Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation

• URL: http://arxiv.org/abs/2304.05286v1
• Date: Tue, 11 Apr 2023 15:36:27 GMT
• Title: Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation
• Authors: Suraj Goel, Matthew Reynolds, Matthew Girling, Will McCutcheon, Saroch Leedumrongwatthanakun, Vatshal Srivastav, David Jennings, Mehul Malik, Jiannis K. Pachos
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $D(S_3)$ non-Abelian anyons with minimal resources. The qudit lattice representation of this planar code supports local encoding of $D(S_3)$ 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 $D(S_3)$ 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.

Related papers

• Demonstrating anyonic non-Abelian statistics with a minimal $d = 6$ qudit lattice [0.0]
  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.
  arXiv  Detail & Related papers  (2024-08-06T18:00:59Z)
• 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)
• Simulation of quantum optics by coherent state decomposition [0.0]
  We introduce a framework for simulating quantum optics by decomposing the system into a finite rank (number of terms) superposition of coherent states. We demonstrate that linear optical simulations with the $n$ photons initially in the same mode scales efficiently, as $O(m2 n)$.
  arXiv  Detail & Related papers  (2023-05-26T17:14:27Z)
• Spin-$S$ $\mathrm{U}(1)$ Quantum Link Models with Dynamical Matter on a Quantum Simulator [3.1192594881563127]
  We present a bosonic mapping for the representation of gauge and electric fields with effective spin-$S$ operators. We then propose an experimental scheme for the realization of a large-scale spin-$1$ $mathrmU(1)$ QLM using spinless bosons in an optical superlattice.
  arXiv  Detail & Related papers  (2023-05-10T18:00:01Z)
• Classical shadow tomography for continuous variables quantum systems [13.286165491120467]
  We introduce two experimentally realisable schemes for obtaining classical shadows of CV quantum states. We are able to overcome new mathematical challenges due to the infinite-dimensionality of CV systems. We provide a scheme to learn nonlinear functionals of the state, such as entropies over any small number of modes.
  arXiv  Detail & Related papers  (2022-11-14T17:56:29Z)
• Validation tests of GBS quantum computers give evidence for quantum advantage with a decoherent target [62.997667081978825]
  We use positive-P phase-space simulations of grouped count probabilities as a fingerprint for verifying multi-mode data. We show how one can disprove faked data, and apply this to a classical count algorithm.
  arXiv  Detail & Related papers  (2022-11-07T12:00:45Z)
• 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)
• Preparation of excited states for nuclear dynamics on a quantum computer [117.44028458220427]
  We study two different methods to prepare excited states on a quantum computer. We benchmark these techniques on emulated and real quantum devices. These findings show that quantum techniques designed to achieve good scaling on fault tolerant devices might also provide practical benefits on devices with limited connectivity and gate fidelity.
  arXiv  Detail & Related papers  (2020-09-28T17:21:25Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)
• Holographic quantum algorithms for simulating correlated spin systems [0.0]
  We present a suite of "holographic" quantum algorithms for efficient ground-state preparation and dynamical evolution of correlated spin-systems. The algorithms exploit the equivalence between matrix-product states (MPS) and quantum channels, along with partial measurement and qubit re-use. As a demonstration of the potential resource savings, we implement a holoVQE simulation of the antiferromagnetic Heisenberg chain on a trapped-ion quantum computer.
  arXiv  Detail & Related papers  (2020-05-06T18:00:01Z)
• 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)

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.