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First-Order Circuits01:15

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First-order electrical circuits, which comprise resistors and a single energy storage element - either a capacitor or an inductor, are fundamental to many electronic systems. These circuits are governed by a first-order differential equation that describes the relationship between input and output signals.
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Learning to decode logical circuits.

Yiqing Zhou1, Chao Wan2, Yichen Xu3

  • 1Department of Physics, Cornell University, Ithaca, NY, USA. yz2728@cornell.edu.

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A new Multi-Core Circuit Decoder (MCCD) framework efficiently decodes errors in deep logical quantum circuits. This data-centric approach offers competitive accuracy and faster decoding times compared to traditional methods, addressing a key challenge in quantum computing.

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Area of Science:

  • Quantum Information Science
  • Quantum Error Correction
  • Computational Complexity

Background:

  • Advancing quantum hardware necessitates efficient decoding algorithms for error-corrected quantum circuits.
  • Correlated errors from entangling gates challenge conventional quantum memory decoding methods.
  • A polynomial-time decoding algorithm is critical for realizing fault-tolerant quantum computation.

Purpose of the Study:

  • To introduce a novel, data-centric, modular decoder framework for deep logical quantum circuits.
  • To address the bottleneck of decoding correlated errors introduced by entangling gates.
  • To develop a noise-model-agnostic decoding solution for scalable quantum computing.

Main Methods:

  • Developed the Multi-Core Circuit Decoder (MCCD) framework with modular components for each logical operation.
  • Trained MCCD using mirror-symmetric random Clifford circuits to learn correlated error patterns.
  • Evaluated MCCD performance on deep circuits, comparing accuracy and decoding time against MWPM, MLE, and BP-OSD.

Main Results:

  • MCCD effectively learns and decodes correlated errors in quantum circuits.
  • Maintained high logical accuracy on circuits deeper than those used for training.
  • Achieved competitive accuracy with significantly improved time efficiency, especially for circuits with entangling gates.

Conclusions:

  • The MCCD framework provides an efficient and accurate solution for decoding deep logical quantum circuits.
  • This approach overcomes limitations of traditional decoders, particularly in handling correlated errors.
  • MCCD represents a significant step towards fault-tolerant quantum computation by addressing a critical decoding bottleneck.