Local tensor-network codes

• URL: http://arxiv.org/abs/2109.11996v1
• Date: Fri, 24 Sep 2021 14:38:06 GMT
• Title: Local tensor-network codes
• Authors: Terry Farrelly, David K. Tuckett, Thomas M. Stace
• Abstract summary: We show how to write some topological codes, including the surface code and colour code, as simple tensor-network codes. We prove that this method is efficient in the case of holographic codes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Tensor-network codes enable the construction of large stabilizer codes out of tensors describing smaller stabilizer codes. An application of tensor-network codes was an efficient and exact decoder for holographic codes. Here, we show how to write some topological codes, including the surface code and colour code, as simple tensor-network codes. We also show how to calculate distances of stabilizer codes by contracting a tensor network. The algorithm actually gives more information, including a histogram of all logical coset weights. We prove that this method is efficient in the case of holographic codes. Using our tensor-network distance calculator, we find a modification of the rotated surface code that has the same distance but fewer minimum-weight logical operators by injecting the non-CSS five-qubit code tensor into the tensor network. This corresponds to an improvement in successful error correction of up to 2% against depolarizing noise (in the perfect-measurement setting), but comes at the cost of introducing four higher-weight stabilizers. Our general construction lets us pick a network geometry (e.g., a Euclidean lattice in the case of the surface code), and, using only a small set of seed codes (constituent tensors), build extensive codes with the potential for optimisation.

Related papers

• Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes [38.729065908701585]
  We introduce a new class of qubit codes that we call Evenbly codes. Our work indicates that Evenbly codes may show promise for practical quantum computing applications.
  arXiv  Detail & Related papers  (2024-07-16T17:18:13Z)
• SSIP: automated surgery with quantum LDPC codes [55.2480439325792]
  We present Safe Surgery by Identifying Pushouts (SSIP), an open-source lightweight Python package for automating surgery between qubit CSS codes. Under the hood, it performs linear algebra over $mathbbF$ governed by universal constructions in the category of chain complexes. We show that various logical measurements can be performed cheaply by surgery without sacrificing the high code distance.
  arXiv  Detail & Related papers  (2024-07-12T16:50:01Z)
• CSS code surgery as a universal construction [51.63482609748332]
  We define code maps between Calderbank-Shor-Steane (CSS) codes using maps between chain complexes. We describe code surgery between such codes using a specific colimit in the category of chain complexes.
  arXiv  Detail & Related papers  (2023-01-31T16:17:25Z)
• Near-Linear Time and Fixed-Parameter Tractable Algorithms for Tensor Decompositions [51.19236668224547]
  We study low rank approximation of tensors, focusing on the tensor train and Tucker decompositions. For tensor train decomposition, we give a bicriteria $(1 + eps)$-approximation algorithm with a small bicriteria rank and $O(q cdot nnz(A))$ running time. In addition, we extend our algorithm to tensor networks with arbitrary graphs.
  arXiv  Detail & Related papers  (2022-07-15T11:55:09Z)
• Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks [0.0]
  We represent complex code constructions as tensor networks built from the tensors of simple codes or states. The framework endows a network geometry to any code it builds and is valid for constructing stabilizer codes. We lay out some examples where we glue together simple stabilizer codes to construct non-trivial codes.
  arXiv  Detail & Related papers  (2021-09-16T18:00:00Z)
• KO codes: Inventing Nonlinear Encoding and Decoding for Reliable Wireless Communication via Deep-learning [76.5589486928387]
  Landmark codes underpin reliable physical layer communication, e.g., Reed-Muller, BCH, Convolution, Turbo, LDPC and Polar codes. In this paper, we construct KO codes, a computationaly efficient family of deep-learning driven (encoder, decoder) pairs. KO codes beat state-of-the-art Reed-Muller and Polar codes, under the low-complexity successive cancellation decoding.
  arXiv  Detail & Related papers  (2021-08-29T21:08:30Z)
• LLC: Accurate, Multi-purpose Learnt Low-dimensional Binary Codes [55.32790803903619]
  We propose a novel method for Learning Low-dimensional binary Codes (LLC) for instances as well as classes. Our method does not require any side-information, like annotated attributes or label meta-data. We demonstrate that the learnt codes capture intrinsically important features in the data, by discovering an intuitive taxonomy over classes.
  arXiv  Detail & Related papers  (2021-06-02T21:57:52Z)
• Cherry-Picking Gradients: Learning Low-Rank Embeddings of Visual Data via Differentiable Cross-Approximation [53.95297550117153]
  We propose an end-to-end trainable framework that processes large-scale visual data tensors by looking emphat a fraction of their entries only. The proposed approach is particularly useful for large-scale multidimensional grid data, and for tasks that require context over a large receptive field.
  arXiv  Detail & Related papers  (2021-05-29T08:39:57Z)
• General tensor network decoding of 2D Pauli codes [0.0]
  We propose a decoder that approximates maximally likelihood decoding for 2D stabiliser and subsystem codes subject to Pauli noise. We numerically demonstrate the power of this decoder by studying four classes of codes under three noise models. We show that the thresholds yielded by our decoder are state-of-the-art, and numerically consistent with optimal thresholds where available.
  arXiv  Detail & Related papers  (2021-01-11T19:00:03Z)
• Parallel decoding of multiple logical qubits in tensor-network codes [0.0]
  We consider tensor-network stabilizer codes and show that their tensor-network decoder has the property that independent logical qubits can be decoded in parallel. As an application, we verify this for the max-rate holographic Steane (heptagon) code.
  arXiv  Detail & Related papers  (2020-12-14T07:58:16Z)
• Tensor-network codes [0.0]
  We introduce tensor-network stabilizer codes which come with a natural tensor-network decoder. We generalize holographic codes beyond those constructed from perfect or block-perfect isometries. For holographic codes exact the tensor-network decoder is efficient with a complexity that is in the number of physical qubits.
  arXiv  Detail & Related papers  (2020-09-22T05:44:50Z)

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.