Braiding quantum gates from partition algebras

• URL: http://arxiv.org/abs/2003.00244v3
• Date: Wed, 19 Aug 2020 11:35:39 GMT
• Title: Braiding quantum gates from partition algebras
• Authors: Pramod Padmanabhan, Fumihiko Sugino, Diego Trancanelli
• Abstract summary: Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solution-generating technique to solve the $(d,m,l)$-generalized Yang-Baxter equation. Explicit examples are given for a 2-, 3-, and 4-qubit system.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solution-generating technique to solve the $(d,m,l)$-generalized Yang-Baxter equation, for $m/2\leq l \leq m$, which allows to systematically construct such braiding operators. This is achieved by using partition algebras, a generalization of the Temperley-Lieb algebra encountered in statistical mechanics. We obtain families of unitary and non-unitary braiding operators that generate the full braid group. Explicit examples are given for a 2-, 3-, and 4-qubit system, including the classification of the entangled states generated by these operators based on Stochastic Local Operations and Classical Communication.

Related papers

• Unitary tetrahedron quantum gates [3.117417023918577]
  Quantum simulations of many-body systems using 2-qubit Yang-Baxter gates offer a benchmark for quantum hardware. This can be extended to the higher dimensional case with $n$-qubit generalisations of Yang-Baxter gates called $n$-simplex operators. Finding them amounts to identifying unitary solutions of the $n$-simplex equations, the building blocks of higher dimensional integrable systems.
  arXiv  Detail & Related papers  (2024-07-15T13:58:33Z)
• Categorical Quantum Volume Operator [41.94295877935867]
  We show a generalization of the quantum volume operator quantifying the volume in curved three-dimensional discrete geometries. In both cases, we obtain a volume operator that is Hermitian, provided that the input category is unitary. As an illustrative example, we consider the case of $mathrmSU(2)_k$ and show that the standard $mathrmSU(2)$ volume operator is recovered in the limit $krightarrowinfty$
  arXiv  Detail & Related papers  (2024-06-04T08:37:10Z)
• Volichenko-type metasymmetry of braided Majorana qubits [0.0]
  This paper presents different mathematical structures connected with the parastatistics of braided Majorana qubits. Mixed-bracket Heisenberg-Lie algebras are introduced.
  arXiv  Detail & Related papers  (2024-06-02T21:50:29Z)
• Toffoli gates solve the tetrahedron equations [1.8434042562191815]
  In particular, factorised scattering operators result in integrable quantum circuits that provide universal quantum computation. A natural question is to extend this construction to higher qubit gates, like the Toffoli gates. We show that unitary families of such operators are constructed by the 3-dimensional generalizations of the Yang-Baxter operators.
  arXiv  Detail & Related papers  (2024-05-26T08:03:24Z)
• Enriching Diagrams with Algebraic Operations [49.1574468325115]
  We extend diagrammatic reasoning in monoidal categories with algebraic operations and equations. We show how this construction can be used for diagrammatic reasoning of noise in quantum systems.
  arXiv  Detail & Related papers  (2023-10-17T14:12:39Z)
• The Schmidt rank for the commuting operator framework [58.720142291102135]
  The Schmidt rank is a measure for the entanglement dimension of a pure bipartite state. We generalize the Schmidt rank to the commuting operator framework. We analyze bipartite states and compute the Schmidt rank in several examples.
  arXiv  Detail & Related papers  (2023-07-21T14:37:33Z)
• The tilted CHSH games: an operator algebraic classification [77.34726150561087]
  This article introduces a general systematic procedure for solving any binary-input binary-output game. We then illustrate on the prominent class of tilted CHSH games. We derive for those an entire characterisation on the region exhibiting some quantum advantage.
  arXiv  Detail & Related papers  (2023-02-16T18:33:59Z)
• Discovering Sparse Representations of Lie Groups with Machine Learning [55.41644538483948]
  We show that our method reproduces the canonical representations of the generators of the Lorentz group. This approach is completely general and can be used to find the infinitesimal generators for any Lie group.
  arXiv  Detail & Related papers  (2023-02-10T17:12:05Z)
• Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles [55.41644538483948]
  We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the transformations symmetry and the corresponding generators. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
  arXiv  Detail & Related papers  (2023-01-13T16:25:25Z)
• A Graphical Calculus for Quantum Computing with Multiple Qudits using Generalized Clifford Algebras [0.0]
  We show that it is feasible to envision implementing the braid operators for quantum computation, by showing that they are 2-local operators. We derive several new identities for the braid elements, which are key to our proofs. In terms of quantum computation, we show that it is feasible to envision implementing the braid operators for quantum computation.
  arXiv  Detail & Related papers  (2021-03-30T05:19:49Z)
• Local invariants of braiding quantum gates -- associated link polynomials and entangling power [0.0]
  We consider certain two-qubit Yang-Baxter operators, which we dub of the X-type', and show that their eigenvalues completely determine the non-local properties of the system. We also compute their entangling power and compare it with that of a generic two-qubit operator.
  arXiv  Detail & Related papers  (2020-10-01T09:28:01Z)

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.