Fault-Tolerant Quantum Error Correction (FTQC) — Quick Recipe¶
Implement real-time syndrome extraction and optimal decoding using Edmonds' Blossom MWPM and modern Bivariate Bicycle qLDPC codes.
1. Surface Code Decoding with Edmonds' Blossom MWPM¶
Quanta provides a native, globally optimal Minimum Weight Perfect Matching (MWPM) decoder based on Edmonds' Blossom algorithm paired with virtual boundary node replication.
Python Code¶
import numpy as np
from quanta.qec.surface_code import SurfaceCode
from quanta.qec.decoder import MWPMDecoder
# 1. Initialize distance-3 Surface Code [[9, 1, 3]]
code = SurfaceCode(distance=3)
print(code.summary())
# 2. Simulate 100 cycles of phenomenological error correction with true Blossom matching
decoder = MWPMDecoder()
result = code.simulate_error_correction(
error_rate=0.01,
rounds=100,
decoder=decoder,
)
print(f"Logical Error Rate: {result.logical_error_rate:.4f}")
print(f"Physical Error Rate: {result.physical_error_rate:.4f}")
print(f"Correction Weight: {result.total_weight}")
2. Bivariate Bicycle qLDPC [[144, 12, 12]] Code¶
Beyond 2D surface codes, Quanta natively supports the canonical Gross \([[144, 12, 12]]\) Bivariate Bicycle quantum LDPC code over the group ring \(\mathbb{F}_2[x, y] / \langle x^{12}-1, y^6-1 \rangle\).
Python Code¶
import numpy as np
from quanta.qec.qldpc import BivariateBicycleCode, BPOSDDecoder
# 1. Construct Gross [[144, 12, 12]] code
# Encodes k=12 logical qubits into n=144 physical qubits with code distance d=12
code = BivariateBicycleCode.gross_144()
print(f"Physical Qubits (n): {code.num_physical_qubits}") # 144
print(f"Logical Qubits (k): {code.num_logical_qubits}") # 12
print(f"Encoding Rate (k/n): {code.encoding_rate:.4f}") # 0.0833 (12x higher than surface code)
# 2. Decode a syndrome using native BP-OSD
decoder = BPOSDDecoder(code, max_iter=30)
# Simulate a physical X error on physical qubit 7
error_x = np.zeros(code.num_physical_qubits, dtype=int)
error_x[7] = 1
# Calculate Z-stabilizer syndrome: s_z = H_Z * e_x mod 2
syndrome_z = (code.hz @ error_x) % 2
# Decode syndrome into physical correction
correction = decoder.decode(syndrome_z)
print(f"Decoding Success: {correction.success}")
print(f"Corrected Qubits: {correction.correction}")
3. 15-to-1 Bravyi-Kitaev Magic State Distillation¶
For non-Clifford logical gates (\(T\) gate, \(CCZ\)), Quanta provides executable distillation factories:
from quanta.qec.distillation import MagicStateDistillationFactory
# Initialize 15-to-1 Bravyi-Kitaev factory
factory = MagicStateDistillationFactory()
# Distill raw noisy magic states (input error rate p = 0.01)
result = factory.distill(input_error_rate=0.01, shots=1000)
print(f"Input Error Rate: {result.input_error_rate:.4f}")
print(f"Output Error Rate: {result.output_error_rate:.6f}") # Cubic suppression: ~35 * p^3
print(f"Acceptance Rate: {result.acceptance_rate * 100:.1f}%")