QENS

Quantum Error and Noise Simulation SDK -- a Python-native toolkit for simulating quantum errors, decoding syndromes, and visualizing error-correcting codes.

QENS provides a layered API for researchers, educators, and engineers working with quantum error correction. It ships with built-in support for surface codes, repetition codes, and color codes, multiple decoder implementations, and publication-quality visualization -- all with only numpy and matplotlib as dependencies.

Installation

pip install -e .

For development (includes pytest, mypy, ruff):

pip install -e ".[dev]"

Requires Python 3.11+.

Documentation

Full documentation is in the docs/ directory:

Guide	Description
Getting Started	Installation, first simulation, project structure
Core Concepts	QEC background, Pauli errors, CSS codes, Pauli frame model
Error Models	All 10 noise models with examples
QEC Codes	Repetition, surface, and color codes
Decoders	Lookup, MWPM, and union-find decoders
Simulation	Monte Carlo sampling, threshold sweeps, Pauli frame simulator
Visualization	Circuit diagrams, lattice views, decoding graphs, plots
Extending QENS	Custom error models, codes, decoders, visualizers
API Reference	Complete reference for every class and function
Architecture	Package design, dependency graph, simulation pipeline

---

Quickstart

import qens

code = qens.RepetitionCode(distance=5)
noise = qens.DepolarizingError(p=0.05)
decoder = qens.LookupTableDecoder(code)

result = qens.ThresholdExperiment.single_point(
    code=code, noise_model=noise, decoder=decoder, shots=10_000, seed=42
)

print(f"Logical error rate: {result.logical_error_rate:.4f}")

---

Detailed Usage Guide

1. Building Quantum Circuits

QENS provides a fluent builder API for constructing quantum circuits gate by gate:

from qens import Circuit, Gate, Moment

# Fluent API -- chain gates together
circuit = Circuit(num_qubits=3).h(0).cx(0, 1).cx(0, 2).measure_all()
print(circuit)  # Circuit(num_qubits=3, depth=4)

# Or build manually with Gate and Moment objects
gate = Gate("H", qubits=(0,))
moment = Moment()
moment.add(gate)
circuit = Circuit(5)
circuit.append_moment(moment)

Available fluent gates: h(q), x(q), z(q), cx(ctrl, tgt), cz(q0, q1), measure(q), measure_all(), reset(q).

Circuit properties: num_qubits, depth, moments.

---

2. Error Models

Every error model subclasses ErrorModel and implements sample_errors(). All models support Pauli-frame sampling and can be composed.

Pauli Errors

from qens import BitFlipError, PhaseFlipError, DepolarizingError, PauliYError
import numpy as np

noise = DepolarizingError(p=0.01)  # X, Y, Z each with prob p/3

rng = np.random.default_rng(42)
error = noise.sample_errors(num_qubits=5, affected_qubits=[0, 1, 2, 3, 4], rng=rng)
# Returns a PauliString: array of 0=I, 1=X, 2=Y, 3=Z

Measurement Errors

from qens import MeasurementError

# Asymmetric readout: different 0->1 and 1->0 flip rates
readout = MeasurementError(p_0to1=0.02, p_1to0=0.005)

# Only applies to measurement gates
readout.applies_to(Gate("M", (0,)))   # True
readout.applies_to(Gate("H", (0,)))   # False

Gate Errors

from qens import CoherentRotationError, CrosstalkError

# Gaussian over/under-rotation on every non-measurement gate
rotation = CoherentRotationError(angle_stddev=0.01)

# ZZ crosstalk between specific qubit pairs
crosstalk = CrosstalkError(coupling_map={(0, 1): 0.002, (1, 2): 0.001})

Correlated and Leakage Errors

from qens import CorrelatedPauliError, LeakageError
from qens.core.types import PauliOp

# Joint Pauli errors on qubit pairs
correlated = CorrelatedPauliError(joint_errors={
    (0, 1): [(0.01, PauliOp.X, PauliOp.X)],  # XX with prob 0.01
    (2, 3): [(0.005, PauliOp.Z, PauliOp.Z)],  # ZZ with prob 0.005
})

