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arXiv:2310.20432 · Physical Review A

Demonstration of a parity-time-symmetry-breaking phase transition using superconducting and trapped-ion qutrits

Alena S. Kazmina, Ilia V. Zalivako, Alexander S. Borisenko, Nikita A. Nemkov, Anastasiia S. Nikolaeva, Ilya A. Simakov, Arina V. Kuznetsova, Elena Yu. Egorova, Kristina P. Galstyan, Nikita V. Semenin, Korolkov Andrey Evgenyevich, Ilya N. Moskalenko, Nikolay N. Abramov, Ilya S. Besedin, Daria A. Kalacheva, Viktor B. Lubsanov, Aleksey N. Bolgar, Evgeniy O. Kiktenko, Ksenia Yu. Khabarova, Alexey Galda, Ilya A. Semerikov, N. Kolachevsky, Nataliya Maleeva, Aleksey K. Fedorov

Published Mar 25, 2024• 25 citations
arXivHTMLPDF

Abstract

Scalable quantum computers hold the promise to solve hard computational problems, such as prime factorization, combinatorial optimization, simulation of many-body physics, and quantum chemistry. While being key to understanding many real-world phenomena, simulation of nonconservative quantum dynamics presents a challenge for unitary quantum computation. In this work, we focus on simulating nonunitary parity-time-symmetric systems, which exhibit a distinctive symmetry-breaking phase transition as well as other unique features that have no counterpart in closed systems. We show that a qutrit, a three-level quantum system, is capable of realizing this nonequilibrium phase transition. By using two physical platforms, an array of trapped ions and a superconducting transmon, and by controlling their three energy levels in a digital manner, we experimentally simulate the parity-time-symmetry-breaking phase transition. Our results indicate the potential advantage of multilevel (qudit) processors in simulating physical effects, where additional accessible levels can play the role of a controlled environment.

