Universal Quantum Computation From 2/3 Bilayer Quantum Hall States

Sergey B. Bravyi

Yangdong Zheng, Anju Sawada, Z. F. Ezawa

D. N. Sheng, Zheng Zhu, Liang Fu

Vladimir Privman A, Israel D. Vagner, G. F. Kventsel

Abolhassan Vaezi, Maissam Barkeshli

The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not powerful enough for universal TQC. In this Letter, we consider a simple bilayer fractional quantum Hall system with the 1/3 Laughlin state in each layer. We show that interlayer tunneling can drive a transition to an exotic non-Abelian state that contains the famous "Fibonacci" anyon, whose non-Abelian statistics is powerful enough for universal TQC. Our analysis rests on startling agreements from a variety of distinct methods, including thin torus limits, effective field theories, and coupled wire constructions. We provide evidence that the transition can be continuous, at which point the charge gap remains open while the neutral gap closes. This raises the question of whether these exotic phases may have already been realized at ν=2/3 in bilayers, as past experiments may not have definitively ruled them out.

Ya-Hui Zhang, Zheng Zhu, Ashvin Vishwanath

XY* transitions represent one of the simplest examples of unconventional quantum criticality, in which fractionally charged excitations condense into a superfluid and display novel features that combine quantum criticality and fractionalization.Nevertheless, their experimental realization is challenging.Here we propose to study the XY* transition in quantum Hall bilayers at filling ðν 1 ; ν 2 Þ ¼ ð 1 3 ; 2 3 Þ where the exciton condensate (EC) phase plays the role of the superfluid.Supported by exact diagonalization calculation, we argue that there is a continuous transition between an EC phase at small bilayer separation to a pair of decoupled fractional quantum Hall states at large separation.The transition is driven by condensation of a fractional exciton, a bound state of a Laughlin quasiparticle and quasihole, and is in the XY* universality class.The fractionalization is manifested by unusual properties including a large anomalous exponent and fractional universal conductivity, which can be conveniently measured through interlayer tunneling and counterflow transport, respectively.We also show that the edge is likely to realize the newly predicted extraordinary log boundary criticality.Our work highlights the promise of quantum Hall bilayers as an ideal platform for exploring exotic bulk and boundary critical behaviors that are amenable to immediate experimental exploration in dual-gated bilayer systems.The XY* critical theory can be generalized to a bilayer system with an arbitrary Abelian state in one layer and its particle-hole partner in the other layer.Therefore, we anticipate many distinct XY* transitions corresponding to the different Laughlin states and Jain sequences in the single-layer case.