Low-overhead non-Clifford topological fault-tolerant circuits for all non-chiral abelian topological phases

• URL: http://arxiv.org/abs/2403.12119v1
• Date: Mon, 18 Mar 2024 18:00:00 GMT
• Title: Low-overhead non-Clifford topological fault-tolerant circuits for all non-chiral abelian topological phases
• Authors: Andreas Bauer,
• Abstract summary: Family of explicit geometrically local circuits realizing any abelian non-chiral topological phase as an actively error-corrected fault-tolerant memory. circuits are constructed from measuring 1-form symmetries in discrete fixed-point path integrals. We prove fault tolerance under arbitrary local (including non-Pauli) noise for a very general class of topological circuits that we call 1-form symmetric fixed-point circuits.
• Score: 0.7873629568804646
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a family of explicit geometrically local circuits realizing any abelian non-chiral topological phase as an actively error-corrected fault-tolerant memory. These circuits are constructed from measuring 1-form symmetries in discrete fixed-point path integrals, which we express through cellular cohomology and higher-order cup products. The specific path integral we use is the abelian Dijkgraaf-Witten state sum on a 3-dimensional cellulation, which is a spacetime representation of the twisted quantum double model. The resulting circuits are based on a syndrome extraction circuit of the (qudit) stabilizer toric code, into which we insert non-Clifford phase gates that implement the ``twist''. The overhead compared to the toric code is moderate, in contrast to known constructions for twisted abelian phases. We also show that other architectures for the (qudit) toric code phase, like measurement-based topological quantum computation or Floquet codes, can be enriched with phase gates to implement twisted quantum doubles instead of their untwisted versions. As a further result, we prove fault tolerance under arbitrary local (including non-Pauli) noise for a very general class of topological circuits that we call 1-form symmetric fixed-point circuits. This notion unifies the circuits in this paper as well as the stabilizer toric code, subsystem toric code, measurement-based topological quantum computation, or the (CSS) honeycomb Floquet code. We also demonstrate how our method can be adapted to construct fault-tolerant circuits for specific non-Abelian phases. In the appendix we present an explicit combinatorial procedure to define formulas for higher cup products on arbitrary cellulations, which might be interesting in its own right to the TQFT and topological-phases community.

Related papers

• Measurement Quantum Cellular Automata and Anomalies in Floquet Codes [3.1170271760249806]
  We investigate the evolution of quantum information under Pauli measurement circuits. We define local reversibility in context of measurement circuits. We prove that the Hastings-Haah honeycomb code belongs to a class with such obstruction.
  arXiv  Detail & Related papers  (2023-04-03T18:10:59Z)
• Topological error correcting processes from fixed-point path integrals [0.7873629568804646]
  We analyze and construct topological quantum error correcting codes as dynamical circuits of geometrically local channels and measurements. We derive two new error-correcting codes, namely a Floquet version of the $3+1$-dimensional toric code using only 2-body measurements, and a dynamic code based on the double-semion string-net path integral.
  arXiv  Detail & Related papers  (2023-03-29T02:32:18Z)
• Non-local finite-depth circuits for constructing SPT states and quantum cellular automata [0.24999074238880484]
  We show how to implement arbitrary translationally invariant quantum cellular automata in any dimension using finite-depth circuits of $k$-local gates. Our results imply that the topological classifications of SPT phases and QCA both collapse to a single trivial phase in the presence of $k$-local interactions.
  arXiv  Detail & Related papers  (2022-12-13T19:00:00Z)
• Crystalline Quantum Circuits [0.0]
  Random quantum circuits continue to inspire a wide range of applications in quantum information science and many-body quantum physics. Motivated by an interest in deterministic circuits with similar applications, we construct classes of textitnonrandom unitary Clifford circuits. A full classification on the square lattice reveals, of particular interest, a "nonfractal good scrambling class" with dense operator spreading.
  arXiv  Detail & Related papers  (2022-10-19T18:00:57Z)
• Adaptive constant-depth circuits for manipulating non-abelian anyons [65.62256987706128]
  Kitaev's quantum double model based on a finite group $G$. We describe quantum circuits for (a) preparation of the ground state, (b) creation of anyon pairs separated by an arbitrary distance, and (c) non-destructive topological charge measurement.
  arXiv  Detail & Related papers  (2022-05-04T08:10:36Z)
• Quantum Error Correction with Gauge Symmetries [69.02115180674885]
  Quantum simulations of Lattice Gauge Theories (LGTs) are often formulated on an enlarged Hilbert space containing both physical and unphysical sectors. We provide simple fault-tolerant procedures that exploit such redundancy by combining a phase flip error correction code with the Gauss' law constraint.
  arXiv  Detail & Related papers  (2021-12-09T19:29:34Z)
• Finding the disjointness of stabilizer codes is NP-complete [77.34726150561087]
  We show that the problem of calculating the $c-disjointness, or even approximating it to within a constant multiplicative factor, is NP-complete. We provide bounds on the disjointness for various code families, including the CSS codes,$d codes and hypergraph codes. Our results indicate that finding fault-tolerant logical gates for generic quantum error-correcting codes is a computationally challenging task.
  arXiv  Detail & Related papers  (2021-08-10T15:00:20Z)
• Decodable hybrid dynamics of open quantum systems with Z_2 symmetry [0.0]
  We explore a class of "open" quantum circuit models with local decoherence ("noise") and local projective measurements. Within the spin glass phase the circuit dynamics can be interpreted as a quantum repetition code. We devise a novel decoding algorithm for recovering an arbitrary initial qubit state in the code space.
  arXiv  Detail & Related papers  (2021-08-09T18:07:55Z)
• 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)
• Efficient simulatability of continuous-variable circuits with large Wigner negativity [62.997667081978825]
  Wigner negativity is known to be a necessary resource for computational advantage in several quantum-computing architectures. We identify vast families of circuits that display large, possibly unbounded, Wigner negativity, and yet are classically efficiently simulatable. We derive our results by establishing a link between the simulatability of high-dimensional discrete-variable quantum circuits and bosonic codes.
  arXiv  Detail & Related papers  (2020-05-25T11:03:42Z)
• Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit [62.997667081978825]
  We present a circuit design composed of a non-reciprocal device and Josephson junctions whose ground space is doubly degenerate and the ground states are approximate codewords of the Gottesman-Kitaev-Preskill (GKP) code. We find that the circuit is naturally protected against the common noise channels in superconducting circuits, such as charge and flux noise, implying that it can be used for passive quantum error correction.
  arXiv  Detail & Related papers  (2020-02-18T16:45:09Z)

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.