Abstract Parity-time-reversal (PT) symmetric quantum mechanics promotes the increasing research interest of non-Hermitian (NH) systems for the theoretical value, novel properties, and links to open and dissipative systems in various areas. Recently, anti-PT–symmetric systems and their featured properties have started to be investigated. In this work, we develop the PT and anti-PT symmetry to PT-arbitrary-phase symmetry (or PT- φ symmetry) for the first time, being analogous to bosons, fermions and anyons. It can also be seen as a complex extension of the PT symmetry, unifying the PT and anti-PT symmetries and having intermediate properties between them. Many of the established concepts and mathematics in the PT-symmetric system are still compatible. We mainly investigate quantum simulation of this novel NH system in two dimensions in detail and discuss for higher-dimensional cases in general using the linear combinations of unitaries in the scheme of duality quantum computing, enabling implementations and experimental investigations of novel properties on both small quantum devices and near-term quantum computers.
The concept of parity-time (PT) symmetry originates from the framework of quantum mechanics, where if the Hamiltonian operator satisfies the commutation relation with the parity and time operators, it shows real energy spectrum. Recently, PT symmetry was introduced into various systems, such as optics, electronic circuits, acoustics, and other classical fields to further study the dynamical behaviors of the Hamiltonian and the energies. To focus on the dynamical evolution of the quantum state, here we experimentally studied the dynamical evolution of a two-level quantum system under the PT symmetric Hamiltonian using single-photon system. By enlarging the system using ancillary qubit and encoding the subsystem under the non-Hermitian Hamiltonian with post-selection, the evolution of the state can be characterized with a high fidelity. Owing to the effectively operation of the dilation method, our work provides a route for further exploiting the exotic properties of PT symmetric Hamiltonian for quantum simulation and quantum information processing.
Exceptional points (EPs) of a non-Hermitian Hamiltonian with parity-time-reversal (PT) symmetry have the potential to drastically enhance the capabilities of metrology and sensing through their power-law growing sensitivity to external perturbation. With the ability of generating and tuning dissipation in a single trapped ion system, we observe rich dynamics and detailed quantum phase transitions from the PT-symmetric phase to the symmetry-breaking phase. In this single qubit full quantum system, we develop a method to precisely determine the location of EP without any fitting parameter, and extract the eigenvalues in a unified way through all parameter regions. We can also obtain the full density matrix by quantum state tomography. Finally, we suggest from theoretical analysis that the periodically driving PT-symmetric non-Hermitian system can be used to measure the magnitude, frequency, and phase of time-dependent perturbation with EP enhancement.
Quantum information platforms enable analog quantum simulations, such as quantum annealing, offering a promising route to solving complex combinatorial optimization problems. Here, we propose a quantum information architecture based on networks of interacting parity-time (PT)-symmetric non-Hermitian qubits. While the dynamics of individual PT-symmetric qubits have been experimentally demonstrated across multiple platforms including NV centers, superconducting circuits, and trapped-ion systems yet coherent dynamics in interacting systems remain largely unexplored. To address this issue we theoretically investigate stationary and time-dependent Hamiltonians relevant to quantum annealing using a minimal model of two interacting XX-coupled PT-symmetric non-Hermitian qubits. We analyze both symmetry-preserving and symmetry-broken regimes and demonstrate that adding even tiny PT-symmetric non-Hermitian terms in the qubits Hamiltonian allows to greatly enhance the probability of reaching the ground state after annealing.
Non-Hermitian systems with parity-time reversal (
PT) or anti-
PT symmetry have attracted a wide range of interest owing to their unique characteristics and counterintuitive phenomena. One of the most extraordinary features is the presence of an exceptional point, across which a phase transition with spontaneously broken
PT symmetry takes place. We implement a Floquet Hamiltonian of a single qubit with anti-
PT symmetry by periodically driving a dissipative quantum system of a single trapped ion. With stroboscopic emission and quantum state tomography, we obtain the time evolution of density matrix for an arbitrary initial state, and directly demonstrate information retrieval, eigenstate coalescence, and topological energy spectra as unique features of non-Hermitian systems.
In recent years, non-Hermitian parity-time (
PT)-symmetric quantum systems have gained significant attention due to their unique physical properties, with experimental realizations demonstrated across diverse platforms. Two popular approaches have been used to implement
PT-symmetric dynamics: one removes quantum jumps from dissipative natural atoms (e.g., cold atoms, trapped ions) or artificial atoms (e.g., superconducting qubits) through postselection whose experimental fidelity is severely limited by unavoidable population backflow effects; the other embeds the desired non-Hermitian Hamiltonian into a larger Hermitian system, which achieves higher fidelity but typically enables simulating
PT-symmetric dynamics only within restricted parameter regimes. This paper proposes and experimentally demonstrates a trapped-ion-based scheme for digital simulation of
PT-symmetric quantum systems with high fidelity across the full parameter space. By leveraging high-fidelity logic gates and postselection on a four-level single ion to synthesize the target
PT-symmetric dynamics, this approach enables accurate characterization of
PT-symmetric properties, especially the exotic features in the vicinity of the exceptional point (EP). Distinct dynamical properties in the
PT-symmetric unbroken phase (PTS),
PT-symmetric broken phase (PTB), and at the EP are experimentally demonstrated with the data agreeing well with theoretical predictions. This high-fidelity simulation scheme also enables precise measurement of quantum Fisher information (QFI) near the EP, essential for evaluating non-Hermitian quantum sensing performance. It is shown that, after accounting for the low postselection probability, QFI divergence near the EP vanishes, providing no more information than their Hermitian counterparts, which echoes with recent theoretical findings. Our scheme establishes a paradigm for full-parameter-space precise simulation of non-Hermitian effects in quantum systems, and is applicable to various other platforms.