EMRG

Error Mitigation Recipe Generator -- Automatic quantum error mitigation for NISQ circuits.

EMRG analyzes your quantum circuit and generates ready-to-run, explained Mitiq-powered error mitigation code. No manual tuning required.

Status: v0.2.0 -- ZNE + PEC support. Actively developed, grant-funded roadmap ahead.

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Why EMRG?

Noise limits every computation on today's hardware. Error mitigation techniques like Zero-Noise Extrapolation (ZNE) and Probabilistic Error Cancellation (PEC) can boost fidelity 2--10x, but configuring them manually is tedious:

• Which technique -- ZNE or PEC?
• Which extrapolation factory? Linear, Richardson, Polynomial?
• What scale factors for your circuit depth?
• How do you balance overhead vs. accuracy?

EMRG handles this automatically. Give it a circuit, get back optimized mitigation code with clear explanations of why each choice was made. EMRG selects between techniques, not just tunes settings.

How It Works

Quantum Circuit --> [Analyze] --> [Technique Selection] --> [Code Generator] --> Mitigated Code
                                   ZNE or PEC

1. Parse & Validate -- Load a Qiskit QuantumCircuit or QASM file
2. Extract Features -- Depth, gate counts, multi-qubit gate density, estimated noise factor, PEC overhead
3. Select Technique -- Choose between ZNE and PEC based on circuit characteristics
4. Generate Code -- Output runnable Python with Mitiq imports, config, and inline rationale

Heuristic Rules (v0.2)

Circuit Profile	Technique	Configuration	Rationale
Depth ≤ 30 + noise model + overhead < 1000	PEC	Depolarizing representations	Unbiased error cancellation when overhead is manageable
Depth < 20, low multi-qubit gates	ZNE LinearFactory	[1.0, 1.5, 2.0]	Conservative for shallow circuits
Depth 20--50	ZNE RichardsonFactory	[1.0, 1.5, 2.0, 2.5]	Better extrapolation for moderate noise
Depth > 50 or high noise	ZNE PolyFactory (deg 2--3)	[1.0, 1.5, 2.0, 2.5, 3.0]	Handles non-linear noise scaling

Quick Start

Installation

pip install emrg

Or from source:

git clone https://github.com/FedorShind/EMRG.git
cd EMRG
pip install -e ".[dev]"

CLI Usage

# Generate mitigation recipe from a QASM file
emrg generate docs/examples/bell_state.qasm

# With verbose explanation
emrg generate docs/examples/bell_state.qasm --explain

# Save to file
emrg generate circuit.qasm -o mitigated.py

# Analyze circuit features
emrg analyze docs/examples/simple_vqe.qasm

# JSON output (for scripting)
emrg analyze circuit.qasm --json

# Force PEC technique (requires noise model)
emrg generate circuit.qasm --technique pec --noise-model

# Force ZNE even when PEC is viable
emrg generate circuit.qasm --technique zne

Python API

from qiskit import QuantumCircuit
from emrg import generate_recipe

# Create a circuit
qc = QuantumCircuit(2, 2)
qc.h(0)
qc.cx(0, 1)
qc.measure([0, 1], [0, 1])

# Generate mitigation recipe (one-liner)
result = generate_recipe(qc)
print(result)             # Ready-to-run Python script
print(result.rationale)   # Why these parameters were chosen
print(result.features)    # Circuit analysis details

# With verbose explanations
result = generate_recipe(qc, explain=True)

# With PEC (when a noise model is available)
result = generate_recipe(qc, noise_model_available=True)
print(result.recipe.technique)  # "pec" for shallow circuits

Example Output

# =============================================================
# EMRG v0.2.0 -- Error Mitigation Recipe
# Circuit: 2 qubits, depth 3, 1 multi-qubit gates
# Noise estimate: 0.011 (low)
# =============================================================
#
# Recommendation: LinearFactory + fold_global
#
# =============================================================

from mitiq.zne import execute_with_zne
from mitiq.zne.inference import LinearFactory
from mitiq.zne.scaling import fold_global

factory = LinearFactory(scale_factors=[1.0, 1.5, 2.0])

def execute(circuit):
    """Execute a circuit and return an expectation value (float)."""
    # Replace with your actual backend
    raise NotImplementedError("Replace this with your executor.")

mitigated_value = execute_with_zne(
    circuit,
    execute,
    factory=factory,
    scale_noise=fold_global,
)

print(f"Mitigated expectation value: {mitigated_value}")

Project Structure

EMRG/
├── src/emrg/
│   ├── __init__.py      # Public API and generate_recipe()
│   ├── _version.py      # Single source of truth for version
│   ├── analyzer.py      # Circuit feature extraction
│   ├── heuristics.py    # Rule-based decision engine
│   ├── codegen.py       # Template-based code generation
│   ├── cli.py           # Click CLI interface
│   └── py.typed         # PEP 561 type marker
├── tests/               # 215+ pytest tests, 99% coverage
├── docs/examples/       # Example circuits (Python + QASM)
└── pyproject.toml       # Package configuration

Benchmarks

Real measurements from EMRG v0.2.5, collected automatically by benchmarks/run_benchmark.py.

