Syndrome Recovery Feedback - Noro-Official/OQS GitHub Wiki

Syndrome, Recovery, Feedback

Quantum error correction is not just about encoding qubits—it’s about responding to noise intelligently and reversibly. That’s where syndrome extraction, decoding, and feedback-based recovery come in.

What is a Syndrome?

A syndrome is a classical measurement result that tells you where or what kind of error has occurred—without collapsing the quantum information itself.

You get it by measuring stabilizers or parity checks.
For example, in the 3-qubit bit-flip code, we can check:

  • Qubit 1 ⊕ Qubit 2
  • Qubit 2 ⊕ Qubit 3

These checks yield two classical bits: the syndrome.

How Recovery Works

Once a syndrome is measured, a decoder interprets the result and determines the appropriate recovery operation.

In OpenQStack:

  • The syndrome is returned as a bitstring (e.g. "010")
  • A majority-vote decoder decides which qubit likely flipped
  • A corrective X gate is applied to restore the logical state

This is quantum feedback control: classical data from quantum measurements is used to inform a conditional operation—without destroying the underlying state.

Feedback Loop Summary

  1. Start with a logical qubit (e.g., |ψ⟩ = α|0⟩ + β|1⟩)
  2. Encode into multiple physical qubits
  3. Noise perturbs one or more qubits
  4. Parity checks extract a syndrome
  5. A decoder maps that syndrome to a correction
  6. The system is restored, and decoding returns the logical state

OpenQStack Implementation

The following functions implement this loop:

  • measure_syndrome(state)
    Returns a bitstring from inferred parity

  • recover(state, syndrome)
    Applies a correction based on majority logic

  • decode(state)
    Projects the recovered state back to logical space

Try editing examples/openq_blink.py to print the syndrome and verify the decoded state manually.

Advanced Recovery Topics

OpenQStack is structured to support more sophisticated recovery mechanisms:

  • Minimum-Weight Perfect Matching (MWPM)
  • Lookup tables for small codes
  • Machine learning–based decoders
  • Fault-tolerant recovery with ancilla measurement feedback

Learn More