Benchmarking a Custom Decoder for Steane Code (7-Qubit)

To evaluate the performance of a custom quantum error decoder in comparison with a pre-built lookup table decoder, using the 7-qubit Steane Code. The experiment includes noise simulation, syndrome extraction, decoding, and benchmarking based on logical fidelity and decoding latency. We have used Steane Code (7-Qubit) Quantum Error Correction Experiment as our base and added custom decoder in that experiment

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Components Used:

Quantum Error Correction Code:

• Code: Steane Code (7-Qubit)
• Stabilizers: 6 total (3 X-type, 3 Z-type)
• Code Distance: 3
• Rounds of Encoding: 1

Initial Logical Qubit:

• |+⟩ state (superposition of |0⟩ and |1⟩)

Noise Model:

• Gate Noise: Depolarizing Channel

  • Probability: 0.05

• Measurement Noise:

  • Probability: 0.01

Custom Decoder

ML-based decoder

• architecture: Feedforward Neural Network
• training_data_size: 10,000 noisy syndrome samples
• loss_metric: Categorical Cross-Entropy
• optimizer: Adam
• inference_latency: Tracked per shot

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Experimental Procedure:

1. Initialization Prepare logical qubit |+⟩ and encode using Steane Code.

2. Noise Injection Apply simulated gate-level depolarizing noise and measurement noise.

3. Syndrome Extraction Measure stabilizer generators to obtain syndrome.

4. Decoding Run both:

   • Lookup Table decoder (baseline)
   • Custom decoder (inference from trained model)

5. Recovery Apply corrections from both decoders.

6. Benchmarking Compare both decoders over 1000 trials using:

   • Logical Fidelity
   • Latency per decoding step
   • Accuracy of correction (how often logical error is prevented)

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Output:

{
  "decoder_results": {
    "lookup_table": {
      "logical_fidelity": 0.91,
      "average_latency_ms": 0.04,
      "correction_success_rate": 0.91
    },
    "custom_decoder": {
      "logical_fidelity": 0.94,
      "average_latency_ms": 0.10,
      "correction_success_rate": 0.94
    }
  },
  "benchmark_summary": {
    "winner": "custom_decoder",
    "justification": "Higher logical fidelity and correction rate despite higher latency"
  }
}

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Conclusion:

The custom decoder outperforms the baseline in terms of logical fidelity and error correction success rate. However, it trades off some latency. This makes it ideal for high-fidelity systems where correction accuracy is critical.