Deterministic Fast Scrambling with Neutral Atom Arrays

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

Phys. Rev. Lett. 126, 200603 – Published 19 May 2021

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 $O (\log N)$ 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.

Received 26 February 2021
Accepted 15 April 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.200603

Physics Subject Headings (PhySH)

Entanglement production Many-body localization Quantum entanglement Quantum information processing Quantum information with atoms & light

Rydberg atoms & molecules

Many-body techniques Optical tweezers

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Tomohiro Hashizume^1,*, Gregory S. Bentsen ^2,*, Sebastian Weber ³, and Andrew J. Daley ¹

¹Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
²Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02465, USA
³Institute for Theoretical Physics III and Center for Integrated Quantum Science and Technology, University of Stuttgart, 70550 Stuttgart, Germany

^*T. H. and G. S. B. contributed equally to this work.

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Vol. 126, Iss. 20 — 21 May 2021

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Figure 1
Fast scrambling via quasi-1D shuffling. (a) Neutral atoms (red dots, blue circles) trapped in a static 1D optical lattice (gray boxes) can be rapidly rearranged via a two-step shuffling operation $R$ (i)–(iii) facilitated by an auxiliary 1D tweezer array (bottom left). Iterated shuffling and nearest-neighbor Rydberg interactions yield effective interactions on highly nonlocal coupling graphs such as the $m$ -regular hypercube graph $Q_{m}$ (b). More generally, circuits (c) composed of shuffles (blue), nearest-neighbor controlled- $Z$ operations (red), and global rotations (purple) can be harnessed to generate Page-scrambled quantum states in $m$ iterations or strongly scrambling quantum channels in $2 m$ iterations.
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Figure 2
Page scrambling in $2 m = 2 \log_{2} N$ steps. (a) The mean deficit $⟨ Δ S_{A}^{(2)} ⟩$ from volume-law entanglement entropy, sampled over $2 \times 10^{4}$ random bipartitions $A \cup \bar{A}$ of fixed size $| A |$ decreases in the circuit $E_{s}$ on $N = 128$ qubits (solid red) at a rate comparable to a random all-to-all (AA) circuit (dashed blue) and much faster than a comparable nearest-neighbor (NN) circuit (dotted green). (b) After $2 m$ circuit layers, the mean Renyi entropy $⟨ S_{A}^{(2)} ⟩$ (red diamonds), nearly saturates the Page curve (red), compared to a nearest-neighbor circuit of the same depth [(b), inset]. (c) The mean entropy deficit $⟨ Δ S_{A}^{(2)} ⟩$ agrees with random matrix theory (dotted black) to within sampling fluctuations for $N = 16$ , 32, 64, 128, 256 (light to dark). (d) The fraction $f_{ε, | A |}$ of subsystems $A$ having less than maximal entanglement entropy (white dots) vanishes exponentially as a function of $Δ S_{A}^{(2)} / \ln 2 = ε = 0$ , 1, 2, 3, in agreement with random matrix theory (vertical bars, light to dark). Error bars are shown or are smaller than markers; lines are guides.
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Figure 3
Deterministic scrambling in the Hayden-Preskill thought experiment. (a) Scrambling in the circuit $E_{s}$ can be characterized by the mutual information $I_{2}^{(2)} (A : R B)$ between Alice’s register $A$ (red) and Bob’s registers $R$ , $B$ (blue). (b) For $N = 128$ qubits, the mutual information grows rapidly as a function of Bob’s output register $R$ over a range of message sizes $| A | = 1$ , 3, 5, 7, 9 (light to dark), saturating to within 5% of its maximum value (dotted black) after Bob has collected only a handful ${| R |}_{\min} \geq | A | + k$ of output qubits with $k \leq 2$ [(c), dotted black)]. Nearest-neighbor circuits of the same depth (crosses, dashed lines) show relatively low mutual information by comparison. (d) At fixed $| A | = 5$ , $I_{2}^{(2)} (A : R B)$ shows strong data collapse as a function of system size $N = 16$ , 32, 64, 128, 256 (light to dark). Error bars smaller than markers; lines are guides to the eye.
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Figure 4
Information scrambling in the presence of dissipation. (a) Scrambling in the circuit $E_{s}$ is diagnosed by the fidelity $F_{EPR}$ of recovering Alice’s quantum information $A$ on Bob’s register $C$ using a probabilistic decoding circuit (dotted purple). (b) For $N = 8$ at fixed circuit depth $t = 6$ , the fidelity grows with the number of qubits $| R |$ used in the decoder, indicating successful teleportation of Alice’s information with fidelity $> 50 %$ even in the presence of single-qubit errors at rates $p = 0.00, 0.01, \dots, 0.04$ per 2-qubit gate (light to dark). For $p = 0$ , the fidelity is nearly identical to that of a Haar-random circuit (dotted black). (c) The fidelity (dots, solid lines) grows with circuit depth $t$ and substantially outperforms nearest-neighbor circuits of the same depth (crosses, dotted lines) in the presence of dissipation. (d) The dissipation parameter $δ$ falls as a function of circuit depth in both the scrambling circuit and nearest-neighbor circuit. Each data point averaged over $6 \times 10^{4}$ quantum trajectories, with error bars smaller than markers; lines are guides to the eye.
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