Demonstrating anyonic non-Abelian statistics with a minimal $d = 6$ qudit lattice

• URL: http://arxiv.org/abs/2408.03377v1
• Date: Tue, 6 Aug 2024 18:00:59 GMT
• Title: Demonstrating anyonic non-Abelian statistics with a minimal $d = 6$ qudit lattice
• Authors: Lucy Byles, Ewan Forbes, Jiannis K. Pachos,
• Abstract summary: We consider a lattice of $d=6$ qudits that give rise to $mathbfD(mathbfS_3)$ non-Abelian anyons. We present a method that demonstrates the non-commutativity of the braiding and fusion evolutions. This work represents a foundational step towards the realisation of non-Abelian quantum error-correcting codes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum double models provide a natural framework for realising anyons by manipulating a lattice of qudits, which can be directly encoded in quantum simulators. In this work, we consider a lattice of $d=6$ qudits that give rise to $\mathbf{D}(\mathbf{S}_3)$ non-Abelian anyons. We present a method that demonstrates the non-commutativity of the braiding and fusion evolutions solely by utilising the operators that create and measure anyons. Furthermore, we provide a dense coding scheme where only two qudits are sufficient to determine the anyonic braiding and fusion matrices. The minimal resource requirement of our approach offers a viable blueprint for demonstrating the non-Abelian nature of anyons in various quantum platforms, including optical, atomic, and solid-state systems, where higher-spin states can be effectively encoded. This work represents a foundational step towards the realisation of non-Abelian quantum error-correcting codes.

Related papers

• A General Quantum Duality for Representations of Groups with Applications to Quantum Money, Lightning, and Fire [8.714677279673738]
  We show that manipulating quantum states in one basis is equivalent to extracting values in a complementary basis. We present the first secure quantum lightning construction based on a plausible cryptographic assumption. We show equivalence among four security notions: quantum lightning security, worst-case and average-case cloning security, and security against preparing a canonical state.
  arXiv  Detail & Related papers  (2024-11-01T11:56:11Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation [0.0]
  Scheme can simulate exotic statistics of $D(S_3)$ non-Abelian anyons with minimal resources. We employ a photonic simulator to encode a single qutrit and manipulate it to perform the fusion and braiding properties of non-Abelian $D(S_3)$ anyons.
  arXiv  Detail & Related papers  (2023-04-11T15:36:27Z)
• Digital simulation of non-Abelian anyons with 68 programmable superconducting qubits [15.75710727890576]
  Non-Abelian anyons are exotic quasiparticle excitations hosted by certain topological phases of matter. We report an experimental quantum digital simulation of projective non-Abelian anyons and their braiding statistics.
  arXiv  Detail & Related papers  (2022-11-17T18:59:10Z)
• Non-Abelian braiding of graph vertices in a superconducting processor [144.97755321680464]
  Indistinguishability of particles is a fundamental principle of quantum mechanics. braiding of non-Abelian anyons causes rotations in a space of degenerate wavefunctions. We experimentally verify the fusion rules of the anyons and braid them to realize their statistics.
  arXiv  Detail & Related papers  (2022-10-19T02:28:44Z)
• Topological Quantum Computation on Supersymmetric Spin Chains [0.0]
  Quantum gates built out of braid group elements form the building blocks of topological quantum computation. We show that the fusion spaces of anyonic systems can be precisely mapped to the product state zero modes of certain Nicolai-like supersymmetric spin chains.
  arXiv  Detail & Related papers  (2022-09-08T13:52:10Z)
• Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans\"atze [13.651587339535961]
  We develop a framework for convolutional quantum circuits with SU$(d)$symmetry. We prove Harrow's statement on equivalence between $nameSU(d)$ and $S_n$ irrep bases.
  arXiv  Detail & Related papers  (2021-12-14T18:03:43Z)
• Sub-bosonic (deformed) ladder operators [62.997667081978825]
  We present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states. In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons.
  arXiv  Detail & Related papers  (2020-09-10T20:53:58Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)
• Quantum Simulation of 2D Quantum Chemistry in Optical Lattices [59.89454513692418]
  We propose an analog simulator for discrete 2D quantum chemistry models based on cold atoms in optical lattices. We first analyze how to simulate simple models, like the discrete versions of H and H$+$, using a single fermionic atom. We then show that a single bosonic atom can mediate an effective Coulomb repulsion between two fermions, leading to the analog of molecular Hydrogen in two dimensions.
  arXiv  Detail & Related papers  (2020-02-21T16:00:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.