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arXiv:2202.00358 · Physical Review Research

Photonic quantum simulations of coupled PT -symmetric Hamiltonians

Nicola Maraviglia, Patrick Yard, Ross Wakefield, Jacques Carolan, Chris Sparrow, Levon Chakhmakhchyan, Chris Harrold, Toshikazu Hashimoto, Nobuyuki Matsuda, Andrew K. Harter, Yogesh N. Joglekar, Anthony Laing

Published Jan 26, 2022• 13 citations
arXivHTMLPDF

Abstract

Parity-time-symmetric ($\mathcal{PT}$-symmetric) Hamiltonians are generally non-Hermitian and give rise to exotic behavior in quantum systems at exceptional points, where eigenvectors coalesce. The recent realization of $\mathcal{PT}$-symmetric Hamiltonians in quantum systems has ignited efforts to simulate and investigate many-particle quantum systems across exceptional points. Here, we use a programmable integrated photonic chip to simulate a model composed of twin pairs of $\mathcal{PT}$-symmetric Hamiltonians, with each the time reverse of its twin. We simulate quantum dynamics across exceptional points including two- and three-particle interference, and a particle-trembling behavior that arises due to interference between subsystems undergoing time-reversed evolutions. These results show how programmable quantum simulators can be used to investigate foundational questions in quantum mechanics.

DOI
10.1103/physrevresearch.4.013051

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Parity-time-symmetric (PT\mathcal{PT}PT-symmetric) Hamiltonians are generally non-Hermitian and give rise to exotic behavior in quantum systems at exceptional points, where eigenvectors coalesce. The recent realization of PT\mathcal{PT}PT-symmetric Hamiltonians in quantum systems has ignited efforts to simulate and investigate many-particle quantum systems across exceptional points. Here, we use a programmable integrated photonic chip to simulate a model composed of twin pairs of PT\mathcal{PT}PT-symmetric Hamiltonians, with each the time reverse of its twin. We simulate quantum dynamics across exceptional points including two- and three-particle interference, and a particle-trembling behavior that arises due to interference between subsystems undergoing time-reversed evolutions. These results show how programmable quantum simulators can be used to investigate foundational questions in quantum mechanics.
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.
Non-Hermitian systems with parity-time (PT\mathcal{PT}PT) symmetry give rise to exceptional points (EPs) with exceptional properties that arise due to the coalescence of eigenvectors. Such systems have been extensively explored in the classical domain, where second- or higher-order EPs have been proposed or realized. In contrast, quantum information studies of PT\mathcal{PT}PT-symmetric systems have been confined to systems with a two-dimensional Hilbert space. Here, by using a single-photon interferometry setup, we simulate the quantum dynamics of a four-dimensional PT\mathcal{PT}PT-symmetric system across a fourth-order exceptional point. By tracking the coherent, nonunitary evolution of the density matrix of the system in PT\mathcal{PT}PT-symmetry unbroken and broken regions, we observe the entropy dynamics for both the entire system, and the gain and loss subsystems. Our setup is scalable to the higher-dimensional PT\mathcal{PT}PT-symmetric systems, and our results point towards the rich dynamics and critical properties.
\n\nThe evolution of a two-level quantum system with a general parity-time-reversal-invariant Hamiltonian is reinterpreted as a subsystem in a four-dimensional Hilbert space, which makes it possible to simulate any two-level parity-time-symmetric (PT-symmetric) quantum system using a conventional quantum mechanics system. We studied the ability to simulate and investigate novel quantum systems and phenomena using a nowadays-available Hermitian quantum computer or a duality quantum computer. The quantum circuits are given for a qubit and two qudit systems, and they would be useful for experimental implementation and applications in the future.\n
Exceptional points facilitate peculiar dynamics in non-Hermitian systems. Yet, in photonics, they have mainly been studied in the classical realm. In this work, we reveal the behavior of two-photon quantum states in non-Hermitian systems across the exceptional point. We probe the lossy directional coupler with an indistinguishable two-photon input state and observe distinct changes of the quantum correlations at the output as the system undergoes spontaneous breaking of parity-time symmetry. Moreover, we demonstrate a switching in the quantum interference of photons directly at the exceptional point, where Hong-Ou-Mandel dips are transformed into peaks by a change of basis. These results show that quantum interference and exceptional points are linked in curious ways that can now be further explored.
Parity-time ( P T ) -symmetric Hamiltonians exhibit nonunitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here, we present a method for simulating the quantum dynamics of P T -symmetric systems on unitary-gate-based quantum computers by leveraging Hermitian equivalents through similarity transformations. We introduce two algorithms for simulating P T -symmetric systems near exceptional points where eigenvalues and eigenstates coalesce. The first is a hybrid classical-quantum algorithm and the second reduces the classical component by using an ancilla qubit. We then use perturbation theory to extend this method to consider the dynamics of two weakly interacting P T -symmetric systems. Demonstrations on a quantum device and noisy simulators validate the algorithm on current quantum devices, offering potential for scalable simulations of P T -symmetric systems and pseudo-Hermitian operators in quantum computation.
Quantum dynamics of two XXXXXX interacting PT-symmetric non-Hermitian qubits: enhancement of quantum annealing
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.