Ergodic theory of diagonal orthogonal covariant quantum channels

• URL: http://arxiv.org/abs/2206.01145v1
• Date: Thu, 2 Jun 2022 16:51:21 GMT
• Title: Ergodic theory of diagonal orthogonal covariant quantum channels
• Authors: Satvik Singh, Nilanjana Datta, Ion Nechita
• Abstract summary: We analyze the ergodic properties of quantum channels that are covariant with respect to diagonal transformations. We study dual unitary circuits which have recently been proposed as minimal models of quantum chaos in many-body systems.
• Score: 7.842152902652214
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We analyze the ergodic properties of quantum channels that are covariant with respect to diagonal orthogonal transformations. We prove that the ergodic behaviour of a channel in this class is essentially governed by a classical stochastic matrix. This allows us to exploit tools from classical ergodic theory to study quantum ergodicity of such channels. As an application of our analysis, we study dual unitary brickwork circuits which have recently been proposed as minimal models of quantum chaos in many-body systems. Upon imposing a local diagonal orthogonal invariance symmetry on these circuits, the long-term behaviour of spatio-temporal correlations between local observables in such circuits is completely determined by the ergodic properties of a channel that is covariant under diagonal orthogonal transformations. We utilize this fact to show that such symmetric dual unitary circuits exhibit a rich variety of ergodic behaviours, thus emphasizing their importance.

Related papers

• Random covariant quantum channels [2.9741863650371805]
  Group symmetries inherent in quantum channels often make them tractable. We introduce natural probability distributions for covariant quantum channels. We discuss the threshold phenomenon for positive partial transpose and entanglement breaking properties.
  arXiv  Detail & Related papers  (2024-03-06T12:39:30Z)
• Flux-charge symmetric theory of superconducting circuits [0.0]
  We present a theory of circuit quantization that treats charges and flux on a manifestly symmetric footing. For planar circuits, known circuit dualities are a natural canonical transformation on the classical phase space. We discuss the extent to which such circuit dualities generalize to non-planar circuits.
  arXiv  Detail & Related papers  (2024-01-16T18:18:52Z)
• All you need is spin: SU(2) equivariant variational quantum circuits based on spin networks [0.0]
  Variational algorithms require architectures that naturally constrain the optimisation space to run efficiently. We propose the use of spin networks, a form of directed tensor network invariant under a group transformation, to devise SU(2) equivariant quantum circuit ans"atze. By changing to the basis that block diagonalises SU(2) group action, these networks provide a natural building block for constructing parameterised equivariant quantum circuits.
  arXiv  Detail & Related papers  (2023-09-13T18:38:41Z)
• Dual symplectic classical circuits: An exactly solvable model of many-body chaos [0.0]
  We prove that two-point dynamical correlation functions are non-vanishing only along the edges of the light cones. We test our theory in a specific family of dual-symplectic circuits, describing the dynamics of a classical Floquet spin chain.
  arXiv  Detail & Related papers  (2023-07-04T15:48:41Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Order-invariant two-photon quantum correlations in PT-symmetric interferometers [62.997667081978825]
  Multiphoton correlations in linear photonic quantum networks are governed by matrix permanents. We show that the overall multiphoton behavior of a network from its individual building blocks typically defies intuition. Our results underline new ways in which quantum correlations may be preserved in counterintuitive ways even in small-scale non-Hermitian networks.
  arXiv  Detail & Related papers  (2023-02-23T09:43:49Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Three-fold way of entanglement dynamics in monitored quantum circuits [68.8204255655161]
  We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles. We obtain insights into the interplay between the local entanglement generation by the gates and the entanglement reduction by the measurements.
  arXiv  Detail & Related papers  (2022-01-28T17:21:15Z)
• Diagonal unitary and orthogonal symmetries in quantum theory II: Evolution operators [1.5229257192293197]
  We study bipartite unitary operators which stay invariant under the local actions of diagonal unitary and orthogonal groups. As a first application, we construct large new families of dual unitary gates in arbitrary finite dimensions. Our scrutiny reveals that these operators can be used to simulate any bipartite unitary gate via local operations and classical communication.
  arXiv  Detail & Related papers  (2021-12-21T11:54:51Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Bulk detection of time-dependent topological transitions in quenched chiral models [48.7576911714538]
  We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction. This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
  arXiv  Detail & Related papers  (2020-01-16T17:44:52Z)

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.