EMRG

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

EMRG analyzes a quantum circuit and generates Mitiq error mitigation code with the right imports, parameters, and rationale. It selects between ZNE, PEC, CDR, and composite ZNE-over-PEC recipes so you only need to connect the generated executor adapter to your simulator or hardware backend.

v0.4.0 -- ZNE + PEC + CDR + Composite + Preview. Roadmap below.

---

Why EMRG?

No single mitigation technique fits every NISQ circuit. ZNE needs useful noise-scaling behavior, PEC needs a noise model and manageable sampling overhead, CDR needs enough non-Clifford structure to train against, and composite ZNE-over-PEC is only worth its cost on moderate-depth PEC-eligible circuits. EMRG automates that choice: give it a circuit, get back runnable mitigation code with rationale for every parameter choice.

How It Works

Quantum Circuit --> [Analyze] --> [Technique Selection] --> [Code Generator] --> Mitigated Code
                                     Composite / PEC / CDR / ZNE

1. Parse & Validate -- Load a Qiskit QuantumCircuit or QASM file.
2. Extract Features -- Depth, gate counts, noise factor, non-Clifford fraction, PEC overhead, layer heterogeneity.
3. Select Technique -- Use priority rules: composite for eligible moderate-depth circuits, PEC for shallow low-overhead noise-model cases, CDR for non-Clifford-heavy circuits, otherwise ZNE.
4. Generate Code -- Runnable Python with Mitiq imports, configuration, and inline rationale.

Heuristic Rules (v0.4.0)

Circuit Profile	Technique	Configuration	Rationale
Depth 15--30 + moderate noise + noise model + combined overhead <= 1000	Composite (ZNE over PEC)	ZNE factory over PEC executor	PEC corrects each noise-scaled circuit before ZNE extrapolates residual bias
Depth ≤ 30 + noise model + overhead < 1000	PEC	Depolarizing representations	Unbiased error cancellation when overhead is manageable
Non-Clifford fraction > 20% + depth 10--40	CDR	8--16 training circuits, linear fit	Clifford substitution + regression outperforms ZNE on non-Clifford-heavy circuits
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

For preview mode (noisy simulation comparison):

pip install emrg[preview]

Or from source:

git clone https://github.com/FedorShind/EMRG.git
cd EMRG
pip install -e ".[dev,preview,qasm3]"

Or try it without installing:

CLI Usage

# Generate mitigation recipe from a QASM file
emrg generate circuit.qasm

# With verbose explanation
emrg generate circuit.qasm --explain

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

# Force a specific technique
emrg generate circuit.qasm --technique pec --noise-model
emrg generate circuit.qasm --technique composite --noise-model
emrg generate circuit.qasm --technique cdr

# Forced techniques bypass automatic viability checks. EMRG still returns the
# requested recipe, but generated output includes warnings when the circuit
# falls outside the automatic selection criteria.

# Preview: simulate and compare before/after mitigation
emrg generate circuit.qasm --preview

# Preview with custom noise level and observable
emrg generate circuit.qasm --preview --noise-level 0.03 --observable ZZ

# Analyze circuit features
emrg analyze circuit.qasm

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

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 PEC (requires noise model availability)
result = generate_recipe(qc, noise_model_available=True)

# Force CDR (requires cirq: pip install emrg[preview])
result = generate_recipe(qc, technique="cdr")

# Force composite ZNE-over-PEC (requires noise model availability)
result = generate_recipe(qc, technique="composite", noise_model_available=True)

# With preview simulation
result = generate_recipe(qc, preview=True, noise_level=0.01)
print(result.preview)     # Simulation comparison results

Example Output

# =============================================================
# EMRG v0.4.0 -- 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)."""
    # Connect this adapter to your simulator or hardware backend.
    raise NotImplementedError("Configure execute() for your backend.")

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

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

Preview Mode

--preview runs a noisy simulation, applies the recommended mitigation, and displays a before/after comparison. This validates the recipe before spending real hardware shots.

emrg generate circuit.qasm --preview

┌─────────────────────────────────────────────────┐
│  EMRG Preview -- Simulation Comparison         │
├─────────────────────────────────────────────────┤
│  Circuit:    2 qubits, depth 3                 │
│  Noise:      depolarizing p=0.01               │
│  Observable: <Z> on qubit 0                    │
│  Technique:  ZNE                               │
├─────────────────────────────────────────────────┤
│  Ideal:      -1.0000                           │
│  Noisy:      -0.9761  (error: 0.0239)          │
│  Mitigated:  -1.0003  (error: 0.0003)          │
│                                                │
│  Error reduction: 77.5x                        │
└─────────────────────────────────────────────────┘

Uses Cirq's DensityMatrixSimulator with per-gate depolarizing noise. Circuits above 10 qubits are skipped (density matrix cost scales as O(4^n)). PEC preview uses 200 samples; composite preview uses 200 PEC samples inside each ZNE scale evaluation; CDR uses the recipe's training circuit count. These stochastic previews are approximate and vary between runs.

Requires pip install emrg[preview].

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
│   ├── preview.py       # Simulation preview engine
│   ├── cli.py           # Click CLI interface
│   └── py.typed         # PEP 561 type marker
├── tests/               # 407 tests, 95% coverage
├── docs/
│   ├── examples/        # Example circuits (Python + QASM)
│   └── tutorials/       # Jupyter notebooks (VQE, QAOA)
├── benchmarks/          # Automated benchmark suite
└── pyproject.toml       # Package configuration

Benchmarks

Reference benchmark snapshot collected by benchmarks/run_benchmark.py on EMRG v0.3.0. Rerun the benchmark script before using these numbers for new release claims.

