Unveiling the non-Abelian statistics of anyons via photonic simulation
arXiv:2304.05286 · doi:10.1103/PhysRevLett.132.110601
Abstract
Simulators can realise novel phenomena by separating them from the complexities of a full physical implementation. Here we put forward a scheme that can simulate the exotic statistics of non-Abelian anyons with minimal resources. The qudit lattice representation of this planar code supports local encoding of anyons. As a proof-of-principle demonstration we employ a photonic simulator to encode a single qutrit and manipulate it to perform the fusion and braiding properties of non-Abelian anyons. The photonic technology allows us to perform the required non-unitary operations with much higher fidelity than what can be achieved with current quantum computers. Our approach can be directly generalised to larger systems or to different anyonic models, thus enabling advances in the exploration of quantum error correction and fundamental physics alike.
References in corpus (49)
- Fault-tolerant quantum computation by anyons
- Non-Abelian Anyons and Topological Quantum Computation
- Unpaired Majorana fermions in quantum wires
- Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
- Non-abelian statistics of half-quantum vortices in p-wave superconductors
- Suppressing quantum errors by scaling a surface code logical qubit
- Hamiltonian Simulation by Qubitization
- Optimal Hamiltonian Simulation by Quantum Signal Processing
- Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
- Topological fault-tolerance in cluster state quantum computation
- Unambiguous Discrimination Between Linearly-Independent Quantum States
- A universal qudit quantum processor with trapped ions
- Machine Learning Topological States
- Quantum Information Scrambling in a Superconducting Qutrit Processor
- The Quantum Double Model with Boundary: Condensations and Symmetries
- A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
- Experimental GHZ Entanglement beyond Qubits
- Non-Majorana states yield nearly quantized conductance in superconductor-semiconductor nanowire devices
- Finite Group Modular Data
- High-Fidelity Qutrit Entangling Gates for Superconducting Circuits
- Demonstrating anyonic fractional statistics with a six-qubit quantum simulator
- Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
- High-Dimensional Pixel Entanglement: Efficient Generation and Certification
- Measuring azimuthal and radial modes of photons
- Characterization of high-dimensional entangled systems via mutually unbiased measurements
- Experimental high-dimensional Greenberger-Horne-Zeilinger entanglement with superconducting transmon qutrits
- Non-abelian vortices and non-abelian statistics
- Quantum symmetries in discrete gauge theories
- Simulations of quantum double models
- Experimental quantum process tomography of non trace-preserving maps
- Simulating the exchange of Majorana zero modes with a photonic system
- Why should anyone care about computing with anyons?
- A scheme for universal high-dimensional quantum computation with linear optics
- Simulating the dynamics of braiding of Majorana zero modes using an IBM quantum computer
- Inverse-design of high-dimensional quantum optical circuits in a complex medium
- Decoding non-Abelian topological quantum memories
- Haag duality for Kitaev's quantum double model for abelian groups
- Demonstrating non-Abelian braiding of surface code defects in a five qubit experiment
- Discriminating single-photon states unambiguously in high dimensions
- Simultaneously sorting overlapping quantum states of light
- Dynamical Quantum Phase Transitions in Extended Toric-Code Models
- Photonic implementation of Majorana-based Berry phases
- Referenceless characterisation of complex media using physics-informed neural networks
- On single-photon and classical interference
- Universal quantum computation in the surface code using non-Abelian islands
- Simulating neutrino oscillations on a superconducting qutrit
- Characterising and Tailoring Spatial Correlations in Multi-Mode Parametric Downconversion
- Anyons are not energy eigenspaces of quantum double Hamiltonians
- Simulation of non-Abelian Anyons using ribbon operators connected to a common base site