Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond

• URL: http://arxiv.org/abs/2202.05442v1
• Date: Fri, 11 Feb 2022 04:41:37 GMT
• Title: Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond
• Authors: Wilbur Shirley, Yu-An Chen, Arpit Dua, Tyler D. Ellison, Nathanan Tantivasadakarn, Dominic J. Williamson
• Abstract summary: We construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We show that the resulting Hamiltonian hosts chiral semion surface topological order in the presence of a boundary and can be realized as a non-Pauli stabilizer code on qubits.
• Score: 2.554567149842799
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e. not a finite-depth circuit of local quantum gates, or there exists a two-dimensional commuting projector Hamiltonian realizing the chiral semion topological order (characterized by $U(1)_2$ Chern-Simons theory). Our QCA is obtained by first constructing the Walker-Wang Hamiltonian of a certain premodular tensor category of order four, then condensing the deconfined bulk boson at the level of lattice operators. We show that the resulting Hamiltonian hosts chiral semion surface topological order in the presence of a boundary and can be realized as a non-Pauli stabilizer code on qubits, from which the QCA is defined. The construction is then generalized to a class of QCAs defined by non-Pauli stabilizer codes on ${2^n}$-dimensional qudits that feature surface anyons described by $U(1)_{2^n}$ Chern-Simons theory. Our results support the conjecture that the group of nontrivial three-dimensional QCAs is isomorphic to the Witt group of non-degenerate braided fusion categories.

Related papers

• Entanglement renormalization of fractonic anisotropic $\mathbb{Z}_N$ Laplacian models [4.68169911641046]
  Gapped fracton phases constitute a new class of quantum states of matter which connects to topological orders but does not fit easily into existing paradigms. We investigate the anisotropic $mathbbZ_N$ Laplacian model which can describe a family of fracton phases defined on arbitrary graphs.
  arXiv  Detail & Related papers  (2024-09-26T18:36:23Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Topological fracton quantum phase transitions by tuning exact tensor network states [1.0753191494611891]
  Gapped fracton phases of matter generalize the concept of topological order. We employ an exact 3D quantum tensor-network approach to study a prototypical X cube fracton model.
  arXiv  Detail & Related papers  (2022-02-28T19:00:01Z)
• Towards a complete classification of non-chiral topological phases in 2D fermion systems [29.799668287091883]
  We argue that all non-chiral fermionic topological phases in 2+1D are characterized by a set of tensors $(Nij_k,Fij_k,Fijm,alphabeta_kln,chidelta,n_i,d_i)$. Several examples with q-type anyon excitations are discussed, including the Fermionic topological phase from Tambara-gami category for $mathbbZ_2N$.
  arXiv  Detail & Related papers  (2021-12-12T03:00:54Z)
• Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies [3.9752110899603053]
  We present Hamiltonian models for bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions. Examples include the beyond group cohomology invertible phase without symmetry in (4+1)D that has an anomalous boundary $mathbbZ$ topological order. We argue that this construction gives a new non-trivial quantum cellular automaton (QCA) in (4+1)D of order two.
  arXiv  Detail & Related papers  (2021-10-27T18:00:00Z)
• 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)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Investigating a (3+1)D Topological $\theta$-Term in the Hamiltonian Formulation of Lattice Gauge Theories for Quantum and Classical Simulations [0.0]
  We derive the (3+1)D topological $theta$-term for Abelian and non-Abelian lattice gauge theories. We study numerically the zero-temperature phase structure of a (3+1)D U(1) lattice gauge theory.
  arXiv  Detail & Related papers  (2021-05-13T01:10:42Z)
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics [58.720142291102135]
  We propose quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions. We show that our system exhibits topologicalband structures under appropriate conditions.
  arXiv  Detail & Related papers  (2020-08-06T19:58:05Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Lattice Gauge Theory for a Quantum Computer [0.0]
  Hamiltonian was introduced two decades ago as an alternative to Wilson's Euclidean lattice QCD with gauge fields represented by bi-linear fermion/anti-fermion operators. D-theory leads naturally to quantum Qubit algorithms. Digital quantum computing for gauge theories, the simplest example of U(1) compact QED on triangular lattice is defined.
  arXiv  Detail & Related papers  (2020-02-24T01:16:49Z)

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.