Improved QLDPC Surgery: Logical Measurements and Bridging Codes

• URL: http://arxiv.org/abs/2407.18393v3
• Date: Fri, 1 Nov 2024 17:43:15 GMT
• Title: Improved QLDPC Surgery: Logical Measurements and Bridging Codes
• Authors: Andrew Cross, Zhiyang He, Patrick Rall, Theodore Yoder,
• Abstract summary: We introduce the gauge-fixed QLDPC surgery scheme, an improved logical measurement scheme based on the construction of Cohen et al.(Sci.Adv.8, eabn1717). Our scheme leverages expansion properties of the Tanner graph to substantially reduce the space overhead of QLDPC surgery. In certain cases, we only require $Theta(w)$ ancilla qubits to fault-tolerantly measure a weight $w$ logical operator.
• Score: 0.568907503750523
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we introduce the gauge-fixed QLDPC surgery scheme, an improved logical measurement scheme based on the construction of Cohen et al.~(Sci.~Adv.~8, eabn1717). Our scheme leverages expansion properties of the Tanner graph to substantially reduce the space overhead of QLDPC surgery. In certain cases, we only require $\Theta(w)$ ancilla qubits to fault-tolerantly measure a weight $w$ logical operator. We provide rigorous analysis for the code distance and fault distance of our schemes, and present a modular decoding algorithm that achieves maximal fault-distance. We further introduce a bridge system to facilitate fault-tolerant joint measurements of logical operators. Augmented by this bridge construction, our scheme can be used to connect different families of QLDPC codes into one universal architecture. Applying our toolbox, we show how to perform all logical Clifford gates on the [[144,12,12]] bivariate bicycle code. Our scheme adds 103 ancilla qubits into the connectivity graph, and one of the twelve logical qubits is used as an ancilla for gate synthesis. Logical measurements are combined with the automorphism gates studied by Bravyi et al.~(Nature 627, 778-782) to implement 288 Pauli product measurements. We demonstrate the practicality of our scheme through circuit-level noise simulations, leveraging our proposed modular decoder that combines BPOSD with matching.

Related papers

• Geometric structure and transversal logic of quantum Reed-Muller codes [51.11215560140181]
  In this paper, we aim to characterize the gates of quantum Reed-Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. A set of stabilizer generators for a RM code can be described via $X$ and $Z$ operators acting on subcubes of particular dimensions.
  arXiv  Detail & Related papers  (2024-10-10T04:07:24Z)
• Efficient fault-tolerant code switching via one-way transversal CNOT gates [0.0]
  We present a code scheme that respects the constraints of FT circuit design by only making use of switching gates. We analyze application of the scheme to low-distance color codes, which are suitable for operation in existing quantum processors. We discuss how the scheme can be implemented with a large degree of parallelization, provided that logical auxiliary qubits can be prepared reliably enough.
  arXiv  Detail & Related papers  (2024-09-20T12:54:47Z)
• Toward a 2D Local Implementation of Quantum LDPC Codes [1.1936126505067601]
  Geometric locality is an important theoretical and practical factor for quantum low-density parity-check (qLDPC) codes. We present an error correction protocol built on a bilayer architecture that aims to reduce operational overheads when restricted to 2D local gates.
  arXiv  Detail & Related papers  (2024-04-26T19:48:07Z)
• Fault-tolerant quantum computing with the parity code and noise-biased qubits [0.0]
  We present a fault-tolerant universal quantum computing architecture based on a code concatenation of noise-biased qubits and the parity architecture. The parity architecture can be understood as a LDPC code tailored specifically to obtain any desired logical connectivity from nearest neighbor physical interactions.
  arXiv  Detail & Related papers  (2024-04-17T12:49:31Z)
• Deep Learning Assisted Multiuser MIMO Load Modulated Systems for Enhanced Downlink mmWave Communications [68.96633803796003]
  This paper is focused on multiuser load modulation arrays (MU-LMAs) which are attractive due to their low system complexity and reduced cost for millimeter wave (mmWave) multi-input multi-output (MIMO) systems. The existing precoding algorithm for downlink MU-LMA relies on a sub-array structured (SAS) transmitter which may suffer from decreased degrees of freedom and complex system configuration. In this paper, we conceive an MU-LMA system employing a full-array structured (FAS) transmitter and propose two algorithms accordingly.
  arXiv  Detail & Related papers  (2023-11-08T08:54:56Z)
• Measurement-free fault-tolerant quantum error correction in near-term devices [0.0]
  We provide a novel scheme to perform QEC cycles without the need of measuring qubits. We benchmark logical failure rates of the scheme in comparison to a flag-qubit based EC cycle. We outline how our scheme could be implemented in ion traps and with neutral atoms in a tweezer array.
  arXiv  Detail & Related papers  (2023-07-25T07:22:23Z)
• Homological Quantum Rotor Codes: Logical Qubits from Torsion [51.9157257936691]
  homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code. We show that the $0$-$pi$-qubit as well as Kitaev's current-mirror qubit are indeed small examples of such codes.
  arXiv  Detail & Related papers  (2023-03-24T00:29:15Z)
• Hierarchical memories: Simulating quantum LDPC codes with local gates [0.05156484100374058]
  Constant-rate low-density parity-check (LDPC) codes are promising candidates for constructing efficient fault-tolerant quantum memories. We construct a new family of hierarchical codes, that encode a number of logical qubits K = Omega(N/log(N)2. Under conservative assumptions, we find that the hierarchical code outperforms the basic encoding where all logical qubits are encoded in the surface code.
  arXiv  Detail & Related papers  (2023-03-08T18:48:12Z)
• Logical blocks for fault-tolerant topological quantum computation [55.41644538483948]
  We present a framework for universal fault-tolerant logic motivated by the need for platform-independent logical gate definitions. We explore novel schemes for universal logic that improve resource overheads. Motivated by the favorable logical error rates for boundaryless computation, we introduce a novel computational scheme.
  arXiv  Detail & Related papers  (2021-12-22T19:00:03Z)
• Software mitigation of coherent two-qubit gate errors [55.878249096379804]
  Two-qubit gates are important components of quantum computing. But unwanted interactions between qubits (so-called parasitic gates) can degrade the performance of quantum applications. We present two software methods to mitigate parasitic two-qubit gate errors.
  arXiv  Detail & Related papers  (2021-11-08T17:37:27Z)
• 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)

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.