Floquet prethermal phase protected by U(1) symmetry on a superconducting quantum processor

Abstract

Periodically driven systems, or Floquet systems, exhibit many novel dynamics and interesting outof-equilibrium phases of matter. Those phases arising with the quantum systems’ symmetries, such as global U(1) symmetry, can even show dynamical stability with symmetry-protection. Here we experimentally demonstrate a U(1) symmetry-protected prethermal phase, via performing a digitalanalog quantum simulation on a superconducting quantum processor. The dynamical stability of this phase is revealed by its robustness against external perturbations. We also find that the spin glass order parameter in this phase is stabilized by the interaction between the spins. Our work reveals a promising prospect in discovering emergent quantum dynamical phases with digital-analog quantum simulators. Introduction: Searching for novel phases of matter is an eternal task in the field of condensed matter. In traditional condensed matter theory, all the phases of equilibrium matter were described by Landau’s symmetry-breaking theory [1] for a long time until the discovery of topological order [2, 3] broadened the range of states of matter. Recently, an evolution has happened in the field of far-from-equilibrium condensed matter [4–6]. The progress of driven quantum time-periodic systems, namely Floquet systems, has stimulated further interest in the search for far-from-equilibrium phases. A conventional view is that, in such a system, the information encoded on the initial state will be rapidly erased due to the inevitable thermalization induced by the continuous driving [7–9]. Two important mechanisms have been considered to prevent the information loss and lead to long-lived phases under the Floquet drive: The first is many-body localization (MBL), in which the eigenstate thermalization hypothesis (ETH) falis [9]; The other one is prethermalization, where the thermalization rate is exponentially small [9–11]. Phenomena of prethermalization have been studied in both on static systems [12–15] and Floquet systems [16–20], whose properties can be captured by their effective static Hamiltonian. Most of the observed non-equilibrium long-lived behaviors [11, 21–24] are considered to be in the prethermal regime, which inspires a lot of interests in the search of the novel phases [7, 10, 16, 25–27]. Prethermal phases are generally featured by a quasi-stationary state with long-lived equilibrium-like properties [7, 8, 11, 12, 28–30]. Typically, these phases can exist in the interacting quantum systems with various symme∗ These authors contributed equally. † minggong@ustc.edu.cn ‡ zqyin@bit.edu.cn 2 tries, such as a U(1) symmetry [7, 9, 28] and spatial symmetries [9, 31]. Figure 1. Schematics of the experiment. a, The illustration of the interacting Floquet system via digital-analog quantum simulation. The spin chain is initialized on the σz basis fully polarized state. Three kinds of Hamiltonians are applied sequentially in time: a global imperfect flip Hamiltonian HFlip (π pulse), strong disorder HDisorder and XX interaction HInt. b, The twelve transmon qubits, illustrated as black crosses, are arranged in a 1D chain. In our experiment, we choose 10 qubits in the right red region. The direct coupling between them is realized via capacitive coupling. Each qubit has individual Z and XY (green) control lines, and is coupled to corresponding readout resonators (blue) for dispersive readout. Six resonators in a group are coupled to a shared transmission line (yellow). c, The Floquet protocol of interacting Floquet matter with digital-analog simulation. Two cases, denoted by “Interaction Off” and “Interaction On”, are shown in the red box and the blue box, respectively. Rotation-X gates and virtual Z gates in the circuits are used to simulate the the flip Hamiltonian HFlip and the disorder Hamiltonian HDisorder. In a complete Floquet period, we apply two cycles of the flip Hamiltonian HFlip and the disorder term HDisorder, and add an interaction Hamiltonian HInt in the “Interaction On” case. We measure the system after repeating complete Floquet periods n times, where n ∈ [1, 50]. By replacing the last complete Floquet period of these sequences with a reduced cycle consisting of a flip term and a disorder term (dashed gates), we can measure the intermediate state of spins under one complete period, which results in “Half Floquet Periods”. Recent theoretical progresses have proven the existence of Floquet prethermal phases with the emergent symmetry-protection [7, 8, 10]. These phases may even exhibit extraordinary