TY - JOUR T1 - Observation of a finite-energy phase transition in a one-dimensional quantum simulator Y1 - 2023 A1 - Alexander Schuckert A1 - Or Katz A1 - Lei Feng A1 - Eleanor Crane A1 - Arinjoy De A1 - Mohammad Hafezi A1 - Alexey V. Gorshkov A1 - Christopher Monroe AB -

One of the most striking many-body phenomena in nature is the sudden change of macroscopic properties as the temperature or energy reaches a critical value. Such equilibrium transitions have been predicted and observed in two and three spatial dimensions, but have long been thought not to exist in one-dimensional (1D) systems. Fifty years ago, Dyson and Thouless pointed out that a phase transition in 1D can occur in the presence of long-range interactions, but an experimental realization has so far not been achieved due to the requirement to both prepare equilibrium states and realize sufficiently long-range interactions. Here we report on the first experimental demonstration of a finite-energy phase transition in 1D. We use the simple observation that finite-energy states can be prepared by time-evolving product initial states and letting them thermalize under the dynamics of a many-body Hamiltonian. By preparing initial states with different energies in a 1D trapped-ion quantum simulator, we study the finite-energy phase diagram of a long-range interacting quantum system. We observe a ferromagnetic equilibrium phase transition as well as a crossover from a low-energy polarized paramagnet to a high-energy unpolarized paramagnet in a system of up to 23 spins, in excellent agreement with numerical simulations. Our work demonstrates the ability of quantum simulators to realize and study previously inaccessible phases at finite energy density.

UR - https://arxiv.org/abs/2310.19869 ER - TY - JOUR T1 - Interactive Protocols for Classically-Verifiable Quantum Advantage Y1 - 2021 A1 - Daiwei Zhu A1 - Gregory D. Kahanamoku-Meyer A1 - Laura Lewis A1 - Crystal Noel A1 - Or Katz A1 - Bahaa Harraz A1 - Qingfeng Wang A1 - Andrew Risinger A1 - Lei Feng A1 - Debopriyo Biswas A1 - Laird Egan A1 - Alexandru Gheorghiu A1 - Yunseong Nam A1 - Thomas Vidick A1 - Umesh Vazirani A1 - Norman Y. Yao A1 - Marko Cetina A1 - Christopher Monroe AB -

Achieving quantum computational advantage requires solving a classically intractable problem on a quantum device. Natural proposals rely upon the intrinsic hardness of classically simulating quantum mechanics; however, verifying the output is itself classically intractable. On the other hand, certain quantum algorithms (e.g. prime factorization via Shor's algorithm) are efficiently verifiable, but require more resources than what is available on near-term devices. One way to bridge the gap between verifiability and implementation is to use "interactions" between a prover and a verifier. By leveraging cryptographic functions, such protocols enable the classical verifier to enforce consistency in a quantum prover's responses across multiple rounds of interaction. In this work, we demonstrate the first implementation of an interactive quantum advantage protocol, using an ion trap quantum computer. We execute two complementary protocols -- one based upon the learning with errors problem and another where the cryptographic construction implements a computational Bell test. To perform multiple rounds of interaction, we implement mid-circuit measurements on a subset of trapped ion qubits, with subsequent coherent evolution. For both protocols, the performance exceeds the asymptotic bound for classical behavior; maintaining this fidelity at scale would conclusively demonstrate verifiable quantum advantage.

UR - https://arxiv.org/abs/2112.05156 ER - TY - JOUR T1 - Observation of a prethermal discrete time crystal Y1 - 2021 A1 - Antonis Kyprianidis A1 - Francisco Machado A1 - William Morong A1 - Patrick Becker A1 - Kate S. Collins A1 - Dominic V. Else A1 - Lei Feng A1 - Paul W. Hess A1 - Chetan Nayak A1 - Guido Pagano A1 - Norman Y. Yao A1 - Christopher Monroe AB -

The conventional framework for defining and understanding phases of matter requires thermodynamic equilibrium. Extensions to non-equilibrium systems have led to surprising insights into the nature of many-body thermalization and the discovery of novel phases of matter, often catalyzed by driving the system periodically. The inherent heating from such Floquet drives can be tempered by including strong disorder in the system, but this can also mask the generality of non-equilibrium phases. In this work, we utilize a trapped-ion quantum simulator to observe signatures of a non-equilibrium driven phase without disorder: the prethermal discrete time crystal (PDTC). Here, many-body heating is suppressed not by disorder-induced many-body localization, but instead via high-frequency driving, leading to an expansive time window where non-equilibrium phases can emerge. We observe a number of key features that distinguish the PDTC from its many-body-localized disordered counterpart, such as the drive-frequency control of its lifetime and the dependence of time-crystalline order on the energy density of the initial state. Floquet prethermalization is thus presented as a general strategy for creating, stabilizing and studying intrinsically out-of-equilibrium phases of matter.

UR - https://arxiv.org/abs/2102.01695 ER -