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Constant-Overhead Quantum Error Correction with Thin Planar Connectivity.

Maxime A Tremblay1, Nicolas Delfosse2, Michael E Beverland2

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Quantum low density parity check (LDPC) codes offer a path to fault-tolerant quantum computing. This study introduces a novel 2D layout for quantum LDPC codes, reducing qubit overhead and crosstalk for efficient hardware implementation.

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Area of Science:

  • Quantum Information Science
  • Quantum Error Correction
  • Computer Engineering

Background:

  • General quantum low-density parity-check (LDPC) codes lack geometric constraints, leading to complex layouts with problematic crosstalk in hardware implementations.
  • Efficient fault-tolerant quantum computers require low-overhead quantum error correction codes.

Purpose of the Study:

  • To propose a novel 2D layout for quantum LDPC codes that overcomes the limitations of general LDPC code layouts.
  • To enable the development of low-overhead, fault-tolerant quantum computers by minimizing hardware complexity and crosstalk.

Main Methods:

  • Decomposition of quantum LDPC code Tanner graphs into a small number of planar layers.
  • Design of stabilizer measurement circuits with optimized depth and layer count for Calderbank-Shor-Steane codes.
  • Analysis of circuit-noise thresholds and logical error rates for a specific quantum LDPC code family.

Main Results:

  • A 2D layout is presented where each planar layer features non-crossing, long-range connections.
  • Stabilizer measurement circuits achieve a depth of at most (2δ+2) using at most ⌈δ/2⌉ layers for degree-δ Tanner graphs.
  • A circuit-noise threshold of 0.28% is observed for a positive-rate code family.
  • A logical error rate of 10⁻¹⁵ is achieved with 49 physical qubits per logical qubit for a physical error rate of 10⁻⁴.

Conclusions:

  • The proposed 2D layout significantly reduces the number of physical qubits required compared to surface codes, achieving high error suppression.
  • This approach offers a promising strategy for building more efficient and practical fault-tolerant quantum computers.