Unlike the fundamental forces of the Standard Model, such as electromagnetic, weak and strong forces, the quantum effects of gravity are still experimentally inaccessible. The weak coupling of gravity with matter makes it significant only for large m
asses where quantum effects are too subtle to be measured with current technology. Nevertheless, insight into quantum aspects of gravity is key to understanding unification theories, cosmology or the physics of black holes. Here we propose the simulation of quantum gravity with optical lattices which allows us to arbitrarily control coupling strengths. More concretely, we consider $(2+1)$-dimensional Dirac fermions, simulated by ultra-cold fermionic atoms arranged in a honeycomb lattice, coupled to massive quantum gravity, simulated by bosonic atoms positioned at the links of the lattice. The quantum effects of gravity induce interactions between the Dirac fermions that can be witnessed, for example, through the violation of Wicks theorem. The similarity of our approach to current experimental simulations of gauge theories suggests that quantum gravity models can be simulated in the laboratory in the near future.
The boundaries of quantum materials can host a variety of exotic effects such as topologically robust edge states or anyonic quasiparticles. Here, we show that fermionic systems such as graphene that admit a low energy Dirac description can exhibit c
ounterintuitive relativistic effects at their boundaries. As an example, we consider carbon nanotubes and demonstrate that relativistic bulk spinor states can have non zero charge density on the boundaries, in contrast to the sinusoidal distribution of non-relativistic wave functions that are necessarily zero at the boundaries. This unusual property of relativistic spinors is complementary to the linear energy dispersion relation exhibited by Dirac materials and can influence their coupling to leads, transport properties or their response to external fields.
The toric code is a simple and exactly solvable example of topological order realising Abelian anyons. However, it was shown to support non-local lattice defects, namely twists, which exhibit non-Abelian anyonic behaviour [1]. Motivated by this resul
t, we investigated the potential of having non-Abelian statistics from puncture defects on the toric code. We demonstrate that an encoding with mixed-boundary punctures reproduces Ising fusion, and a logical Pauli-$X$ upon their braiding. Our construction paves the way for local lattice defects to exhibit non-Abelian properties that can be employed for quantum information tasks.
Quasiparticle poisoning, expected to arise during the measurement of Majorana zero mode state, poses a fundamental problem towards the realization of Majorana-based quantum computation. Parafermions, a natural generalization of Majorana fermions, can
encode topological qudits immune to quasiparticle poisoning. While parafermions are expected to emerge in superconducting fractional quantum Hall systems, they are not yet attainable with current technology. To bypass this problem, we employ a photonic quantum simulator to experimentally demonstrate the key components of parafermion-based universal quantum computation. Our contributions in this article are twofold. First, by manipulating the photonic states, we realize Clifford operator Berry phases that correspond to braiding statistics of parafermions. Second, we investigate the quantum contextuality in a topological system for the first time by demonstrating the contextuality of parafermion encoded qudit states. Importantly, we find that the topologically-encoded contextuality opens the way to magic state distillation, while both the contextuality and the braiding-induced Clifford gates are resilient against local noise. By introducing contextuality, our photonic quantum simulation provides the first step towards a physically robust methodology for realizing topological quantum computation.
We demonstrate that $mathbb{Z}_2$ gauge transformations and lattice deformations in Kitaevs honeycomb lattice model can have the same description in the continuum limit of the model in terms of chiral gauge fields. The chiral gauge fields are coupled
to the Majorana fermions that satisfy the Dirac dispersion relation in the non-Abelian sector of the model. For particular values, the effective chiral gauge field becomes equivalent to the $mathbb{Z}_2$ gauge field, enabling us to associate effective fluxes to lattice deformations. Motivated by this equivalence, we consider Majorana-bounding $pi$ vortices and Majorana-bounding lattice twists and demonstrate that they are adiabatically connected to each other. This equivalence opens the possibility for novel encoding of Majorana-bounding defects that might be easier to realise in experiments.
Here, we analyse two Dirac fermion species in two spatial dimensions in the presence of general quartic contact interactions. By employing functional bosonisation techniques, we demonstrate that depending on the couplings of the fermion interactions
the system can be effectively described by a rich variety of topologically massive gauge theories. Among these effective theories, we obtain an extended Chern-Simons theory with higher order derivatives as well as two coupled Chern-Simons theories. Our formalism allows for a general description of interacting fermions emerging, for example, at the gapped boundary of three-dimensional topological crystalline insulators.
We provide evidence that, alongside topologically protected edge states, two-dimensional Chern insulators also support localised bulk states deep in their valance and conduction bands. These states manifest when local potential gradients are applied
to the bulk, while all parts of the system remain adiabatically connected to the same phase. In turn, the bulk states produce bulk current transverse to the strain. This occurs even when the potential is always below the energy gap, where one expects only edge currents to appear. Bulk currents are topologically protected and behave like edge currents under external influence, such as temperature or local disorder. Detecting topologically resilient bulk currents offers a direct means to probe the localised bulk states.
Very few topological systems with long-range couplings have been considered so far due to our lack of analytic approaches. Here we extend the Kitaev chain, a 1D quantum liquid, to infinite-range couplings and study its topological properties. We demo
nstrate that, even though topological phases are intimately linked to the notion of locality, the infinite-range couplings give rise to topological zero and non-zero energy Majorana end modes depending on the boundary conditions of the system. We show that the analytically derived properties are to a large degree stable against modifications to decaying long-range couplings. Our work opens new frontiers for topological states of matter that are relevant to current experiments where suitable interactions can be designed.
We evaluate the entanglement entropy of exactly solvable Hamiltonians corresponding to general families of three-dimensional topological models. We show that the modification to the entropic area law due to three-dimensional topological properties is
richer than the two-dimensional case. In addition to the reduction of the entropy caused by non-zero vacuum expectation value of contractible loop operators a new topological invariant appears that increases the entropy if the model consists of non-trivially braiding anyons. As a result the three-dimensional topological entanglement entropy provides only partial information about the two entropic topological invariants.
To use quantum systems for technological applications we first need to preserve their coherence for macroscopic timescales, even at finite temperature. Quantum error correction has made it possible to actively correct errors that affect a quantum mem
ory. An attractive scenario is the construction of passive storage of quantum information with minimal active support. Indeed, passive protection is the basis of robust and scalable classical technology, physically realized in the form of the transistor and the ferromagnetic hard disk. The discovery of an analogous quantum system is a challenging open problem, plagued with a variety of no-go theorems. Several approaches have been devised to overcome these theorems by taking advantage of their loopholes. Here we review the state-of-the-art developments in this field in an informative and pedagogical way. We give the main principles of self-correcting quantum memories and we analyze several milestone examples from the literature of two-, three- and higher-dimensional quantum memories.
