Cellular automaton decoders for topological quantum codes with noisy measurements and beyond

• URL: http://arxiv.org/abs/2004.07247v2
• Date: Mon, 25 Jan 2021 17:50:40 GMT
• Title: Cellular automaton decoders for topological quantum codes with noisy measurements and beyond
• Authors: Michael Vasmer, Dan E. Browne, Aleksander Kubica
• Abstract summary: We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes. For simplicity, we focus on the three-dimensional (3D) toric code on the rhombic dodecahedral lattice with boundaries and prove that the resulting local decoder has a non-zero error threshold. We find that this error correction procedure is remarkably robust against measurement errors and is also essentially insensitive to the details of the lattice and noise model.
• Score: 68.8204255655161
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes. For simplicity, however, we focus on the three-dimensional (3D) toric code on the rhombic dodecahedral lattice with boundaries and prove that the resulting local decoder has a non-zero error threshold. We also numerically benchmark the performance of the decoder in the setting with measurement errors using various noise models. We find that this error correction procedure is remarkably robust against measurement errors and is also essentially insensitive to the details of the lattice and noise model. Our work constitutes a step towards finding simple and high-performance decoding strategies for a wide range of quantum low-density parity-check codes.

Related papers

• Fault-Tolerant Quantum Memory using Low-Depth Random Circuit Codes [0.24578723416255752]
  Low-depth random circuit codes possess many desirable properties for quantum error correction. We design a fault-tolerant distillation protocol for preparing encoded states of one-dimensional random circuit codes. We show through numerical simulations that our protocol can correct erasure errors up to an error rate of $2%$.
  arXiv  Detail & Related papers  (2023-11-29T19:00:00Z)
• Testing the Accuracy of Surface Code Decoders [55.616364225463066]
  Large-scale, fault-tolerant quantum computations will be enabled by quantum error-correcting codes (QECC) This work presents the first systematic technique to test the accuracy and effectiveness of different QECC decoding schemes.
  arXiv  Detail & Related papers  (2023-11-21T10:22:08Z)
• The END: An Equivariant Neural Decoder for Quantum Error Correction [73.4384623973809]
  We introduce a data efficient neural decoder that exploits the symmetries of the problem. We propose a novel equivariant architecture that achieves state of the art accuracy compared to previous neural decoders.
  arXiv  Detail & Related papers  (2023-04-14T19:46:39Z)
• Improved decoding of circuit noise and fragile boundaries of tailored surface codes [61.411482146110984]
  We introduce decoders that are both fast and accurate, and can be used with a wide class of quantum error correction codes. Our decoders, named belief-matching and belief-find, exploit all noise information and thereby unlock higher accuracy demonstrations of QEC. We find that the decoders led to a much higher threshold and lower qubit overhead in the tailored surface code with respect to the standard, square surface code.
  arXiv  Detail & Related papers  (2022-03-09T18:48:54Z)
• Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements [58.720142291102135]
  We analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit. We find that with the currently achievable measurement efficiencies in microwave optics, bosonic rotation codes undergo a substantial decrease in their break-even potential.
  arXiv  Detail & Related papers  (2021-08-02T16:12:13Z)
• Efficient Concatenated Bosonic Code for Additive Gaussian Noise [0.0]
  Bosonic codes offer noise resilience for quantum information processing. We propose using a Gottesman-Kitaev-Preskill code to detect discard error-prone qubits and a quantum parity code to handle residual errors. Our work may have applications in a wide range of quantum computation and communication scenarios.
  arXiv  Detail & Related papers  (2021-02-02T08:01:30Z)
• Efficient and robust certification of genuine multipartite entanglement in noisy quantum error correction circuits [58.720142291102135]
  We introduce a conditional witnessing technique to certify genuine multipartite entanglement (GME) We prove that the detection of entanglement in a linear number of bipartitions by a number of measurements scales linearly, suffices to certify GME. We apply our method to the noisy readout of stabilizer operators of the distance-three topological color code and its flag-based fault-tolerant version.
  arXiv  Detail & Related papers  (2020-10-06T18:00:07Z)
• Efficiently computing logical noise in quantum error correcting codes [0.0]
  We show that measurement errors on readout qubits manifest as a renormalization on the effective logical noise. We derive general methods for reducing the computational complexity of the exact effective logical noise by many orders of magnitude.
  arXiv  Detail & Related papers  (2020-03-23T19:40:56Z)
• Correcting spanning errors with a fractal code [7.6146285961466]
  We propose an efficient decoder for the Fibonacci code'; a two-dimensional classical code that mimics the fractal nature of the cubic code. We perform numerical experiments that show our decoder is robust to one-dimensional, correlated errors.
  arXiv  Detail & Related papers  (2020-02-26T19:00:06Z)

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.