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arXiv:2102.13117 · Physical Review Letters

Deterministic Fast Scrambling with Neutral Atom Arrays

Tomohiro Hashizume, Gregory S. Bentsen, Sebastian Weber, Andrew J. Daley

Published May 19, 2021• 18 citations
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Abstract

Fast scramblers are dynamical quantum systems that produce many-body entanglement on a timescale that grows logarithmically with the system size N. We propose and investigate a family of deterministic, fast scrambling quantum circuits realizable in near-term experiments with arrays of neutral atoms. We show that three experimental tools-nearest-neighbor Rydberg interactions, global single-qubit rotations, and shuffling operations facilitated by an auxiliary tweezer array-are sufficient to generate nonlocal interaction graphs capable of scrambling quantum information using only O(logN) parallel applications of nearest-neighbor gates. These tools enable direct experimental access to fast scrambling dynamics in a highly controlled and programmable way and can be harnessed to produce highly entangled states with varied applications.

DOI
10.1103/physrevlett.126.200603

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Fast scramblers are dynamical quantum systems that produce many-body entanglement on a timescale that grows logarithmically with the system size N. We propose and investigate a family of deterministic, fast scrambling quantum circuits realizable in near-term experiments with arrays of neutral atoms. We show that three experimental tools-nearest-neighbor Rydberg interactions, global single-qubit rotations, and shuffling operations facilitated by an auxiliary tweezer array-are sufficient to generate nonlocal interaction graphs capable of scrambling quantum information using only O(logN) parallel applications of nearest-neighbor gates. These tools enable direct experimental access to fast scrambling dynamics in a highly controlled and programmable way and can be harnessed to produce highly entangled states with varied applications.
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We propose an experimentally realizable quantum spin model that exhibits fast scrambling, based on nonlocal interactions that couple sites whose separation is a power of 2. By controlling the relative strengths of deterministic, nonrandom couplings, we can continuously tune from the linear geometry of a nearest-neighbor spin chain to an ultrametric geometry in which the effective distance between spins is governed by their positions on a tree graph. The transition in geometry can be observed in quench dynamics, and is furthermore manifest in calculations of the entanglement entropy. Between the linear and treelike regimes, we find a peak in entanglement and exponentially fast spreading of quantum information across the system. Our proposed implementation, harnessing photon-mediated interactions among cold atoms in an optical cavity, offers a test case for experimentally observing the emergent geometry of a quantum many-body system.
In a fast-scrambling many-body quantum system, information is spread and entanglement is built up on a time scale that grows logarithmically with the system size.This is of fundamental interest in understanding the dynamics of many-body systems, as well as in efficiently producing entangled resource states and error-correcting codes.In this work, we identify a dynamical transition marking the onset of scrambling in quantum circuits with different levels of long-range connectivity.In particular, we show that as a function of the interaction range for circuits of different structures, the tripartite mutual information exhibits a scaling collapse around a critical point between two clearly defined regimes of different dynamical behavior.We study this transition analytically in a related long-range Brownian-circuit model and show how the transition can be mapped onto the statistical mechanics of a long-range Ising model in a particular region of parameter space.This mapping predicts mean-field critical exponents ν = -1/(1 + s c ), which are consistent with the critical exponents extracted from Clifford-circuit numerics.In addition to systems with conventional power-law interactions, we identify the same phenomenon in deterministic sparse circuits that can be realized in experiments with neutral-atom arrays.
A frontier challenge in quantum science and technology is the construction of scalable quantum systems which can operate in regimes beyond classical simulatability. Such systems can be used as tools for simulating and exploring complex phenomena in quantum physics; they can also be used to benchmark and test quantum algorithms. Several experimental platforms, based on a variety of quantum mechanical building blocks, are currently being pursued with these goals in mind, with state-of-the-art systems capable of controlling up to around fifty particles. In this thesis, we present the development of a new platform based on individually controlled neutral atoms. In this approach, hundreds of individual atoms are trapped in an array of optical tweezers, and they are sorted in real-time into programmable geometries in one and two dimensions. After initialization of an array, atom interactions are switched on by coherent excitation to highly excited Rydberg states, resulting in a rich spin Hamiltonian. We experimentally advance several key aspects of this platform, developing new tools for controlling strongly interacting atom arrays and probing novel quantum phases and non-equilibrium dynamics. We additionally utilize Rydberg interactions to entangle atoms, demonstrating high fidelity universal quantum logic gates as well as the preparation of fully entangled Schrödinger cat states. This work highlights the prospects for scalable quantum simulation and quantum information processing beyond the limit of classical computation using neutral atom arrays.
The creation and coherent control of systems of many strongly-interacting quantum particles represents one of the most important challenges in quantum science and technology. Devices capable of performing such a task have applications ranging from sensing and simulation, to communications and computation. The past few decades have seen remarkable progress in the development of different platforms to address the challenges of isolating and controlling individual quantum objects and increasing the number of interacting elements. This thesis presents a novel platform using arrays of individually controlled neutral atoms in optical tweezers which enables high-fidelity control of large systems of strongly interacting particles. Using real-time imaging and feedback, we initialize the positions of hundreds of atoms in arbitrary one- and two-dimensional geometries. By coupling the internal state of the atoms to highly excited Rydberg states, we are able to introduce spatially-dependent interactions to the system. Combining the remarkable coherence properties of isolated neutral atoms with strong Rydberg interactions, we study complex spin Hamiltonians in regimes beyond classical simulability. In the context of quantum simulation, we use this platform to study the phase diagram of regular arrays, including the critical properties of some of the associated quantum phase transitions. Additionally, we report on the discovery of special slowly-thermalizing states known as quantum many-body scars, which are then used as a starting point to stabilize many-body dynamics across the Hilbert space. Through the addition of specialized local controls, we demonstrate the ability to generate large N-partite entangled states with up to 20 atoms, as well as the ability to implement quantum logic gates. We combine quantum simulation with quantum information processing by preparing states with signatures of quantum spin liquids, which may be developed as topologically protected qubits. Lastly, we explore the potential applications of this platform to classical combinatorial optimization problems by approximating the Maximum Independent Set of different graphs.
We study quantum information scrambling in spin models with both long-range all-to-all and short-range interactions. We argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give rise to fast scrambling, which describes the spread of quantum information over the entire system in a time that is logarithmic in the system size. This is illustrated in two tractable models: (1) a random circuit with Haar random local unitaries and a global interaction and (2) a classical model of globally coupled nonlinear oscillators. We use exact numerics to provide further evidence by studying the time evolution of an out-of-time-order correlator and entanglement entropy in spin chains of intermediate sizes. Our results pave the way towards experimental investigations of fast scrambling and aspects of quantum gravity with quantum simulators.