Circuit Execution Quality Metrics

This tutorial covers benchmarks for measuring full circuit performance.

from qcmet import QuantumVolumeFixedQubits
from qcmet.devices import IdealSimulator, NoisySimulator
import matplotlib.pyplot as plt

The circuit execution quality metrics consist of:

• Quantum volume (QuantumVolumeFixedQubits)

• Mirrored circuits average polarization (MirroredCircuits)

• Upper bound on the variation distance (UpperBoundOnVD)

Quantum Volume

Quantum Volume (QV) is a holistic benchmark that measures the largest random circuit a quantum computer can execute successfully.

How Quantum Volume Works

1. Generate random unitary circuits of depth = width = n

2. Execute circuits and collect measurement statistics

3. Compute Heavy Output Probability (HOP)

4. If HOP > 2/3 with high confidence, QV = 2^n

QV captures:

• Gate fidelity

• Measurement fidelity

• Circuit connectivity

• Crosstalk

• Compilation quality

# Setup Quantum Volume benchmark
qv = QuantumVolumeFixedQubits(
    qubits=3,      # Test 3-qubit QV
    trials=20,     # Number of random circuits
    seed=42,       # For reproducibility
)

# Generate circuits
qv.generate_circuits()
print(f"Generated {len(qv.circuits)} QV circuits")
print(f"Each circuit has width={qv.num_qubits} and depth={qv.num_qubits}")

Generated 20 QV circuits
Each circuit has width=3 and depth=3

# Look at a QV circuit
print("Example Quantum Volume circuit:")
print(qv.circuits[-1])

Example Quantum Volume circuit:
           ┌──────┐      ┌──────┐   ┌──────┐ ░ ┌─┐      
   q_0: ─X─┤0     ├─X────┤0     ├───┤0     ├─░─┤M├──────
         │ │  su4 │ │    │  su4 │   │  su4 │ ░ └╥┘┌─┐   
   q_1: ─X─┤1     ├─X──X─┤1     ├─X─┤1     ├─░──╫─┤M├───
           └──────┘    │ └──────┘ │ └──────┘ ░  ║ └╥┘┌─┐
   q_2: ───────────────X──────────X──────────░──╫──╫─┤M├
                                             ░  ║  ║ └╥┘
meas: 3/════════════════════════════════════════╩══╩══╩═
                                                0  1  2 

# Run on ideal simulator
device = IdealSimulator()
qv.run(device, num_shots=1024)

# Analyze
results = qv.analyze()
print("\nQuantum Volume Results:")
for key, value in results.items():
    print(f"  {key}: {value}")

Quantum Volume Results:
  mean: 0.844384765625
  mean-2sigma: 0.6822742272843888
  outcome: Pass
  quantum_volume: >= 8

# Plot
qv.plot()
plt.show()

Testing Different Qubit Counts

# Test QV for different system sizes
device = NoisySimulator(overrotation_amount = 0, detuning_amount = 0, error_1q = 0.00, error_2q = 0.01, t1 = 0, t2 = 0 )
qv_results = {}

for n_qubits in [3, 4]:
    print(f"\nTesting QV for {n_qubits} qubits...")

    qv_test = QuantumVolumeFixedQubits(
        qubits=n_qubits,
        trials=50,
        seed=42,
    )

    qv_test.generate_circuits()
    qv_test.run(device, num_shots=1024)
    result = qv_test.analyze()
    qv_results[n_qubits] = result
    print(f"  QV = {result.get('quantum_volume', 'N/A')}")
    print(f"  mean HOP = {result.get('mean', 'N/A'):.3f}")
    print(f"  mean HOP - 2sigma = {result.get('mean-2sigma', 'N/A'):.3f}")
    print(f"  Passed: {result.get('outcome', 'N/A')}")

Testing QV for 3 qubits...
  QV = >= 8
  mean HOP = 0.809
  mean HOP - 2sigma = 0.698
  Passed: Pass

Testing QV for 4 qubits...
  QV = < 16
  mean HOP = 0.743
  mean HOP - 2sigma = 0.620
  Passed: Fail

Interpreting the Results

What QV Tells You:

• QV = $2^{n}$ means the system can handle n-qubit circuits of depth n

• Higher QV = better overall quantum computer

• QV = 64 means 6 qubits × depth 6

Heavy Output Probability (HOP):

• Must exceed 2/3 (66.7%) to pass with a confidence of 2 sigma

• Measures fraction of “heavy” outputs (above median probability)

• HOP > 2/3 means circuits are executed correctly

Other Benchmarks

QCMet furthermore implements mirrored circuits average polarization and the upper bound on the variation distance as circuit execution quality metrics.