# Leakage to |2> state with relaxation back
leakage = LeakageError(p_leak=0.001, p_relax=0.1)
print(leakage.leaked_qubits)  # Track which qubits are leaked
leakage.reset()                # Clear leakage state

Composing Noise Models

Stack multiple error models into a single composed model. Each model's applies_to() filter is respected.

from qens import ComposedNoiseModel, DepolarizingError, MeasurementError, CrosstalkError

noise = ComposedNoiseModel([
    DepolarizingError(p=0.001),
    MeasurementError(p_0to1=0.01, p_1to0=0.005),
    CrosstalkError(coupling_map={(0, 1): 0.002}),
])

# Sample errors for a specific gate (respects filters)
from qens import Gate
error = noise.sample_errors_for_gate(
    num_qubits=5, gate=Gate("CX", (0, 1)), rng=rng
)

Kraus Representations

Pauli error models provide Kraus operator representations for density-matrix simulation:

channel = DepolarizingError(p=0.01).to_channel(affected_qubits=[0])
print(channel.validate())      # True (completeness relation holds)
print(channel.probabilities())  # [0.99, 0.0033, 0.0033, 0.0033]

---

3. Error-Correcting Codes

All codes subclass QECCode and provide stabilizers, logical operators, check matrices, and syndrome extraction circuits.

Repetition Code

from qens import RepetitionCode

code = RepetitionCode(distance=5)
print(code.num_data_qubits)     # 5
print(code.num_ancilla_qubits)  # 4
print(code.code_distance)       # 5

# Stabilizer generators (ZZ on adjacent pairs)
for stab in code.stabilizer_generators():
    print(f"  {stab.stabilizer_type}: qubits {stab.qubits}")

# Parity check matrix
H = code.check_matrix()  # shape (4, 5)

# Syndrome extraction circuit
circuit = code.syndrome_circuit(rounds=3)

Surface Code

from qens import SurfaceCode
import numpy as np

code = SurfaceCode(distance=3)  # Rotated surface code
print(code.num_data_qubits)     # 9
print(code.num_ancilla_qubits)  # 8

# Inject an X error and compute the syndrome
error = np.zeros(9, dtype=np.uint8)
error[4] = 1  # X on center qubit
syndrome = code.compute_syndrome(error)
print(f"Syndrome: {syndrome}")  # Non-trivial where Z-stabilizers detect X

# Check if an error is a logical error
residual = np.zeros(9, dtype=np.uint8)
residual[0] = 1; residual[3] = 1; residual[6] = 1  # X on left column = X_L
print(code.is_logical_error(residual))  # True

Color Code

from qens import ColorCode

# 4.8.8 lattice (default)
code_488 = ColorCode(distance=3, lattice_type="4.8.8")
print(code_488.supports_transversal_clifford)  # True

# 6.6.6 lattice
code_666 = ColorCode(distance=5, lattice_type="6.6.6")

Qubit Coordinates

Every code provides coordinates for visualization:

coords = code.qubit_coordinates()
# {0: (0, 0), 1: (0, 1), ...} -- maps qubit index to (row, col)

---

4. Decoders

All decoders subclass Decoder and implement decode(syndrome) -> DecoderResult.

Lookup Table Decoder

Exact decoding via precomputed syndrome-to-correction table. Best for small codes (d <= 7).

from qens import RepetitionCode, LookupTableDecoder
import numpy as np

code = RepetitionCode(5)
decoder = LookupTableDecoder(code)
decoder.precompute()  # Build lookup table

# Decode a syndrome
error = np.zeros(5, dtype=np.uint8)
error[2] = 1  # X error on qubit 2
syndrome = code.compute_syndrome(error)

result = decoder.decode(syndrome)
print(result.correction)  # Correction to apply
print(result.metadata)     # {"table_hit": True}

MWPM Decoder

Greedy minimum-weight perfect matching. Good balance of speed and accuracy.

from qens import SurfaceCode, MWPMDecoder

code = SurfaceCode(5)
decoder = MWPMDecoder(code)
decoder.precompute()  # Build decoding graph

result = decoder.decode(syndrome)
print(result.metadata["matching"])  # List of matched defect pairs

# Access the decoding graph structure (for visualization)
graph = decoder.build_decoding_graph()
print(graph.keys())  # ['nodes', 'edges', 'boundary_nodes']