DOI
10.1103/physreva.109.032619

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Scalable quantum computers hold the promise to solve hard computational problems, such as prime factorization, combinatorial optimization, simulation of many-body physics, and quantum chemistry. While being key to understanding many real-world phenomena, simulation of nonconservative quantum dynamics presents a challenge for unitary quantum computation. In this work, we focus on simulating nonunitary parity-time-symmetric systems, which exhibit a distinctive symmetry-breaking phase transition as well as other unique features that have no counterpart in closed systems. We show that a qutrit, a three-level quantum system, is capable of realizing this nonequilibrium phase transition. By using two physical platforms, an array of trapped ions and a superconducting transmon, and by controlling their three energy levels in a digital manner, we experimentally simulate the parity-time-symmetry-breaking phase transition. Our results indicate the potential advantage of multilevel (qudit) processors in simulating physical effects, where additional accessible levels can play the role of a controlled environment.
Quantum processors based on superconducting circuitry have reached the scale of hundreds of qubits and demonstrated computational capabilities that challenge state-of-the-art classical methods for carefully designed problems. Despite these advances, fundamental questions persist over how to best improve and scale the computational power of this emerging technology. Most transmon-based quantum processors encode information in two-level systems, or qubits, leaving the rich multilevel structure of the transmon largely unexploited. In this thesis, we demonstrate how the capabilities of these devices can be meaningfully extended by harnessing this intrinsic multilevel structure to encode qudits — d-level quantum systems that access a larger and more connected Hilbert space than their qubit counterparts. We begin by demonstrating universal single-qudit operation before turning to microwave-activated entanglement to realize scalable two-qudit gates. We present a high-fidelity, fully entangling two-qutrit CZ gate based on a novel tunable cross-Kerr mechanism. We further explore two-qudit gates that selectively entangle subspaces of the full Hilbert space via two-photon multipartite Raman transitions, employing these operations to generate large entangled states across a transmon array. To address the noisy nature of near-term qudit computation, we introduce and characterize error suppression techniques for qudit circuits, including dynamical decoupling and quantum error mitigation. We then synthesize these directions by exploring simulations of quantum systems that have innate multilevel interactions and are therefore well tailored to qudit operation. First we investigate digital quantum simulations of collective neutrino oscillations and the spin-1 truncated Abelian Higgs model, finding error mitigation methods critical for improving circuit performance. Finally, out of equilibrium --- or Floquet --- spin-1 systems are realized using an array of 15 superconducting qutrits to probe a novel Z3 discrete time crystalline (DTC) phase of matter with intrinsically chiral interactions. This DTC result demonstrates that native qudit hardware provides powerful access to non-equilibrium phases rooted in higher discrete symmetries, opening a route to a broader landscape of dynamical orders beyond the Z2 Ising paradigm.
Non-Hermitian Hamiltonians are a fascinating class of many-body models that describe the effective dynamics of quantum systems interacting with the environment through particle, energy, or information exchange. Although their theoretical framework is well established, the controlled engineering of such Hamiltonians in the context of quantum simulations remains challenging, even more so when the non-Hermitian part describes a kkk-body interaction. Qudit quantum simulators offer a compelling framework to implement such models. We theoretically investigate the dynamics of a one-dimensional chain of qudits undergoing hybrid unitary-projective evolution, where suitably designed measurements constrain the dynamics to a Zeno subspace. As we illustrate for the case of qutrits, within the Zeno subspace the dynamics is governed by an effective non-Hermitian Hamiltonian for an ensemble of pseudo-spins 1/21/21/2, which can inherit non-Hermitian two-body interactions with the same connectivity as the full qutrit chain. We derive an analytical relation linking the monitored qutrits' evolution to a desired target non-Hermitian Hamiltonian and validate the effective description through numerical simulations of a representative model. Our scheme provides a constructive route for the realization of a large class of interacting non-Hermitian many-body Hamiltonians in experimentally relevant multilevel quantum platforms, including trapped ions and superconducting circuits.
Many-body systems of quantum interacting particles in which time-reversal symmetry is broken give rise to a variety of rich collective behaviors and are, therefore, a major target of research in modern physics.Quantum simulators can potentially be used to explore and understand such systems, which are often beyond the computational reach of classical simulation.Of these, platforms with universal quantum control can experimentally access a wide range of physical properties.However, simultaneously achieving strong programmable interactions, strong time-reversal symmetry breaking, and high-fidelity quantum control in a scalable manner is challenging.Here, we realize quantum simulations of interacting, time-reversal-broken quantum systems in a universal trapped-ion quantum processor.Using a recently proposed, scalable scheme, we implement time-reversal-breaking synthetic gauge fields, shown for the first time in a trappedion chain, along with unique coupling geometries, potentially extendable to simulation of multidimensional systems.Our high-fidelity single-site resolution in control and measurement, along with highly programmable interactions, allow us to perform full state tomography of a ground state showcasing persistent current and to observe dynamics of a time-reversal-broken system with nontrivial interactions.Our results open a path toward simulation of time-reversal-broken many-body systems with a wide range of features and coupling geometries.
Abstract The observation of genuine quantum effects in systems governed by non-Hermitian Hamiltonians has been an outstanding challenge in the field. Here we simulate the evolution under such Hamiltonians in the quantum regime on a superconducting quantum processor by using a dilation procedure involving an ancillary qubit. We observe the parity–time ( PT{\mathcal{PT}}PT PT )-symmetry breaking phase transition at the exceptional points, obtain the critical exponent, and show that this transition is associated with a loss of state distinguishability. In a two-qubit setting, we show that the entanglement can be modified by local operations.
Parity-time (PT\mathcal{PT}PT)-symmetric systems, featuring real eigenvalues despite their non-Hermitian nature, undergo spontaneous PT\mathcal{PT}PT symmetry breaking at the exceptional point (EP). The phase transition from PT\mathcal{PT}PT symmetry to PT\mathcal{PT}PT symmetry breaking has shown exotic functionalities in the classical realm, such as loss-induced transparency or lasing revival. This transition is also expected to produce a more unconventional effect in pure quantum PT\mathcal{PT}PT devices. Here, we report experimental evidences of spontaneous PT\mathcal{PT}PT symmetry breaking in a single cold 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion and, more importantly, a counterintuitive effect of perfect quantum coherence occurring at the EP. Excellent agreement between experimental results and theoretical predictions is identified. In view of the versatile role of cold ions in building a quantum memory or processor, our experiment provides an alternative platform to explore PT\mathcal{PT}PT-symmetric physics and utilize pure quantum EP effects.
Symmetry is crucial for gaining insights into the fundamental properties of physical systems, bringing possibilities in studying exotic phenomena such as quantum phase transitions and ground-state entanglement. Here, we experimentally simulate a highly controllable extended quantum Rabi model, capable of tuning into the ultrastrong or deep coupling regime, in a spin-motion-coupled trapped ion. We observe that the phonon driven by such a model with Z_{2} symmetry preserved (broken) would experience double (single) excitation in the ultrastrong coupling regime. Quantum phenomena such as strong ground-state entanglement and quantum superposition in systems occur with parity symmetry, and these phenomena disappear following the symmetry breaking. We also find sensitive responses for the two-level system entropy and phonon Wigner function in the deep coupling regime, depending on the parameter across the symmetry transition point. This Letter offers the prospect of exploring symmetry-controlled quantum phenomena and their applications in high-precision quantum technologies.