Noise and Quantum Error Correction¶

Tested with: Quanta SDK v0.8.1

What You'll Learn¶

Understand why quantum errors happen and how error correction codes protect computations.

Prerequisites¶

03 — Simulation

Why QEC?¶

Real quantum hardware has ~0.1-1% gate error and ~1-2% readout error. Without error correction, a 100-gate circuit has ~60% chance of at least one error. QEC codes detect and correct these errors.

Available Codes¶

Code	Notation	Physical Qubits	Logical Qubits	Correctable Errors
BitFlip	[[3,1,3]]	3	1	1 bit-flip
PhaseFlip	[[3,1,3]]	3	1	1 phase-flip
Steane	[[7,1,3]]	7	1	1 arbitrary
Surface	[[d²,1,d]]	d²	1	⌊(d-1)/2⌋
Color	transversal	varies	1	distance-based

BitFlip Code — Simplest Example¶

from quanta.qec.codes import BitFlipCode

code = BitFlipCode()
print(f"Code: {code.info}")
# [[3,1,3]] BitFlip — 1 errors correctable

# Build the encoding circuit
enc = code.encode()
print(f"Encoding circuit: {enc.num_qubits} qubits")

Steane Code — Full Error Correction¶

from quanta.qec.codes import SteaneCode

steane = SteaneCode()
print(f"Code: {steane.info}")
# [[7,1,3]] Steane — 1 errors correctable

enc = steane.encode()
print(f"Steane encoding: {enc.num_qubits} physical qubits")

Understanding Code Parameters¶

[[n, k, d]]
  n = physical qubits needed
  k = logical qubits encoded
  d = code distance (minimum weight of undetectable error)

Correctable errors = ⌊(d-1)/2⌋

Example: Steane [[7,1,3]] uses 7 physical qubits to encode 1 logical qubit with distance 3, correcting 1 arbitrary error.

QEC Decoders¶

Decoder	Complexity	Best For
MWPM	O(n³)	High accuracy
Union-Find	O(n·α(n))	Real-time decoding

Noise + QEC Pipeline¶

The full pipeline: encode → apply gates → inject noise → decode → measure:

from quanta import circuit, H, CX, measure, run
from quanta.simulator.noise import NoiseModel, BitFlip

# Without QEC: noise corrupts the result
noise = NoiseModel().add(BitFlip(probability=0.05))

@circuit(qubits=2)
def bell(q):
    H(q[0])
    CX(q[0], q[1])
    return measure(q)

# Noisy result — observe error states
result = run(bell, shots=4096, noise=noise)
p_error = 1 - (result.counts.get("00", 0) + result.counts.get("11", 0)) / 4096
print(f"Error rate without QEC: {p_error:.1%}")

Try It Yourself¶

Compare BitFlipCode vs PhaseFlipCode — when would you use each?
Run a Bell state with different noise levels — at what point does fidelity drop below 90%?
Look at SteaneCode.encode() — how many gates does it use?

What's Next¶

→ 08 — MCP AI Integration: Use Quanta from Claude, GPT, and other AI assistants