🎓 Academic Research

Professional quantum computing infrastructure for universities and research institutions.

Why QCOS for Academia?

Challenge	QCOS Solution
Limited HPC access	Cloud-based GPU acceleration
Reproducibility requirements	Deterministic execution + logging
Publication deadlines	Fast turnaround (minutes, not days)
Budget constraints	Free tier + academic discounts
Student training	Interactive playground + docs

Academic Pricing

Tier	Features	Price
Student	50 jobs/day, 30 qubits	Free
Researcher	200 jobs/day, 50 qubits	€29/mo
Lab	1000 jobs/day, 100 qubits	€199/mo
Department	Unlimited, priority	Custom

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Use Case: Quantum Algorithm Research

Implementing Novel Algorithms

from softqcos_sdk import QCOSClient
import numpy as np

client = QCOSClient()

def grover_search(n_qubits: int, target: int, iterations: int) -> str:
    """
    Implement Grover's algorithm for n qubits.
    """
    qasm = f"""
OPENQASM 2.0;
include "qelib1.inc";
qreg q[{n_qubits}];
creg c[{n_qubits}];

// Initialize superposition
"""
    for i in range(n_qubits):
        qasm += f"h q[{i}];\n"

    for _ in range(iterations):
        # Oracle (mark target state)
        qasm += f"\n// Oracle for |{format(target, f'0{n_qubits}b')}>\n"
        for i, bit in enumerate(format(target, f'0{n_qubits}b')):
            if bit == '0':
                qasm += f"x q[{i}];\n"

        # Multi-controlled Z
        qasm += f"h q[{n_qubits-1}];\n"
        qasm += f"mcx q[0],q[1]" + "".join(f",q[{i}]" for i in range(2, n_qubits)) + f";\n"
        qasm += f"h q[{n_qubits-1}];\n"

        for i, bit in enumerate(format(target, f'0{n_qubits}b')):
            if bit == '0':
                qasm += f"x q[{i}];\n"

        # Diffusion
        qasm += "\n// Diffusion operator\n"
        for i in range(n_qubits):
            qasm += f"h q[{i}];\n"
        for i in range(n_qubits):
            qasm += f"x q[{i}];\n"

        qasm += f"h q[{n_qubits-1}];\n"
        qasm += f"mcx q[0],q[1]" + "".join(f",q[{i}]" for i in range(2, n_qubits)) + f";\n"
        qasm += f"h q[{n_qubits-1}];\n"

        for i in range(n_qubits):
            qasm += f"x q[{i}];\n"
        for i in range(n_qubits):
            qasm += f"h q[{i}];\n"

    qasm += "\nmeasure q -> c;\n"
    return qasm

# Run Grover's algorithm
n = 5
target = 13  # Binary: 01101
iterations = int(np.floor(np.pi/4 * np.sqrt(2**n)))

circuit = grover_search(n, target, iterations)
result = client.execute(qasm=circuit, shots=1024)

print(f"Searching for |{format(target, f'0{n}b')}> in {2**n} items")
print(f"Iterations: {iterations}")
print(f"\nTop 5 results:")
sorted_counts = sorted(result.counts.items(), key=lambda x: x[1], reverse=True)
for state, count in sorted_counts[:5]:
    prob = count / 1024
    print(f"  |{state}> : {count} ({prob:.1%})")

Quantum Error Analysis

from softqcos_sdk import QCOSClient
import numpy as np
import matplotlib.pyplot as plt

client = QCOSClient()

def analyze_decoherence(circuit_depth: int, n_qubits: int = 5) -> dict:
    """
    Analyze how circuit depth affects state fidelity.
    """
    # Create increasingly deep circuits
    qasm = f"""
OPENQASM 2.0;
include "qelib1.inc";
qreg q[{n_qubits}];
creg c[{n_qubits}];

// Prepare GHZ state
h q[0];
"""
    for i in range(n_qubits - 1):
        qasm += f"cx q[{i}], q[{i+1}];\n"

    # Add identity layers (depth simulation)
    for layer in range(circuit_depth):
        qasm += f"\n// Layer {layer + 1}\n"
        for i in range(n_qubits):
            qasm += f"id q[{i}];\n"  # Identity gate

    qasm += "\nmeasure q -> c;\n"

    result = client.execute(qasm=qasm, shots=4096)