Environment: Python 3.12, Windows 11 | Qiskit 2.3.0, Mitiq 0.48.1

Tool Performance

EMRG relies on pure Qiskit introspection (no simulation), so generate_recipe() completes in sub-millisecond time even for large circuits. Median of 100 runs:

Circuit	Qubits	Depth	Gates	Multi-Q	Het	Technique / Config	Time	Memory
Bell state	2	3	2	1	0.00	LinearFactory + fold_global	0.069 ms	9.4 KB
Bell state (PEC)	2	3	2	1	0.00	PEC	0.068 ms	9.4 KB
GHZ-5	5	6	5	4	0.50	LinearFactory + fold_global	0.114 ms	15.2 KB
GHZ-10	10	11	10	9	0.50	LinearFactory + fold_global	0.193 ms	24.9 KB
Random 10q, 3 layers	10	7	45	15	0.83	LinearFactory + fold_global	0.296 ms	21.2 KB
VQE 10q, 4 layers	10	20	76	36	1.50	PolyFactory + fold_gates_at_random	0.492 ms	43.8 KB
Random 20q, 6 layers	20	13	180	60	0.91	PolyFactory + fold_gates_at_random	0.836 ms	40.4 KB
Random 30q, 10 layers	30	21	450	150	0.94	PolyFactory + fold_gates_at_random	1.917 ms	69.6 KB
Random 50q, 15 layers	50	31	1125	375	0.96	PolyFactory + fold_gates_at_random	4.518 ms	124.6 KB

A 50-qubit, 1125-gate circuit is analyzed and produces a full mitigation recipe in under 5 ms with ~125 KB memory overhead.

ZNE Fidelity

End-to-end ZNE on noisy simulations (Cirq DensityMatrixSimulator with per-gate depolarizing noise), comparing the ⟨Z⟩ expectation value on qubit 0:

Circuit	Qubits	Depth	Noise	Technique / Config	Ideal	Noisy	Mitigated	Error Reduction
X-flip, 2q	2	3	p=0.01	LinearFactory + fold_global	-1.0000	-0.9761	-1.0003	77x
X-flip, 3q	3	4	p=0.01	LinearFactory + fold_global	-1.0000	-0.9761	-1.0003	77x
X-flip, 2q	2	3	p=0.05	LinearFactory + fold_global	-1.0000	-0.8836	-0.9906	12x
X-flip, 3q	3	4	p=0.05	LinearFactory + fold_global	-1.0000	-0.8836	-0.9906	12x
VQE 4q, 2 layers	4	8	p=0.01	LinearFactory + fold_global	0.0850	0.0775	0.0794	1.4x
VQE 4q, 4 layers	4	14	p=0.01	LinearFactory + fold_global	-0.1915	-0.1766	-0.1850	2.3x
VQE 4q, 2 layers	4	8	p=0.05	LinearFactory + fold_global	0.0850	0.0523	0.0586	1.2x

PEC vs ZNE: Head-to-Head

Same circuits, same noise, both techniques. PEC uses 1000 samples for benchmark accuracy. ZNE is deterministic; PEC results have inherent variance due to stochastic sampling.

Single-qubit observable ⟨Z⟩:

Circuit	Noise	ZNE Error	ZNE Reduction	PEC Error	PEC Reduction	Better
VQE 4q, 2 layers	p=0.01	0.0055	1.4x	0.0007	10.4x	PEC
VQE 4q, 2 layers	p=0.03	0.0162	1.3x	0.0138	1.5x	PEC
VQE 4q, 2 layers	p=0.05	0.0264	1.2x	0.0176	1.9x	PEC
X-flip, 3q	p=0.03	0.0024	28.9x	0.0245	2.9x	ZNE

Multi-qubit observable ⟨ZZ⟩:

Circuit	Noise	ZNE Error	ZNE Reduction	PEC Error	PEC Reduction	Better
VQE 4q, 2 layers	p=0.01	0.0021	5.7x	0.0064	1.9x	ZNE
VQE 4q, 2 layers	p=0.03	0.0102	3.4x	0.0173	2.0x	ZNE
VQE 4q, 2 layers	p=0.05	0.0216	2.5x	0.0147	3.6x	PEC

The pattern: ZNE excels on structured circuits where the noise-vs-scale relationship is predictable (X-flip: 28.9x). PEC excels on irregular circuits at higher noise levels, where ZNE's extrapolation assumptions start to break down. On multi-qubit observables, PEC overtakes ZNE as noise increases -- at p=0.05, PEC achieves 3.6x vs ZNE's 2.5x on ⟨ZZ⟩. This is the tradeoff EMRG's heuristic engine navigates: it recommends PEC for shallow, noisy circuits where a noise model is available, and ZNE elsewhere.