Union-Find Decoder

Fast approximate decoding with almost-linear time complexity.

from qens import UnionFindDecoder

decoder = UnionFindDecoder(code)
decoder.precompute()
result = decoder.decode(syndrome)

---

5. Running Simulations

Single-Point Simulation

Run a fixed number of Monte Carlo shots at one noise level:

from qens import (
    RepetitionCode, DepolarizingError, MWPMDecoder,
    ThresholdExperiment, NoisySampler,
)

code = RepetitionCode(5)
noise = DepolarizingError(p=0.05)
decoder = MWPMDecoder(code)

# Option A: via ThresholdExperiment convenience method
result = ThresholdExperiment.single_point(
    code=code, noise_model=noise, decoder=decoder,
    shots=10_000, seed=42
)
print(f"Logical error rate: {result.logical_error_rate:.4f}")
print(f"Logical errors: {result.logical_error_count} / {result.num_shots}")

# Option B: via NoisySampler directly
sampler = NoisySampler(seed=42)
result = sampler.run(code, noise, decoder, shots=10_000)

# Access individual shots
syn_0 = result.sample_syndrome(0)
err_0 = result.sample_error(0)

Sampling Without Decoding

Generate error samples and syndromes without the decoding step:

sampler = NoisySampler(seed=42)
result = sampler.sample_errors(code, noise, shots=1_000)
# result.syndromes and result.errors are populated
# result.corrections and result.logical_errors are empty

Threshold Sweep

Sweep physical error rates across multiple code distances to find the error threshold:

from qens import SurfaceCode, DepolarizingError, MWPMDecoder, ThresholdExperiment

experiment = ThresholdExperiment(
    code_class=SurfaceCode,
    distances=[3, 5, 7],
    physical_error_rates=[0.001, 0.003, 0.005, 0.008, 0.01, 0.015, 0.02],
    noise_model_factory=lambda p: DepolarizingError(p=p),
    decoder_class=MWPMDecoder,
    shots_per_point=10_000,
    seed=42,
)

# Run with progress tracking
def on_progress(completed, total):
    print(f"  [{completed}/{total}] {100*completed/total:.0f}%")

result = experiment.run(progress_callback=on_progress)

# Access results
print(result.distances)             # [3, 5, 7]
print(result.physical_error_rates)  # [0.001, ..., 0.02]
print(result.logical_error_rates)   # shape (3, 7) numpy array

Pauli Frame Simulator

Track Pauli errors through Clifford circuits efficiently (O(n) per gate):

from qens.simulation import PauliFrameSimulator
from qens import Circuit, PauliOp
import numpy as np

sim = PauliFrameSimulator(num_qubits=3)

# Inject an X error on qubit 0
error = np.array([PauliOp.X, PauliOp.I, PauliOp.I], dtype=np.uint8)
sim.apply_error(error)

# Propagate through a circuit
circuit = Circuit(3).h(0).cx(0, 1)
sim.propagate_circuit(circuit)

print(sim.frame)      # See how the error propagated
print(sim.measure(0)) # 1 if X/Y error on qubit, else 0

---

6. Visualization

All visualization functions return a FigureHandle with .save(path), .show(), and .close() methods. Use matplotlib.use('Agg') for headless environments.

Circuit Diagrams

from qens import SurfaceCode, DepolarizingError, draw_circuit

code = SurfaceCode(3)
circuit = code.syndrome_circuit(rounds=1)
noise = DepolarizingError(p=0.01)

# Basic circuit diagram
fig = draw_circuit(circuit)
fig.save("circuit.png")

# With error annotations highlighting noise-prone gates
fig = draw_circuit(circuit, noise_model=noise, highlight_errors=True)
fig.save("noisy_circuit.png")

# With explicit error locations
fig = draw_circuit(circuit, error_locations=[(0, 2), (1, 5)])
fig.save("marked_circuit.png")

Lattice Views

from qens import RepetitionCode, SurfaceCode, draw_lattice
import numpy as np

code = SurfaceCode(3)