    # Calculate GHZ fidelity
    ideal_states = ['0' * n_qubits, '1' * n_qubits]
    fidelity = sum(result.counts.get(s, 0) for s in ideal_states) / 4096

    return {
        'depth': circuit_depth,
        'fidelity': fidelity,
        'counts': result.counts
    }

# Run analysis
depths = [0, 10, 20, 50, 100, 200]
results = []

for d in depths:
    res = analyze_decoherence(d)
    results.append(res)
    print(f"Depth {d:3d}: Fidelity = {res['fidelity']:.4f}")

# Plot results
plt.figure(figsize=(10, 6))
plt.plot([r['depth'] for r in results], [r['fidelity'] for r in results], 'o-')
plt.xlabel('Circuit Depth')
plt.ylabel('GHZ State Fidelity')
plt.title('Decoherence Analysis')
plt.grid(True)
plt.savefig('decoherence_analysis.png')

Use Case: Quantum Machine Learning Research

Quantum Kernel Methods

from softqcos_sdk import QCOSClient
import numpy as np
from sklearn.svm import SVC
from sklearn.datasets import make_moons

client = QCOSClient()

def quantum_kernel_circuit(x1: list, x2: list) -> str:
    """
    Create circuit for computing quantum kernel between two points.
    """
    n = len(x1)
    qasm = f"""
OPENQASM 2.0;
include "qelib1.inc";
qreg q[{n}];
creg c[{n}];

// Encode x1
"""
    for i, val in enumerate(x1):
        qasm += f"ry({val * np.pi}) q[{i}];\n"

    qasm += "\n// Entangle\n"
    for i in range(n - 1):
        qasm += f"cx q[{i}], q[{i+1}];\n"

    # Inverse encoding for x2
    qasm += "\n// Inverse encode x2\n"
    for i in range(n - 1, -1, -1):
        if i < n - 1:
            qasm += f"cx q[{i}], q[{i+1}];\n"
    for i, val in enumerate(x2):
        qasm += f"ry({-val * np.pi}) q[{i}];\n"

    qasm += "\nmeasure q -> c;\n"
    return qasm

def compute_kernel_matrix(X: np.ndarray, shots: int = 1024) -> np.ndarray:
    """
    Compute quantum kernel matrix for dataset X.
    """
    n_samples = len(X)
    kernel = np.zeros((n_samples, n_samples))

    for i in range(n_samples):
        for j in range(i, n_samples):
            circuit = quantum_kernel_circuit(X[i].tolist(), X[j].tolist())
            result = client.execute(qasm=circuit, shots=shots)

            # Kernel value = probability of measuring |00...0>
            zeros_state = '0' * len(X[i])
            kernel[i, j] = result.counts.get(zeros_state, 0) / shots
            kernel[j, i] = kernel[i, j]

    return kernel

# Generate dataset
X, y = make_moons(n_samples=50, noise=0.1, random_state=42)
X = (X - X.mean(axis=0)) / X.std(axis=0)  # Normalize

# Compute quantum kernel
print("Computing quantum kernel matrix...")
K = compute_kernel_matrix(X)

# Train SVM with quantum kernel
svm = SVC(kernel='precomputed')
svm.fit(K, y)

# Evaluate
accuracy = svm.score(K, y)
print(f"Training accuracy: {accuracy:.2%}")

Use Case: Variational Algorithm Benchmarking

from softqcos_sdk import QCOSClient
import numpy as np
from dataclasses import dataclass
from typing import List, Callable

client = QCOSClient()

@dataclass
class BenchmarkResult:
    name: str
    qubits: int
    depth: int
    parameters: int
    iterations: int
    final_cost: float
    execution_time: float
    shots_per_iter: int

def benchmark_ansatz(
    name: str,
    ansatz_generator: Callable[[List[float]], str],
    n_params: int,
    cost_function: Callable[[dict], float],
    max_iterations: int = 100,
    shots: int = 1024
) -> BenchmarkResult:
    """
    Benchmark a variational ansatz.
    """
    import time

    # Initialize random parameters
    params = np.random.uniform(-np.pi, np.pi, n_params)

    start_time = time.time()

    for iteration in range(max_iterations):
        # Evaluate current parameters
        circuit = ansatz_generator(params.tolist())
        result = client.execute(qasm=circuit, shots=shots)
        cost = cost_function(result.counts)

