Add support for Qiskit from IBM: software stack for quantum computing and algorithms research. Build, optimize, and execute quantum workloads at scale.

2026-03-27 07:09:27 +08:00 · 2025-11-30 08:46:41 -05:00
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+# Qiskit Patterns: The Four-Step Workflow
+
+Qiskit Patterns provide a general framework for solving domain-specific quantum computing problems in four stages: Map, Optimize, Execute, and Post-process.
+
+## Overview
+
+The patterns framework enables seamless composition of quantum capabilities and supports heterogeneous computing infrastructure (CPU/GPU/QPU). Execute locally, through cloud services, or via Qiskit Serverless.
+
+## The Four Steps
+
+```
+Problem → [Map] → [Optimize] → [Execute] → [Post-process] → Solution
+```
+
+### 1. Map
+Translate classical problems into quantum circuits and operators
+
+### 2. Optimize
+Prepare circuits for target hardware through transpilation
+
+### 3. Execute
+Run circuits on quantum hardware using primitives
+
+### 4. Post-process
+Extract and refine results with classical computation
+
+## Step 1: Map
+
+### Goal
+Transform domain-specific problems into quantum representations (circuits, operators, Hamiltonians).
+
+### Key Decisions
+
+**Choose Output Type:**
+- **Sampler**: For bitstring outputs (optimization, search)
+- **Estimator**: For expectation values (chemistry, physics)
+
+**Design Circuit Structure:**
+```python
+from qiskit import QuantumCircuit
+from qiskit.circuit import Parameter
+import numpy as np
+
+# Example: Parameterized circuit for VQE
+def create_ansatz(num_qubits, depth):
+    qc = QuantumCircuit(num_qubits)
+    params = []
+
+    for d in range(depth):
+        # Rotation layer
+        for i in range(num_qubits):
+            theta = Parameter(f'θ_{d}_{i}')
+            params.append(theta)
+            qc.ry(theta, i)
+
+        # Entanglement layer
+        for i in range(num_qubits - 1):
+            qc.cx(i, i + 1)
+
+    return qc, params
+
+ansatz, params = create_ansatz(num_qubits=4, depth=2)
+```
+
+### Considerations
+
+- **Hardware topology**: Design with backend coupling map in mind
+- **Gate efficiency**: Minimize two-qubit gates
+- **Measurement basis**: Determine required measurements
+
+### Domain-Specific Examples
+
+**Chemistry: Molecular Hamiltonian**
+```python
+from qiskit_nature.second_q.drivers import PySCFDriver
+from qiskit_nature.second_q.mappers import JordanWignerMapper
+
+# Define molecule
+driver = PySCFDriver(atom='H 0 0 0; H 0 0 0.735', basis='sto3g')
+problem = driver.run()
+
+# Map to qubit Hamiltonian
+mapper = JordanWignerMapper()
+hamiltonian = mapper.map(problem.hamiltonian)
+```
+
+**Optimization: QAOA Circuit**
+```python
+from qiskit.circuit import QuantumCircuit, Parameter
+
+def qaoa_circuit(graph, p):
+    """Create QAOA circuit for MaxCut problem"""
+    num_qubits = len(graph.nodes())
+    qc = QuantumCircuit(num_qubits)
+
+    # Initial superposition
+    qc.h(range(num_qubits))
+
+    # Alternating layers
+    betas = [Parameter(f'β_{i}') for i in range(p)]
+    gammas = [Parameter(f'γ_{i}') for i in range(p)]
+
+    for i in range(p):
+        # Problem Hamiltonian
+        for edge in graph.edges():
+            qc.cx(edge[0], edge[1])
+            qc.rz(2 * gammas[i], edge[1])
+            qc.cx(edge[0], edge[1])
+
+        # Mixer Hamiltonian
+        qc.rx(2 * betas[i], range(num_qubits))
+
+    return qc
+```
+
+## Step 2: Optimize
+
+### Goal
+Transform abstract circuits to hardware-compatible ISA (Instruction Set Architecture) circuits.
+
+### Transpilation
+
+```python
+from qiskit import transpile
+
+# Basic transpilation
+qc_isa = transpile(qc, backend=backend, optimization_level=3)
+
+# With specific initial layout
+qc_isa = transpile(
+    qc,
+    backend=backend,
+    optimization_level=3,
+    initial_layout=[0, 2, 4, 6],  # Map to specific physical qubits
+    seed_transpiler=42  # