of transition probabilities on time and the replacement of conservation of total probability by other dynamical invariants in agreement with predictions based on a theoretical treatment of the pseudo-Hermitian LZSM system.

Original languageEnglish
Article number023246
Pages (from-to)1-10
Number of pages10
Issue number2
Publication statusPublished - Apr 2024
MoE publication typeA1 Journal article-refereed


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