Topological order and criticality in (2+1)D monitored random quantum circuits

• URL: http://arxiv.org/abs/2011.06595v3
• Date: Thu, 2 Dec 2021 00:44:21 GMT
• Title: Topological order and criticality in (2+1)D monitored random quantum circuits
• Authors: Ali Lavasani, Yahya Alavirad, Maissam Barkeshli
• Abstract summary: We study (2+1)D random circuits with random Clifford unitary gates. We find a phase diagram involving a tricritical point that maps to (2+1)D percolation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: It has recently been discovered that random quantum circuits provide an avenue to realize rich entanglement phase diagrams, which are hidden to standard expectation values of operators. Here we study (2+1)D random circuits with random Clifford unitary gates and measurements designed to stabilize trivial area law and topologically ordered phases. With competing single qubit Pauli-Z and toric code stabilizer measurements, in addition to random Clifford unitaries, we find a phase diagram involving a tricritical point that maps to (2+1)D percolation, a possibly stable critical phase, topologically ordered, trivial, and volume law phases, and lines of critical points separating them. With Pauli-Y single qubit measurements instead, we find an anisotropic self-dual tricritical point, with dynamical exponent $z \approx 1.46$, exhibiting logarithmic violation of the area law and an anomalous exponent for the topological entanglement entropy, which thus appears distinct from any known percolation fixed point. The phase diagram also hosts a measurement-induced volume law entangled phase in the absence of unitary dynamics.

Related papers

• Quantum entanglement in the multicritical disordered Ising model [0.0]
  entanglement entropy is calculated at the quantum multicritical point of the random transverse-field Ising model. We find a universal logarithmic corner contribution to the area law b*ln(l) that is independent of the form of disorder.
  arXiv  Detail & Related papers  (2024-04-19T16:42:43Z)
• Probing quantum floating phases in Rydberg atom arrays [61.242961328078245]
  We experimentally observe the emergence of the quantum floating phase in 92 neutral-atom qubits. The site-resolved measurement reveals the formation of domain walls within the commensurate ordered phase. As the experimental system sizes increase, we show that the wave vectors approach a continuum of values incommensurate with the lattice.
  arXiv  Detail & Related papers  (2024-01-16T03:26:36Z)
• Majorana Loop Models for Measurement-Only Quantum Circuits [0.0]
  Projective measurements in random quantum circuits lead to a rich breadth of entanglement phases and extend the realm of non-unitary quantum dynamics. Here we explore the connection between measurement-only quantum circuits in one spatial dimension and the statistical mechanics of loop models in two dimensions.
  arXiv  Detail & Related papers  (2023-05-29T18:45:11Z)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• Structured volume-law entanglement in an interacting, monitored Majorana spin liquid [0.0]
  We show that random, measurement-only circuits give rise to a structured volume-law entangled phase with subleading $L ln L$ liquid scaling behavior. The sphere itself is a critical boundary with quantum Lifshitz scaling separating the volume-law phase from proximate area-law phases, a color code or a toric code.
  arXiv  Detail & Related papers  (2023-03-30T18:00:01Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Topological order and entanglement dynamics in the measurement-only XZZX quantum code [0.0]
  We study the dynamics of a $(1+1)$-dimensional measurement-only circuit defined by the stabilizers of the quantum error correcting code. The code corrects arbitrary single-qubit errors and it stabilizes an area law entangled with a $D = mathbbZ times mathbbZ$ symmetry protected topological (SPT) order. The Pauli measurements break the topological order and induce a phase transition into a trivial area law phase.
  arXiv  Detail & Related papers  (2022-04-18T18:00:04Z)
• Topological transitions with continuously monitored free fermions [68.8204255655161]
  We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
  arXiv  Detail & Related papers  (2021-12-17T22:01:54Z)
• Quantum phase transition in the one-dimensional Dicke-Hubbard model with coupled qubits [20.002319486166016]
  We study the ground state phase diagram of a one-dimensional two qubits Dicke-Hubbard model with XY qubit-qubit interaction.
  arXiv  Detail & Related papers  (2021-11-05T13:17:49Z)
• Multipartite entanglement of the topologically ordered state in a perturbed toric code [18.589873789289562]
  We demonstrate that multipartite entanglement, witnessed by the quantum Fisher information (QFI), can characterize topological quantum phase transitions in the spin-$frac12$ toric code model. Our results provide insights to topological phases, which are robust against external disturbances, and are candidates for topologically protected quantum computation.
  arXiv  Detail & Related papers  (2021-09-07T20:20:21Z)
• Measurement-induced topological entanglement transitions in symmetric random quantum circuits [0.0]
  We study a class of (1+1)D symmetric random quantum circuits with two competing types of measurements. The circuit exhibits a rich phase diagram involving robust symmetry-protected topological (SPT), trivial, and volume law entangled phases.
  arXiv  Detail & Related papers  (2020-04-15T18:00:00Z)

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.