Prediction of Toric Code Topological Order from Rydberg Blockade
- URL: http://arxiv.org/abs/2011.12310v3
- Date: Sun, 29 Aug 2021 17:59:10 GMT
- Title: Prediction of Toric Code Topological Order from Rydberg Blockade
- Authors: Ruben Verresen, Mikhail D. Lukin, Ashvin Vishwanath
- Abstract summary: We find a topological quantum liquid (TQL) as evidenced by multiple measures.
We show how these can be measured experimentally using a dynamic protocol.
We discuss the implications for exploring fault-tolerant quantum memories.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The physical realization of $\mathbb Z_2$ topological order as encountered in
the paradigmatic toric code has proven to be an elusive goal. We predict that
this phase of matter can be realized in a two-dimensional array of Rydberg
atoms placed on the ruby lattice, at specific values of the Rydberg blockade
radius. First, we show that the blockade model -- also known as a `PXP' model
-- realizes a monomer-dimer model on the kagome lattice with a single-site
kinetic term. This can be interpreted as a $\mathbb Z_2$ gauge theory whose
dynamics is generated by monomer fluctuations. We obtain its phase diagram
using the numerical density matrix renormalization group method and find a
topological quantum liquid (TQL) as evidenced by multiple measures including
(i) a continuous transition between two featureless phases, (ii) a topological
entanglement entropy of $\ln 2$ as measured in various geometries, (iii)
degenerate topological ground states and (iv) the expected modular matrix from
ground state overlap. Next, we show that the TQL persists upon including
realistic, algebraically-decaying van der Waals interactions $V(r) \sim 1/r^6$
for a choice of lattice parameters. Moreover, we can directly access
topological loop operators, including the Fredenhagen-Marcu order parameter. We
show how these can be measured experimentally using a dynamic protocol,
providing a ``smoking gun'' experimental signature of the TQL phase. Finally,
we show how to trap an emergent anyon and realize different topological
boundary conditions, and we discuss the implications for exploring
fault-tolerant quantum memories.
Related papers
- Predicting Topological Entanglement Entropy in a Rydberg analog simulator [0.0]
This work focuses on the dynamical preparation of a quantum-spin-liquid state on a Rydberg-atom simulator.
The flexibility of our approach does not only allow one to match the physically correct form of the Rydberg-atom Hamiltonian but also the relevant lattice topology.
We show that, while the simulated state exhibits (global) topological order and local properties resembling those of a resonating-valence-bond (RVB) state, it lacks the latter's characteristic topological entanglement entropy signature.
arXiv Detail & Related papers (2024-06-28T12:27:42Z) - A Floquet-Rydberg quantum simulator for confinement in $\mathbb{Z}_2$
gauge theories [44.99833362998488]
Recent advances in the field of quantum technologies have opened up the road for the realization of small-scale quantum simulators.
We present a scalable Floquet scheme for the quantum simulation of the real-time dynamics in a $mathbbZ$ LGT.
We show that an observation of gauge-invariant confinement dynamics in the Floquet-Rydberg setup is at reach of current experimental techniques.
arXiv Detail & Related papers (2023-11-28T13:01:24Z) - Theory of free fermions under random projective measurements [43.04146484262759]
We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers.
We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
arXiv Detail & Related papers (2023-04-06T15:19:33Z) - Tuning the Topological $\theta$-Angle in Cold-Atom Quantum Simulators of
Gauge Theories [3.4075669047370125]
We show how a tunable topological $theta$-term can be added to a prototype theory with gauge symmetry.
The model can be realized experimentally in a single-species Bose--Hubbard model in an optical superlattice with three different spatial periods.
This work opens the door towards studying the rich physics of topological gauge-theory terms in large-scale cold-atom quantum simulators.
arXiv Detail & Related papers (2022-04-13T18:00:01Z) - Accessing the topological Mott insulator in cold atom quantum simulators
with realistic Rydberg dressing [58.720142291102135]
We investigate a realistic scenario for the quantum simulation of such systems using cold Rydberg-dressed atoms in optical lattices.
We perform a detailed analysis of the phase diagram at half- and incommensurate fillings, in the mean-field approximation.
We furthermore study the stability of the phases with respect to temperature within the mean-field approximation.
arXiv Detail & Related papers (2022-03-28T14:55:28Z) - Topological transitions with continuously monitored free fermions [68.8204255655161]
We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits.
We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
arXiv Detail & Related papers (2021-12-17T22:01:54Z) - Critical phase boundary and finite-size fluctuations in
Su-Schrieffer-Heeger model with random inter-cell couplings [0.0]
In this work, we investigate a special sort of a disorder when inter-cell hopping amplitudes are random.
Using a definition for $mathbbZ$-topological invariant $nuin 0; 1$ in terms of a non-Hermitian part of the total Hamiltonian, we calculate $langlenurangle averaged by random realizations.
arXiv Detail & Related papers (2021-11-30T15:35:58Z) - Multipartite entanglement of the topologically ordered state in a
perturbed toric code [18.589873789289562]
We demonstrate that multipartite entanglement, witnessed by the quantum Fisher information (QFI), can characterize topological quantum phase transitions in the spin-$frac12$ toric code model.
Our results provide insights to topological phases, which are robust against external disturbances, and are candidates for topologically protected quantum computation.
arXiv Detail & Related papers (2021-09-07T20:20:21Z) - Quantitative Propagation of Chaos for SGD in Wide Neural Networks [39.35545193410871]
In this paper, we investigate the limiting behavior of a continuous-time counterpart of the Gradient Descent (SGD)
We show 'propagation of chaos' for the particle system defined by this continuous-time dynamics under different scenarios.
We identify two under which different mean-field limits are obtained, one of them corresponding to an implicitly regularized version of the minimization problem at hand.
arXiv Detail & Related papers (2020-07-13T12:55:21Z) - Measuring the Unique Identifiers of Topological Order Based on
Boundary-Bulk Duality and Anyon Condensation [6.191686890868695]
A topological order is a new quantum phase beyond Landau's symmetry-breaking paradigm.
It is known that $R$- and $F$-matrices, which characterize the fusion-braiding properties of anyons, can be used to identify topological order.
We show that the braidings can be completely determined by the half braidings of boundary excitations.
The $F$-matrices can also be measured in a scattering quantum circuit involving the fusion of three anyons in two different orders.
arXiv Detail & Related papers (2020-05-07T03:55:06Z) - Dynamical solitons and boson fractionalization in cold-atom topological
insulators [110.83289076967895]
We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities.
We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors.
Using a pumping argument, we show that it survives also for finite interactions.
arXiv Detail & Related papers (2020-03-24T17:31:34Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.