# Basic lattice
fig = draw_lattice(code)

# With syndrome overlay
error = np.zeros(9, dtype=np.uint8)
error[4] = 1  # X error
syndrome = code.compute_syndrome(error)
fig = draw_lattice(code, syndrome=syndrome, error=error, title="X error on center")
fig.save("lattice_with_error.png")

Decoding Graphs

from qens import SurfaceCode, MWPMDecoder, draw_decoding_graph
import numpy as np

code = SurfaceCode(3)
decoder = MWPMDecoder(code)
decoder.precompute()

error = np.zeros(9, dtype=np.uint8)
error[4] = 1
syndrome = code.compute_syndrome(error)
decode_result = decoder.decode(syndrome)

fig = draw_decoding_graph(
    decoder, syndrome=syndrome, decode_result=decode_result,
    show_matching=True, title="MWPM Decoding"
)
fig.save("decoding_graph.png")

Statistical Plots

from qens import plot_threshold, plot_logical_rates, plot_histogram

# Threshold plot (from a ThresholdExperiment result)
fig = plot_threshold(result, log_scale=True, title="Surface Code Threshold")
fig.save("threshold.pdf")  # Publication-quality PDF

# Bar chart of logical error rates
fig = plot_logical_rates(
    distances=[3, 5, 7, 9],
    logical_rates=[0.05, 0.01, 0.002, 0.0004],
)
fig.save("rates_by_distance.png")

# Histogram of any simulation data
fig = plot_histogram(data, bins=50, xlabel="Error weight", title="Error Distribution")
fig.save("histogram.png")

---

7. Extending QENS

Every subsystem uses the ABC + Registry pattern. Extension points are marked with comments in the source.

Custom Error Model

from qens.noise.base import ErrorModel
from qens.noise import noise_registry
import numpy as np

class ThermalRelaxationError(ErrorModel):
    def __init__(self, t1: float, t2: float, gate_time: float):
        self.p_x = 1 - np.exp(-gate_time / t1)
        self.p_z = 1 - np.exp(-gate_time / t2)

    def sample_errors(self, num_qubits, affected_qubits, rng):
        error = np.zeros(num_qubits, dtype=np.uint8)
        for q in affected_qubits:
            if rng.random() < self.p_x:
                error[q] = 1  # X
            elif rng.random() < self.p_z:
                error[q] = 3  # Z
        return error

    def __repr__(self):
        return f"ThermalRelaxationError(p_x={self.p_x:.4f}, p_z={self.p_z:.4f})"

noise_registry.register("thermal", ThermalRelaxationError)

Custom Decoder

from qens.decoders.base import Decoder, DecoderResult
from qens.decoders import decoder_registry

class MyDecoder(Decoder):
    def decode(self, syndrome):
        correction = np.zeros(self._code.num_data_qubits, dtype=np.uint8)
        # ... your decoding logic ...
        return DecoderResult(correction=correction, success=True)

decoder_registry.register("my_decoder", MyDecoder)

Registry Lookup

from qens.noise import noise_registry
from qens.codes import code_registry
from qens.decoders import decoder_registry

print(noise_registry.list_registered())
# ['bit_flip', 'coherent_rotation', 'correlated_pauli', 'crosstalk',
#  'depolarizing', 'leakage', 'measurement', 'pauli_y', 'phase_flip']

cls = noise_registry.get("depolarizing")
model = cls(p=0.01)

---

Architecture

qens/
  core/        Types, Circuit, Gate, NoiseChannel, Registry
  noise/       ErrorModel ABC + 8 built-in models + ComposedNoiseModel
  codes/       QECCode ABC + RepetitionCode, SurfaceCode, ColorCode
  decoders/    Decoder ABC + Lookup, UnionFind, MWPM
  simulation/  NoisySampler, PauliFrameSimulator, ThresholdExperiment
  viz/         Circuit diagrams, lattice views, decoding graphs, stats plots
  utils/       Pauli algebra, GF(2) sparse matrices, seeded RNG

Examples

python3 examples/01_quickstart.py              # Basic workflow
python3 examples/02_surface_code_threshold.py   # Threshold sweep
python3 examples/03_custom_noise_model.py       # Composed noise + visualization
python3 examples/04_visualization_gallery.py    # All visualization types

Testing

pytest                    # 194 tests
ruff check src/qens/      # Lint

License

MIT