Measurement-based quantum computation in symmetry protected topological states of one-dimensional integer spin systems

• URL: http://arxiv.org/abs/2409.16109v1
• Date: Tue, 24 Sep 2024 14:12:54 GMT
• Title: Measurement-based quantum computation in symmetry protected topological states of one-dimensional integer spin systems
• Authors: Wang Yang, Arnab Adhikary, Robert Raussendorf,
• Abstract summary: In addition to half-odd-integer spins, the integer spin chains can also be incorporated in the framework. The computational order parameter characterizing the efficiency of MBQC is identified, which, for spin-$1$ chains in the Haldane phase, coincides with the conventional string order parameter in condensed matter physics.
• Score: 2.231201892342328
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we generalize the algebraic framework for measurement-based quantum computation (MBQC) in one-dimensional symmetry protected topological states recently developed in [Quantum 7, 1215 (2023)], such that in addition to half-odd-integer spins, the integer spin chains can also be incorporated in the framework. The computational order parameter characterizing the efficiency of MBQC is identified, which, for spin-$1$ chains in the Haldane phase, coincides with the conventional string order parameter in condensed matter physics.

Related papers

• Classification of symmetry protected states of quantum spin chains for continuous symmetry groups [0.0]
  We show that SPT's corresponding to finite on-site symmetry groups $G$ are classified by the second cohomology group $H2(G,U(1))$. We also strengthen the existing results in the sense that our classification results hold within the class of spin chains with locally bounded on-site dimensions.
  arXiv  Detail & Related papers  (2024-09-02T09:41:13Z)
• Non-equilibrium Quantum Monte Carlo Algorithm for Stabilizer Rényi Entropy in Spin Systems [0.552480439325792]
  Quantum magic, or nonstabilizerness, provides a crucial characterization of quantum systems. We propose a novel and efficient algorithm for computing stabilizer R'enyi entropy, one of the measures for quantum magic, in spin systems with sign-problem free Hamiltonians.
  arXiv  Detail & Related papers  (2024-05-29T23:59:02Z)
• Discrete dynamics in the set of quantum measurements [0.0]
  A quantum measurement, often referred to as positive operator-valued measurement (POVM), is a set of positive operators $P_i=P_idaggeq 0$ summing to identity. We analyze dynamics induced by blockwise bistochastic matrices, in which both columns and rows sum to the identity.
  arXiv  Detail & Related papers  (2023-08-10T19:34:04Z)
• Generalized quantum geometric tensor for excited states using the path integral approach [0.0]
  The quantum geometric tensor encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral formalism that can handle both the ground and excited states. We then generalize the quantum geometric tensor to incorporate variations of the system parameters and the phase-space coordinates.
  arXiv  Detail & Related papers  (2023-05-19T08:50:46Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Quantum circuits for the preparation of spin eigenfunctions on quantum computers [63.52264764099532]
  Hamiltonian symmetries are an important instrument to classify relevant many-particle wavefunctions. This work presents quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers.
  arXiv  Detail & Related papers  (2022-02-19T00:21:46Z)
• Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
  We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems. Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
  arXiv  Detail & Related papers  (2021-08-30T23:50:05Z)
• Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers [0.0]
  We establish relations between the quantum metric and the topological invariants of generic Dirac Hamiltonians. We show that topological indices are bounded by the quantum volume determined by the quantum metric. This work suggests unexplored topological responses and metrological applications in a broad class of quantum-engineered systems.
  arXiv  Detail & Related papers  (2021-06-01T21:10:48Z)
• Rectification induced by geometry in two-dimensional quantum spin lattices [58.720142291102135]
  We address the role of geometrical asymmetry in the occurrence of spin rectification in two-dimensional quantum spin chains. We show that geometrical asymmetry, along with inhomogeneous magnetic fields, can induce spin current rectification even in the XX model.
  arXiv  Detail & Related papers  (2020-12-02T18:10:02Z)
• Hilbert-space geometry of random-matrix eigenstates [55.41644538483948]
  We discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles. Our results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
  arXiv  Detail & Related papers  (2020-11-06T19:00:07Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

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.