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Correlated Decoding of Logical Algorithms with Transversal Gates.

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Quantum error correction is vital for quantum computing. Jointly decoding qubits with correlated decoding significantly reduces the space-time overhead for logical quantum algorithms.

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Area of Science:

  • Quantum Computing
  • Quantum Information Science
  • Error Correction Codes

Background:

  • Scalable quantum computation relies on quantum error correction.
  • High space-time overhead is a major challenge for current quantum error correction methods.
  • Recent experiments show efficient logical qubit manipulation using transversal gates.

Purpose of the Study:

  • To improve the performance of logical quantum algorithms.
  • To reduce the space-time overhead of quantum error correction.
  • To investigate the benefits of correlated decoding for transversal gates.

Main Methods:

  • Jointly decoding qubits to account for error propagation during transversal entangling gates.
  • Exploring two decoders with varying computational runtimes and accuracies.
  • Leveraging deterministic propagation of stabilizer measurement errors.

Main Results:

  • Correlated decoding enhances performance for both Clifford and non-Clifford transversal entangling gates.
  • Reduced noisy syndrome extraction rounds from O(d) to O(1) for transversal Clifford circuits.
  • Substantial reduction in space-time cost for deep logical Clifford circuits verified numerically.

Conclusions:

  • Correlated decoding offers a significant advantage for early fault-tolerant quantum computation.
  • This approach has considerable potential to decrease space-time costs in large-scale logical algorithms.
  • The findings align with and extend recent experimental advancements in quantum computing.