From non-unitary anyons to unconventional superfluidity

Yu-Jie Liu, Kirill Shtengel, Adam Smith +1 more

The finding of physical realizations of topologically ordered states in experimental settings, from condensed matter to artificial quantum systems, has been the main challenge en route to utilizing their unconventional properties.We show how to realize a large class of topologically ordered states and simulate their quasiparticle excitations on a digital quantum computer.To achieve this, we design a set of linear-depth quantum circuits to generate ground states of general string-net models together with unitary open-string operators to simulate the creation and braiding of Abelian and non-Abelian anyons.We show that the Abelian (non-Abelian) unitary string operators can be implemented with a constant-(linear-) depth quantum circuit.Our scheme allows us to directly probe characteristic topological properties, including topological entanglement entropy, braiding statistics, and fusion channels of anyons.Moreover, this set of efficiently prepared topologically ordered states has potential applications in the development of fault-tolerant quantum computers.

D. Boyanovsky, David Jasnow

Yu-Hsueh Chen, Tarun Grover

A topological phase can undergo a phase transition driven by anyon condensation. A potential obstruction to such a mechanism could arise if there exists a symmetry between anyons that have non-trivial mutual statistics. Here we consider toric code subjected to errors that tend to proliferate anyons with non-trivial mutual statistics. Using triangle inequality, we show that in the presence of electromagnetic duality and a partial-transpose symmetry, a decoherence induced phase transition out of the topological phase must be rather unconventional and lie beyond standard rules of anyon condensation. To explore such physics, we first subject toric code to a self-dual quantum channel where Kraus operators are proportional to X+Z. We find that the topological phase is stable up to the maximal error rate, when viewing density matrix as a pure state in the double Hilbert space. To access an unconventional transition, we then consider a perturbed toric code subjected to the self-dual channel, and find numerical evidence that beyond a critical error rate, the topological phase is destroyed resulting in a critical phase where anyons are only power-law condensed.

Carlo A. Trugenberger

D. ELIEZER, Gordon Walter Semenoff, Shiying Wu

We prove, working in the Hamiltonian formalism, that a U(1) Chern-Simons theory coupled to fermions on a lattice can be mapped exactly onto a theory of interacting lattice anyons. This map does not involve any singular gauge transformations, and is everywhere well defined. We also prove that, when the statistics parameter is an odd integer so that the anyons are bosons, the ground state, which consists of a condensate of bound pairs of flux tubes and fermions, breaks phase invariance. The ensuing long range order implies that the system is an unconventional superfluid.