Quantum Error Correction

The QEC module provides automatic quantum error correction as a service. Submit a logical circuit and QCOS compiles it to a fault-tolerant physical circuit using your chosen error correction code, runs syndrome decoding in real time, and returns logically-corrected measurement outcomes.

Why QEC Matters

Near-term QPUs (NISQ devices) have physical error rates of 0.1%–5% per gate. For circuits deeper than ~100 gates, errors accumulate and results become unreliable. QEC encodes each logical qubit into many physical qubits and continuously corrects errors, enabling arbitrarily long computations in principle.

Method	Physical qubits per logical	Overhead	Error threshold
Surface code (distance 3)	9	Low	< 1% physical error rate
Surface code (distance 5)	25	Medium	< 1%
Steane [[7,1,3]]	7	Very low	< 0.1%
Color code	17	Medium	< 0.3%
Shor [[9,1,3]]	9	Low	< 1%

List Supported Codes

GET /api/v1/qec/codes

{
  "codes": [
    {
      "id": "surface_d3",
      "name": "Surface Code (distance 3)",
      "physical_per_logical": 9,
      "threshold_pct": 1.0,
      "supported_backends": ["aws_ionq_aria_1", "ibm_eagle_r3"]
    },
    {
      "id": "steane_7_1_3",
      "name": "Steane [[7,1,3]]",
      "physical_per_logical": 7,
      "threshold_pct": 0.1,
      "supported_backends": ["statevector_sim", "aws_sv1"]
    },
    {
      "id": "shor_9_1_3",
      "name": "Shor [[9,1,3]]",
      "physical_per_logical": 9,
      "threshold_pct": 1.0,
      "supported_backends": ["statevector_sim"]
    }
  ]
}

Compile with QEC

Convert a logical circuit to a fault-tolerant physical circuit (Pauli-based computation compiler):

POST /api/v1/qec/pbc/compile

{
  "circuit": "OPENQASM 2.0; include \"qelib1.inc\"; qreg q[2]; creg c[2]; h q[0]; cx q[0],q[1]; measure q -> c;",
  "code": "surface_d3",
  "backend": "aws_ionq_aria_1"
}

{
  "compile_id": "qec_cmp_001",
  "physical_circuit": "OPENQASM 2.0; ...",
  "physical_qubits_required": 18,
  "logical_qubits": 2,
  "code": "surface_d3",
  "estimated_physical_gates": 4820,
  "estimated_credits": 42.0,
  "warnings": []
}

Run the QEC Pipeline

Compile and execute in one call.

POST /api/v1/qec/pipeline

{
  "circuit": "OPENQASM 2.0; ...",
  "code": "surface_d3",
  "backend": "aws_ionq_aria_1",
  "shots": 1024,
  "decoder": "MWPM"
}

Field	Options	Description
`code`	`surface_d3`, `surface_d5`, `steane_7_1_3`, `shor_9_1_3`	QEC code
`decoder`	`MWPM`, `union_find`, `neural`	Syndrome decoder algorithm

curl -X POST https://api.softquantus.com/api/v1/qec/pipeline \
  -H "Authorization: Bearer $QCOS_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "circuit": "OPENQASM 2.0; include \"qelib1.inc\"; qreg q[2]; creg c[2]; h q[0]; cx q[0],q[1]; measure q -> c;",
    "code": "steane_7_1_3",
    "backend": "statevector_sim",
    "shots": 1024,
    "decoder": "MWPM"
  }'

Syndrome Measurement

During execution, ancilla qubits are measured every syndrome cycle to detect errors without collapsing the logical state. Extract and decode syndromes:

POST /api/v1/qec/syndrome/extract
POST /api/v1/qec/decode

Job-level QEC state is on the job record:

GET /api/v1/qec/jobs/{job_id}

{
  "job_id": "qec_job_abc",
  "cycles": 45,
  "errors_detected": 12,
  "errors_corrected": 12,
  "logical_error_rate": 0.0002,
  "decoder": "MWPM",
  "decoder_latency_us": 1.2
}

Python Example — Fault-Tolerant Bell State

import os
import time
import requests

API_KEY = os.environ["QCOS_API_KEY"]
BASE_URL = "https://api.softquantus.com"
HEADERS = {"Authorization": f"Bearer {API_KEY}", "Content-Type": "application/json"}

bell_circuit = (
    'OPENQASM 2.0; include "qelib1.inc"; '
    'qreg q[2]; creg c[2]; '
    'h q[0]; cx q[0],q[1]; measure q -> c;'
)

# Step 1: Compile to fault-tolerant physical circuit
cmp = requests.post(
    f"{BASE_URL}/api/v1/qec/pbc/compile",
    headers=HEADERS,
    json={"circuit": bell_circuit, "code": "steane_7_1_3", "backend": "statevector_sim"}
)
cmp.raise_for_status()
info = cmp.json()
print(f"Compiled: {info['logical_qubits']} logical → {info['physical_qubits_required']} physical qubits")
print(f"Physical gates: {info['estimated_physical_gates']}")

# Step 2: Run the QEC pipeline
resp = requests.post(
    f"{BASE_URL}/api/v1/qec/pipeline",
    headers=HEADERS,
    json={
        "circuit": bell_circuit,
        "code": "steane_7_1_3",
        "backend": "statevector_sim",
        "shots": 2048,
        "decoder": "MWPM"
    }
)
resp.raise_for_status()
job_id = resp.json()["job_id"]
print(f"Pipeline started: {job_id}")

# Poll
while True:
    s = requests.get(f"{BASE_URL}/api/v1/qec/jobs/{job_id}", headers=HEADERS).json()
    if s["status"] in ("completed", "failed"):
        break
    time.sleep(5)

# Results arrive on the job record
r = requests.get(f"{BASE_URL}/api/v1/qec/jobs/{job_id}", headers=HEADERS).json()
print(f"\nLogical results: {r['logical_counts']}")
print(f"Logical error rate: {r['logical_error_rate']:.6f}")
print(f"Physical error rate (raw): {r['physical_error_rate']:.6f}")
print(f"Improvement factor: {r['physical_error_rate']/max(r['logical_error_rate'],1e-9):.1f}x")

Probabilistic Braiding Compilation (PBC)

For topological codes (surface code), QCOS supports probabilistic braiding compilation, which constructs fault-tolerant gates through anyon braiding operations.

POST /api/v1/qec/pbc/compile

This feature is available on select backends with topological qubit support (research preview).

Backends Overview
Algorithms — All standard algorithms support optional QEC wrapping
HPC Backend — Large QEC simulations may require HPC

Core

Modules

Certification

Quantum Error Correction (QEC)

Quantum Error Correction

Why QEC Matters

List Supported Codes

Compile with QEC

Run the QEC Pipeline

Syndrome Measurement

Python Example — Fault-Tolerant Bell State

Probabilistic Braiding Compilation (PBC)

​Quantum Error Correction

​Why QEC Matters

​List Supported Codes

​Compile with QEC

​Run the QEC Pipeline

​Syndrome Measurement

​Python Example — Fault-Tolerant Bell State

​Probabilistic Braiding Compilation (PBC)

​Related

Quantum Error Correction

Why QEC Matters

List Supported Codes

Compile with QEC

Run the QEC Pipeline

Syndrome Measurement

Python Example — Fault-Tolerant Bell State

Probabilistic Braiding Compilation (PBC)

Related