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We describe a continuous-variable scheme for simulating the Kitaev lattice model and for detecting statistics of abelian anyons. The corresponding quantum optical implementation is solely based upon Gaussian resource states and Gaussian operations, hence allowing for a highly efficient creation, manipulation, and detection of anyons. This approach extends our understanding of the control and application of anyons and it leads to the possibility for experimental proof-of-principle demonstrations of anyonic statistics using continuous-variable systems.
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Anyons, particles displaying a fractional exchange statistics intermediate between bosons and fermions, play a central role in the fractional quantum Hall effect and various spin lattice models, and have been proposed for topological quantum computing schemes due to their resilience to noise. Here we use parametric down-conversion in an integrated semiconductor chip to generate biphoton states simulating anyonic particle statistics, in a reconfigurable manner. Our scheme exploits the frequency entanglement of the photon pairs, which is directly controlled through the spatial shaping of the pump beam. These results, demonstrated at room temperature and telecom wavelength on a chip-integrated platform, pave the way to the practical implementation of quantum simulation tasks with tailored particle statistics.
Anyons are exotic quasiparticles living in two dimensions that do not fit into the usual categories of fermions and bosons, but obey a new form of fractional statistics. Following a recent proposal [Phys. Rev. Lett. 98, 150404 (2007)], we present an experimental demonstration of the fractional statistics of anyons in the Kitaev spin lattice model using a photonic quantum simulator. We dynamically create the ground state and excited states (which are six-qubit graph states) of the Kitaev model Hamiltonian, and implement the anyonic braiding and fusion operations by single-qubit rotations. A phase shift of $pi$ related to the anyon braiding is observed, confirming the prediction of the fractional statistics of Abelian 1/2-anyons.
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 show how a qubit can be fault-tolerantly encoded in the infinite-dimensional Hilbert space of an optical mode. The scheme is efficient and realizable with present technologies. In fact, it involves two travelling optical modes coupled by a cross-Kerr interaction, initially prepared in coherent states, one of which is much more intense than the other. At the exit of the Kerr medium, the weak mode is subject to a homodyne measurement and a quantum codeword is conditionally generated in the quantum fluctuations of the intense mode.
We generalize the operational quasiprobability involving sequential measurements proposed by Ryu {em et al.} [Phys. Rev. A {bf 88}, 052123] to a continuous-variable system. The quasiprobabilities in quantum optics are incommensurate, i.e., they represent a given physical observation in different mathematical forms from their classical counterparts, making it difficult to operationally interpret their negative values. Our operational quasiprobability is {em commensurate}, enabling one to compare quantum and classical statistics on the same footing. We show that the operational quasiprobability can be negative against the hypothesis of macrorealism for various states of light. Quadrature variables of light are our examples of continuous variables. We also compare our approach to the Glauber-Sudarshan $mathcal{P}$ function. In addition, we suggest an experimental scheme to sequentially measure the quadrature variables of light.
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