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

Tool Performance

generate_recipe() uses pure Qiskit introspection (no simulation), so it 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	0.09 ms	9.4 KB
Bell state (PEC)	2	3	2	1	0.00	PEC	0.09 ms	9.4 KB
GHZ-5	5	6	5	4	0.50	LinearFactory + fold_global	0.14 ms	15.2 KB
GHZ-10	10	11	10	9	0.50	LinearFactory + fold_global	0.24 ms	24.9 KB
Random 10q, 3 layers	10	7	45	15	0.83	LinearFactory + fold_global	0.39 ms	21.2 KB
VQE 10q, 4 layers	10	20	76	36	1.50	CDR (16 training)	0.64 ms	43.8 KB
Hetero 4q, 8 layers	4	17	42	10	1.00	CDR (12 training)	0.40 ms	34.6 KB
T-gate 4q	4	7	12	3	0.50	LinearFactory + fold_global	0.15 ms	16.7 KB
Rz-rot 4q, 4 layers	4	14	28	12	0.50	CDR (12 training)	0.29 ms	29.3 KB
Random 20q, 6 layers	20	13	180	60	0.91	CDR (16 training)	1.06 ms	49.0 KB
Random 30q, 10 layers	30	21	450	150	0.94	CDR (16 training)	2.41 ms	116.3 KB
Random 50q, 15 layers	50	31	1125	375	0.96	CDR (16 training)	5.81 ms	282.0 KB

A 50-qubit, 1125-gate circuit is analyzed and produces a full mitigation recipe in under 6 ms. Circuits with non-Clifford rotations are automatically routed to CDR.

ZNE Fidelity

End-to-end ZNE on Cirq DensityMatrixSimulator with per-gate depolarizing noise, comparing ⟨Z⟩ 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; its results have inherent variance from stochastic sampling. ZNE is deterministic.

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

ZNE excels on structured circuits where noise scales predictably with folding (X-flip: 28.9x). PEC excels on irregular circuits at higher noise, where ZNE's extrapolation assumptions break down. On ⟨ZZ⟩, PEC overtakes ZNE as noise increases: 3.6x vs 2.5x at p=0.05. EMRG recommends PEC for shallow, noisy circuits with an available noise model, and ZNE otherwise.

Layerwise Folding

fold_gates_at_random targets the noisiest gates in circuits with uneven layer structure, instead of folding uniformly. Benchmarks show mixed results; 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

fold_global is more reliable at this scale because fold_gates_at_random adds stochastic variation to the extrapolation fit. Layerwise folding shows occasional strong results (12.6x on VQE at low noise) but is not consistent enough to be the default. EMRG defaults to fold_global and uses layerwise folding conservatively for high-heterogeneity circuits.

CDR vs ZNE

CDR replaces non-Clifford gates with Clifford substitutes to create classically simulable training circuits, then fits a regression model to correct the noisy result. Compared to ZNE on circuits with non-Clifford gates:

Circuit	Noise	ZNE Error	ZNE Reduction	CDR Error	CDR Reduction	Better
Rz-rot 4q	p=0.01	0.0253	2.8x	~0.0000	>1000x	CDR
Rz-rot 4q	p=0.03	0.0866	2.3x	~0.0000	>1000x	CDR
VQE 4q, 2 layers	p=0.01	0.0055	1.4x	0.0036	2.1x	CDR
VQE 4q, 2 layers	p=0.03	0.0162	1.3x	0.0108	1.9x	CDR

CDR recovers near-ideal expectation values on rotation-heavy circuits and consistently outperforms ZNE on VQE circuits at both low and moderate noise. EMRG auto-selects CDR when the non-Clifford gate fraction exceeds 20% and depth is between 10 and 40.

Reproduce

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

Roadmap

Phase 1 -- MVP (complete)

• 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

Phase 2 -- Multi-technique support (current)

• Probabilistic Error Cancellation (PEC) support
• Multi-technique selection (ZNE vs PEC)
• PEC code generation template
• --technique override and --noise-model CLI flags
• Layerwise Richardson integration
• --preview mode (noisy simulation + before/after comparison)
• Expanded tutorials (VQE, QAOA)
• 407 tests, 95% coverage, zero lint warnings
• Clifford Data Regression (CDR) support
• Composite recipes -- combine ZNE + PEC for circuits that benefit from both
• Real hardware benchmarks (IBM Quantum devices)

Phase 3 -- Multi-framework support

• Cirq, PennyLane, and Amazon Braket 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 -- Data-driven selection

• Train on benchmark data to predict optimal mitigation strategy
• Circuit similarity search against known-good configurations
• Auto-tuning via internal --preview iterations before output
• Cost-aware optimization within user-specified shot budgets

Phase 5 -- Ecosystem integration

• Qiskit Runtime integration
• Mitiq Calibration API integration
• VS Code extension for inline circuit analysis
• CI/CD integration for quantum testing pipelines

Tech Stack

• Python 3.11+
• Qiskit >= 1.0 -- circuit representation and introspection
• Mitiq >= 0.48 -- error mitigation primitives
• Click >= 8.0 -- CLI framework
• Cirq >= 1.0 -- simulation backend (optional, for preview and CDR)

Contributing

Open an issue or PR on GitHub.

License

MIT

Acknowledgments

Built on Mitiq by Unitary Foundation.