Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory

• URL: http://arxiv.org/abs/2410.14860v1
• Date: Fri, 18 Oct 2024 21:03:07 GMT
• Title: Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
• Authors: Filippo Iulianelli, Sung Kim, Joshua Sussan, Aaron D. Lauda,
• Abstract summary: We propose a framework for topological quantum computation using newly discovered non-semisimple analogs of topological quantum field theories in 2+1 dimensions. We show that the non-semisimple theory introduces new anyon types that extend the Ising framework.
• Score: 0.058331173224054456
• License:
• Abstract: We propose a framework for topological quantum computation using newly discovered non-semisimple analogs of topological quantum field theories in 2+1 dimensions. These enhanced theories offer more powerful models for quantum computation. The conventional theory of Ising anyons, which is believed to describe excitations in the $\nu = 5/2$ fractional quantum Hall state, is not universal for quantum computation via braiding of quasiparticles. However, we show that the non-semisimple theory introduces new anyon types that extend the Ising framework. By adding just one new anyon type, universal quantum computation can be achieved through braiding alone. This result opens new avenues for realizing fault-tolerant quantum computing in topologically ordered systems.

Related papers

• A Quadratic Speedup in Finding Nash Equilibria of Quantum Zero-Sum Games [102.46640028830441]
  We introduce the Optimistic Matrix Multiplicative Weights Update (OMMWU) algorithm and establish its average-iterate convergence complexity as $mathcalO(d/epsilon)$ to $epsilon$-Nash equilibria. This quadratic speed-up sets a new benchmark for computing $epsilon$-Nash equilibria in quantum zero-sum games.
  arXiv  Detail & Related papers  (2023-11-17T20:38:38Z)
• A simple formulation of no-cloning and no-hiding that admits efficient and robust verification [0.0]
  Incompatibility is a feature of quantum theory that sets it apart from classical theory. The no-hiding theorem is another such instance that arises in the context of the black-hole information paradox. We formulate both of these fundamental features of quantum theory in a single form that is amenable to efficient verification.
  arXiv  Detail & Related papers  (2023-03-05T12:48:11Z)
• Simple Tests of Quantumness Also Certify Qubits [69.96668065491183]
  A test of quantumness is a protocol that allows a classical verifier to certify (only) that a prover is not classical. We show that tests of quantumness that follow a certain template, which captures recent proposals such as (Kalai et al., 2022) can in fact do much more. Namely, the same protocols can be used for certifying a qubit, a building-block that stands at the heart of applications such as certifiable randomness and classical delegation of quantum computation.
  arXiv  Detail & Related papers  (2023-03-02T14:18:17Z)
• Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
  Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle. We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm. We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
  arXiv  Detail & Related papers  (2022-05-26T20:32:36Z)
• Testing real quantum theory in an optical quantum network [1.6720048283946962]
  We show that tests in the spirit of a Bell inequality can reveal quantum predictions in entanglement swapping scenarios. We disproving real quantum theory as a universal physical theory.
  arXiv  Detail & Related papers  (2021-11-30T05:09:36Z)
• Towards a variational Jordan-Lee-Preskill quantum algorithm [9.548089725859297]
  We formulate the theory of (time-dependent) variational quantum simulation, explicitly designed for quantum simulation of quantum field theory. We develop hybrid quantum-classical algorithms for crucial ingredients in particle scattering experiments, including encoding, state preparation, and time evolution.
  arXiv  Detail & Related papers  (2021-09-12T16:04:44Z)
• Advancing Hybrid Quantum-Classical Algorithms via Mean-Operators [0.30905468888217874]
  Entanglement in quantum many-body systems is the key concept for future technology and science. We propose a theory which overcomes the limitations by combining advantages of the hybrid algorithms and the standard mean-field-theory in condensed matter physics.
  arXiv  Detail & Related papers  (2021-07-15T18:00:04Z)
• Depth-efficient proofs of quantumness [77.34726150561087]
  A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify quantum advantage of an untrusted prover. In this paper, we give two proof of quantumness constructions in which the prover need only perform constant-depth quantum circuits.
  arXiv  Detail & Related papers  (2021-07-05T17:45:41Z)
• The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning [84.33745072274942]
  We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles. On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing.
  arXiv  Detail & Related papers  (2021-03-08T17:24:29Z)
• Probabilistic Theories and Reconstructions of Quantum Theory (Les Houches 2019 lecture notes) [0.0]
  These lecture notes provide a basic introduction to the framework of generalized probabilistic theories (GPTs) I present two conceivable phenomena beyond quantum: superstrong nonlocality and higher-order interference. I summarize a reconstruction of quantum theory from the principles of Tomographic Locality, Continuous Reversibility, and the Subspace Axiom.
  arXiv  Detail & Related papers  (2020-11-02T20:03:13Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)

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.