Quantum Compiler Analysis

EE798V Course Project — Qiskit Transpiler Pipeline Study

This project benchmarks Qiskit's transpiler pipeline across optimization levels 0–5 on two quantum algorithms (Grover's Search and QFT), measuring how compilation quality affects circuit structure and output fidelity under realistic noise.

Core thesis: Better compilation = sharper probability peaks at correct answer states and fewer noisy gates. The primary quality metric is TVD (Total Variation Distance) between ideal statevector probabilities and noisy simulation output.

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Setup

Requirements: Python 3.11+

pip install qiskit>=1.0 qiskit-aer>=0.14 qiskit-ibm-runtime>=0.20 matplotlib numpy

# Optional (for level 5):
pip install z3-solver   # Level 5: HoareOptimizer

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Quick Start

Step 1 — Transpile and simulate (generates metrics JSON and QPY files in results/):

# Run for each algorithm and qubit count you want to plot
python compiler/transpile_all.py --algorithm grover --n_qubits 4 --max_level 5
python compiler/transpile_all.py --algorithm qft    --n_qubits 4 --max_level 5

# For qubit scaling plots, also run for 3, 5, 6 qubits
for n in 2 3 4 5 ; do
    python compiler/transpile_all.py --algorithm grover --n_qubits $n --max_level 5
    python compiler/transpile_all.py --algorithm qft    --n_qubits $n --max_level 5
done

Step 2 — Generate all three plots:

python plots/plots.py

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Plots

All three plots are generated by plots/plots.py and saved to results/.

Plot	Output file	Description
1. Histogram	results/histogram_4q.png	Output state probability distribution for 4 qubits at L0 vs L5. Ideal (blue) vs noisy (red) side by side for both algorithms.
2. Metrics vs Level	results/metrics_vs_level.png	Gate count and circuit depth vs optimization level (0–5) for both algorithms at 4 qubits.
3. Qubit Scaling	results/qubit_scaling.png	Gate count, CX count, and circuit depth vs qubit count (3–6) for optimization levels 0, 3, 5.

# With custom qubit count for plots 1 and 2:
python plots/plots.py --n_qubits 5

# Interactive display instead of saving:
python plots/plots.py --show

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Optimization Levels

Levels 0–3 use Qiskit's built-in presets. Levels 4–5 are custom extensions that clone Level 3 and add progressively more aggressive passes.

Level	Layout	Routing	Optimization
0	TrivialLayout	BasicSwap	None
1	Trivial → DenseLayout	BasicSwap	Optimize1qGates
2	DenseLayout → VF2Layout	LookaheadSwap	CommutativeCancellation, CXCancellation
3	SabreLayout	SabreSwap	Full peephole + UnitarySynthesis (KAK)
4	SabreLayout	SabreSwap	Level 3 + TemplateOptimization + diagonal removal
5	SabreLayout	SabreSwap	Level 4 + HoareOptimizer (z3-solver required)

All stochastic passes are seeded (seed_transpiler=42, seed_simulator=42) for reproducible results.

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Algorithm Suite

Algorithm	File	Ideal Output
Grover's Search	circuits/grover.py	Sharp peak at marked state
Quantum Fourier Transform	circuits/qft.py	Uniform distribution

Both expose build(n_qubits, **kwargs) → QuantumCircuit.

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Error Metric: TVD

TVD = 0.5 × Σₛ |P_ideal(s) − P_noisy(s)|

• TVD = 0 → noisy output matches ideal exactly (perfect compilation)
• TVD = 1 → no overlap between ideal and noisy distributions

TVD is the primary quality signal because it directly corresponds to how peaked vs spread the probability histogram looks. Secondary structural metrics (gate count, CX count, depth) are proxies that predict TVD.

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Hardware Platform

from qiskit_ibm_runtime.fake_provider import FakeNairobiV2  # 7 qubits, real IBM noise data

Basis gate set: ['cx', 'rz', 'sx', 'x']. Statevector simulation is skipped for circuits with more than 20 qubits; those report structural metrics only (TVD = None).

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Architecture

circuits/       →  compiler/              →  hardware/        →  analysis/ + plots/
build circuit      transpile_all.py          simulate w/ noise    metrics + figures
                   (levels 0–5, serialise
                    to results/*.qpy)

Each stage is independent. Compiled circuits are serialised to results/*.qpy via qiskit.qpy, so transpilation runs once and plotting reads cached results.

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Project Structure

quantum-compiler/
├── circuits/
│   ├── __init__.py          # Registry: build_circuit(algorithm, n_qubits)
│   ├── grover.py            # Grover's search
│   └── qft.py               # Quantum Fourier Transform
├── compiler/
│   ├── __init__.py
│   ├── transpile_all.py     # Top-level runner (CLI entry point)
│   ├── preset_pass_managers.py  # Levels 0–5 PassManagers
│   └── pass_manager.py      # PassManager / AnalysisPass / TransformationPass
├── hardware/
│   ├── __init__.py
│   ├── backends.py          # Backend selection (FakeNairobi / FakeSherbrooke)
│   └── noise_models.py      # Base + scaled noise models
├── analysis/
│   ├── __init__.py
│   ├── metrics.py           # TVD, gate_count, cx_count, depth, compute_all_metrics
│   └── benchmark.py         # Sweep all qubit counts → benchmark_report.json
├── plots/
│   ├── __init__.py
│   └── plots.py             # All three benchmark plots
└── results/                 # Generated outputs (QPY, JSON, PNG)

Output Files

All outputs land in results/:

File pattern	Description
<algo>_<n>q_level<l>.qpy	Compiled circuit in QPY format
<algo>_<n>q_metrics.json	Gate count, CX count, depth, TVD, and probability dicts per level
histogram_<n>q.png	State probability histograms: L0 vs L5 for both algorithms
metrics_vs_level.png	Gate count + depth vs optimization level for both algorithms
qubit_scaling.png	Gate count, CX, depth vs qubit count for both algorithms