Defects in topologically ordered models have interesting properties that are reminiscent of the anyonic excitations of the models themselves. For example, dislocations in the toric code model are known as twists and possess properties that are analogous to Ising anyons. We strengthen this analogy by using the topological entanglement entropy as a diagnostic tool to identify properties of both defects and excitations in the toric code. Specifically, we show, through explicit calculation, that the toric code model including twists and dyon excitations has the same quantum dimensions, the same total quantum dimension, and the same fusion rules as an Ising anyon model.
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http://dx.doi.org/10.1103/PhysRevLett.111.220402 | DOI Listing |
Sci Rep
November 2024
Department of Ophthalmology, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, 430022, China.
Compare Zcalc with other formulas on spherical equivalent prediction errors (PE) and explore the relationship between PE and ocular parameters. Optimize 709 IOL power calculation. 114 eyes with age-related cataract and preoperative regular corneal astigmatism of more than 1.
View Article and Find Full Text PDFPhys Rev Lett
July 2024
Technische Universität Berlin, Institut für Theoretische Physik, Hardenbergstraße 36, 10623 Berlin.
We show that non-Abelian anyons can emerge from an Abelian topologically ordered system subject to local time-periodic driving. This is illustrated with the toric-code model, as the canonical representative of a broad class of Abelian topological spin liquids. The Abelian anyons in the toric code include fermionic and bosonic quasiparticle excitations which see each other as π fluxes; namely, they result in the accumulation of a π phase if wound around each other.
View Article and Find Full Text PDFPhys Rev Lett
April 2024
Department of Physics, University of California at San Diego, La Jolla, California 92093, USA.
We study states with intrinsic topological order subjected to local decoherence from the perspective of separability, i.e., whether a decohered mixed state can be expressed as an ensemble of short-range entangled pure states.
View Article and Find Full Text PDFPhys Rev Lett
April 2024
Tencent Quantum Laboratory, Tencent, Shenzhen, Guangdong 518057, China.
Ground state preparation is classically intractable for general Hamiltonians. On quantum devices, shallow parametrized circuits can be effectively trained to obtain short-range entangled states under the paradigm of variational quantum eigensolver, while deep circuits are generally untrainable due to the barren plateau phenomenon. In this Letter, we give a general lower bound on the variance of circuit gradients for arbitrary quantum circuits composed of local 2-designs.
View Article and Find Full Text PDFPhys Rev Lett
February 2024
Department of Physics, University of California, Santa Barbara, California 93106, USA.
The Floquet code utilizes a periodic sequence of two-qubit measurements to realize the topological order. After each measurement round, the instantaneous stabilizer group can be mapped to a honeycomb toric code, explaining the topological feature. The code also possesses a time-crystal order-the e-m transmutation after every cycle, breaking the Floquet symmetry of the measurement schedule.
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