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arXiv:1607.08560 · Physical Review Letters

Digital Quantum Simulation of Minimal AdS/CFT

Laura García-Álvarez, I. L. Egusquiza, Lucas Lamata, Adolfo del Campo, Julian Sonner, E. Solano

Published Jul 25, 2017• 152 citations
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Abstract

We propose the digital quantum simulation of a minimal AdS/CFT model in controllable quantum platforms. We consider the Sachdev-Ye-Kitaev model describing interacting Majorana fermions with randomly distributed all-to-all couplings, encoding nonlocal fermionic operators onto qubits to efficiently implement their dynamics via digital techniques. Moreover, we also give a method for probing nonequilibrium dynamics and the scrambling of information. Finally, our approach serves as a protocol for reproducing a simplified low-dimensional model of quantum gravity in advanced quantum platforms as trapped ions and superconducting circuits.

DOI
10.1103/physrevlett.119.040501

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We propose the digital quantum simulation of a minimal AdS/CFT model in controllable quantum platforms. We consider the Sachdev-Ye-Kitaev model describing interacting Majorana fermions with randomly distributed all-to-all couplings, encoding nonlocal fermionic operators onto qubits to efficiently implement their dynamics via digital techniques. Moreover, we also give a method for probing nonequilibrium dynamics and the scrambling of information. Finally, our approach serves as a protocol for reproducing a simplified low-dimensional model of quantum gravity in advanced quantum platforms as trapped ions and superconducting circuits.
Abstract The Sachdev-Ye-Kitaev (SYK) model incorporates rich physics, ranging from exotic non-Fermi liquid states without quasiparticle excitations, to holographic duality and quantum chaos. However, its experimental realization remains a daunting challenge due to various unnatural ingredients of the SYK Hamiltonian such as its strong randomness and fully nonlocal fermion interaction. At present, constructing such a nonlocal Hamiltonian and exploring its dynamics is best through digital quantum simulation, where state-of-the-art techniques can already handle a moderate number of qubits. Here, we demonstrate a first step towards simulation of the SYK model on a nuclear-spin-chain simulator. We observed the fermion paring instability of the non-Fermi liquid state and the chaotic-nonchaotic transition at simulated temperatures, as was predicted by previous theories. As the realization of the SYK model in practice, our experiment opens a new avenue towards investigating the key features of non-Fermi liquid states, as well as the quantum chaotic systems and the AdS/CFT duality.
We show that one can quantum simulate the dynamics of a Sachdev-Ye-Kitaev model with NNN Majorana modes for time ttt to precision $\ensuremath{\epsilon}$ with gate complexity $O({N}^{7/2}t+{N}^{5/2}t\phantom{\rule{0.16em}{0ex}}\mathrm{polylog}(N/\ensuremath{\epsilon}))$. In addition to scaling sublinearly in the number of Hamiltonian terms, this gate complexity represents an exponential improvement in $1/\ensuremath{\epsilon}$ and large polynomial improvement in NNN and ttt over prior state-of-the-art algorithms which scale as $O({N}^{10}{t}^{2}/\ensuremath{\epsilon})$. Our approach involves a variant of the qubitization technique in which we encode the Hamiltonian HHH as an asymmetric projection of a signal oracle UUU onto two different signal states prepared by state oracles, $A|0\ensuremath{\rangle}\ensuremath{\mapsto}|A\ensuremath{\rangle}$ and $B|0\ensuremath{\rangle}\ensuremath{\mapsto}|B\ensuremath{\rangle}$, such that $H=\ensuremath{\langle}B|U|A\ensuremath{\rangle}$. Our strategy for applying this method to the Sachdev-Ye-Kitaev model involves realizing BBB using only Hadamard gates and realizing AAA as a random quantum circuit.
Gate-based digital quantum simulations offer an exciting new paradigm for studying the many-body physics of strongly correlated systems. In this context, electron-phonon models are challenging for qubit-only quantum simulators, as bosonic degrees of freedom require costly finite-dimensional encodings. Here, we elaborate on an alternative approach based on a digital-analog circuit QED architecture, where fermions are encoded in transmon qubits while bosons are represented directly by microwave resonators. The central building block of this framework is a qubit-resonator Rabi gate that emulates strong electron-phonon coupling and can be implemented through a sequence of resonant Jaynes-Cummings gates interleaved with layers of single-qubit rotations. Using this Rabi gate as the fundamental unitary operation, we construct quantum circuits for the Hubbard-Holstein and Yukawa-Sachdev-Ye-Kitaev models, which describe, respectively, strongly correlated electrons coupled to phonons and phonon-mediated interactions among Majorana fermions. We further demonstrate how nonclassical phonon physics and signatures of quantum chaos in these models can be probed through circuit simulations, and develop measurement and variational protocols tailored to near-term superconducting quantum hardware.
We propose a low energy model for simulating an analog black hole on an optical lattice using ultracold atoms. Assuming the validity of the holographic principle, we employ the Sachdev-Ye-Kitaev (SYK) model, which describes a system of randomly infinite range interacting fermions, also conjectured to be an exactly solvable UV-complete model for an extremal black hole in a higher dimensional Anti-de Sitter (AdS) dilaton gravity. At low energies, the SYK model exhibits an emergent conformal symmetry and is dual to the extremal black hole solution in near AdS2 spacetime. Furthermore, we show how the SYK maximally chaotic behaviour at large N limit, found to be dual to a gauge theory in higher dimensions, can also be employed as a non-trivial investigation tool for the holographic principle. The proposed setup is a theoretical platform to realize the SYK model with relevant exotic effects and behaviour at low energies as a highly non-trivial example of the AdS/CFT duality and a framework for studying black holes.
The Sachdev-Ye-Kitaev (SYK) model is an all-to-all interacting Majorana fermion model for many-body quantum chaos and the holographic correspondence. Here we construct fermionic all-to-all Floquet quantum circuits of random four-body gates designed to capture key features of SYK dynamics. Our circuits can be built using local ingredients in Majorana devices, namely, charging-mediated interactions and braiding Majorana zero modes. This offers an analog-digital route to SYK quantum simulations that reconciles all-to-all interactions with the topological protection of Majorana zero modes, a key feature missing in existing proposals for analog SYK simulation. We also describe how dynamical, including out-of-time-ordered, correlation functions can be measured in such analog-digital implementations by employing foreseen capabilities in Majorana devices.
Randomly interacting Majorana fermions governed by the Sachdev-Ye-Kitaev model have recently been shown to exhibit profound links to quantum chaos and black holes. Here, the authors propose a solid-state implementation of the model that exploits hardware components that are now widely pursued for topological quantum computation -- namely, an array of Majorana wires interfaced with a disordered quantum dot that mediates the desired interactions. This work highlights a potential pathway for using table-top condensed-matter systems to probe novel concepts from high-energy physics and quantum information.