        # Simple gradient estimation (parameter shift)
        gradient = np.zeros(n_params)
        for i in range(n_params):
            params_plus = params.copy()
            params_plus[i] += np.pi / 2
            params_minus = params.copy()
            params_minus[i] -= np.pi / 2

            result_plus = client.execute(qasm=ansatz_generator(params_plus.tolist()), shots=shots)
            result_minus = client.execute(qasm=ansatz_generator(params_minus.tolist()), shots=shots)

            gradient[i] = (cost_function(result_plus.counts) - cost_function(result_minus.counts)) / 2

        # Update parameters
        learning_rate = 0.1
        params -= learning_rate * gradient

        if iteration % 10 == 0:
            print(f"  Iter {iteration}: cost = {cost:.6f}")

    execution_time = time.time() - start_time

    # Get circuit info
    final_circuit = ansatz_generator(params.tolist())
    depth = final_circuit.count('\n')  # Approximate

    return BenchmarkResult(
        name=name,
        qubits=4,  # Extract from circuit
        depth=depth,
        parameters=n_params,
        iterations=max_iterations,
        final_cost=cost,
        execution_time=execution_time,
        shots_per_iter=shots
    )

# Benchmark different ansätze
results = []

# Hardware-efficient ansatz
def hea(params):
    return f"""
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
creg c[4];
ry({params[0]}) q[0];
ry({params[1]}) q[1];
ry({params[2]}) q[2];
ry({params[3]}) q[3];
cx q[0], q[1];
cx q[2], q[3];
ry({params[4]}) q[0];
ry({params[5]}) q[1];
ry({params[6]}) q[2];
ry({params[7]}) q[3];
measure q -> c;
"""

def cost_fn(counts):
    # Target: maximize |0000> probability
    return 1 - counts.get('0000', 0) / sum(counts.values())

result = benchmark_ansatz("HEA", hea, 8, cost_fn, max_iterations=50)
results.append(result)

# Print benchmark table
print("\n" + "="*80)
print("BENCHMARK RESULTS")
print("="*80)
for r in results:
    print(f"""
Ansatz: {r.name}
  Qubits: {r.qubits}
  Parameters: {r.parameters}
  Iterations: {r.iterations}
  Final Cost: {r.final_cost:.6f}
  Total Time: {r.execution_time:.1f}s
  Shots/Iter: {r.shots_per_iter}
""")

Publication Support

Reproducibility Package

Every QCOS execution includes:

result = client.execute(qasm=circuit, shots=1024)

# Reproducibility metadata
print(result.metadata)
# {
#   'qcos_version': '1.0.0',
#   'backend': 'cuStateVec',
#   'device': 'NVIDIA A100',
#   'seed': 42,
#   'timestamp': '2024-01-15T10:30:00Z',
#   'job_id': 'abc123',
#   'checksum': 'sha256:...'
# }

# Export for publication
result.export_reproducibility_package("experiment_data.zip")

Citation

@software{qcos2024,
  title = {QCOS: Quantum Circuit Optimization Service},
  author = {SoftQuantus},
  year = {2024},
  url = {https://softquantus.com},
  version = {1.0.0}
}

Integration with Research Tools

Jupyter Notebooks

# In Jupyter
from softqcos_sdk import QCOSClient
from softqcos.visualization import plot_histogram, plot_bloch_sphere

client = QCOSClient()

# Interactive widgets
from softqcos.widgets import CircuitBuilder
builder = CircuitBuilder()
builder.display()  # Interactive circuit builder

LaTeX Export

# Export circuit as TikZ
result = client.execute(qasm=circuit, shots=1024)
tikz_code = result.to_tikz()

# Save for paper
with open('circuit.tex', 'w') as f:
    f.write(tikz_code)

Student Resources

Tutorial Series

Interactive Playground

Try circuits directly in the browser:

👉 Launch Playground

Contact

For academic partnerships and institutional licenses:

📧 academic@softquantus.com

Include:

Institution name
Research group/department
Estimated usage (jobs/month)
Research area

Why QCOS for Academia?​

Academic Pricing​

Use Case: Quantum Algorithm Research​

Implementing Novel Algorithms​

Quantum Error Analysis​

Use Case: Quantum Machine Learning Research​

Quantum Kernel Methods​

Use Case: Variational Algorithm Benchmarking​

Publication Support​

Reproducibility Package​

Citation​

Integration with Research Tools​

Jupyter Notebooks​

LaTeX Export​

Student Resources​

Tutorial Series​

Interactive Playground​

Contact​