Topologically Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State

Abstract

The Pfaffian state is an attractive candidate for the observed quantized Hall plateau at a Landau-level filling fraction nu=5/2. This is particularly intriguing because this state has unusual topological properties, including quasiparticle excitations with non-Abelian braiding statistics. In order to determine the nature of the nu=5/2 state, one must measure the quasiparticle braiding statistics. Here, we propose an experiment which can simultaneously determine the braiding statistics of quasiparticle excitations and, if they prove to be non-Abelian, produce a topologically protected qubit on which a logical Not operation is performed by quasiparticle braiding. Using the measured excitation gap at nu=5/2, we estimate the error rate to be 10(-30) or lower.

Fractional quantum Hall hierarchy and the second Landau level

“…Several types of experiments are needed to determine the true nature of the observed FQH states. Interferometry experiments that probe braiding statistics can provide a "smoking gun," to unambiguously identify states as non-Abelian [48][49][50][51][52] and can be used to distinguish between certain classes of topological order, 53 for example, between Abelian, Ising, and Fibonacci ͑i.e., between HH, MR/BS, and k =3 RR͒ type states. However, certain "similar" states, such as those with Ising fusion rules in the non-Abelian sector, cannot be distinguished from braiding alone.…”

Influence of device geometry on tunneling in theν=52quantum Hall liquid

“…A number of methods [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] were invented and several experiments [29][30][31][32][33][34][35][36][37][38][39][40] were performed in an attempt to determine the right ground state. One approach 39,40 consists in the measurement of the tunneling current through a quantum point contact (QPC) between the edges of a 5/2 FQH liquid.…”

Spin and Charge Ordering in the Quantum Hall Regime

“…Several proposals for interference experiments at the 5 ⁄2 state have been made [133][134][135][136][137], and first steps towards their realization were undertaken [138,139]. Interestingly, first characteristic signatures of non-abelian anyons at = 5 ⁄2 were reported in an interferometer structure [140,141].…”