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We introduce many-hypercube codes, a new family of high-rate quantum error-correcting codes. These codes enable efficient parallel gate operations, crucial for high-performance fault-tolerant quantum computing.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Error Correction Codes

Background:

  • Standard quantum error correction methods incur significant resource overheads due to low encoding rates.
  • High-rate quantum codes like quantum low-density parity-check codes offer better rates but struggle with parallel logical gate operations.
  • Existing approaches face challenges in balancing high encoding rates with efficient parallelizability for fault-tolerant quantum computing.

Purpose of the Study:

  • To propose a novel family of high-rate quantum error-detecting codes.
  • To address the limitations of existing codes regarding encoding rates and parallel gate execution.
  • To develop a new class of codes suitable for high-performance fault-tolerant quantum computing.

Main Methods:

  • Introduction of concatenated high-rate small-size quantum error-detecting codes, termed many-hypercube codes.
  • Utilizing a geometrical interpretation of code structure using hypercubes for logical qubits.
  • Development of dedicated decoders and encoders tailored for the many-hypercube code architecture.

Main Results:

  • Achieved high encoding rates, demonstrated by encoding 64 logical qubits into 216 physical ones (30% rate).
  • Enabled parallelizability of logical gates, overcoming a key limitation of previous high-rate codes.
  • Demonstrated high error thresholds, even under a circuit-level noise model, using developed decoders and encoders.

Conclusions:

  • Many-hypercube codes offer a promising solution for high-rate quantum error correction.
  • The proposed codes facilitate efficient parallel gate operations, essential for scalable quantum computation.
  • These advancements pave the way for high-performance fault-tolerant quantum computing systems.