Layerwise Folding

EMRG supports layerwise folding (fold_gates_at_random) as an alternative to global folding for circuits with heterogeneous layer structure. This feature is in active development -- current benchmarks show mixed results, and the heuristic thresholds are being refined.

Circuit	Qubits	Depth	Het	Noise	Global	Layerwise	Winner
VQE 10q, 3 reps	10	13	2.50	p=0.01	0.9x	12.6x	layerwise
VQE 10q, 3 reps	10	13	2.50	p=0.03	1.1x	1.1x	--
QAOA 10q	10	14	2.50	p=0.01	4.2x	0.2x	global
QAOA 10q	10	14	2.50	p=0.03	5.9x	0.7x	global
Extreme 10q	10	13	2.50	p=0.01	0.5x	0.4x	--
Extreme 10q	10	13	2.50	p=0.03	0.5x	0.1x	global

At this scale, fold_global is generally more reliable because fold_gates_at_random introduces stochastic variation into the extrapolation fit. Layerwise folding shows occasional strong results (12.6x on VQE at low noise) but is not yet consistent enough to be the default. EMRG currently defaults to fold_global for most circuits and recommends layerwise folding conservatively. Improvements to the layerwise heuristic -- including noise-aware layer selection and deterministic layer folding strategies -- are planned for future releases.

Reproduce

pip install -e ".[dev]" qiskit-aer
python benchmarks/run_benchmark.py

Roadmap

Phase 1 -- MVP (complete)

Everything needed to go from circuit to mitigation recipe in one command:

• Project structure and packaging
• Circuit analyzer (feature extraction)
• Heuristic engine (ZNE: Linear + Richardson + Poly)
• Code generator (template-based)
• CLI with generate and analyze commands
• Public Python API (generate_recipe())
• Example circuits (Python + QASM) and documentation
• 144 tests, 98% coverage, zero lint warnings

Phase 2 -- More techniques, better validation (current)

Expand beyond ZNE so EMRG can recommend the right technique, not just the right ZNE settings:

• Probabilistic Error Cancellation (PEC) support
• Multi-technique selection (ZNE vs PEC)
• PEC code generation template
• --technique override and --noise-model CLI flags
• 215+ tests, 99% coverage, zero lint warnings
• Clifford Data Regression (CDR) support
• Layerwise Richardson integration
• Composite recipes -- combine ZNE + PEC for circuits that benefit from both
• --preview mode (noisy simulation + fidelity plots)
• Real hardware benchmarks (IBM Quantum devices)
• Expanded tutorials (VQE for H₂, QAOA on MaxCut, random circuits)

Phase 3 -- Multi-framework and community

Make EMRG useful regardless of which framework you use:

• Cirq and PennyLane circuit input support
• Noise model import from Qiskit Aer / real device calibration data
• Configurable heuristics via YAML/JSON
• Jupyter widget for interactive recipe exploration
• Web/Colab interface

Phase 4 -- Intelligence layer

Replace static rules with data-driven mitigation selection:

• Train on benchmark data to predict optimal mitigation strategy
• Circuit similarity search -- match against known-good configurations
• Auto-tuning -- run --preview internally and iterate on parameters before output
• Cost-aware optimization -- user specifies a shot budget, EMRG optimizes within that constraint

Phase 5 -- Ecosystem integration

Make EMRG part of the standard quantum development workflow:

• Qiskit Runtime integration
• Mitiq Calibration API integration -- use calibration data to refine recommendations
• VS Code extension -- analyze circuits inline while writing them
• CI/CD integration -- add EMRG to quantum testing pipelines for automatic mitigation

Tech Stack

• Python 3.11+
• Qiskit >= 1.0 -- Circuit representation and introspection
• Mitiq >= 0.48 -- Error mitigation primitives
• Click >= 8.0 -- CLI framework

Contributing

EMRG is open source and contributions are welcome. If you have ideas, find bugs, or want to add support for new mitigation techniques, open an issue or PR.

License

MIT -- Free for academic and commercial use.

Acknowledgments

Built on Mitiq by Unitary Foundation. Inspired by the need to make quantum error mitigation accessible to everyone working with NISQ hardware.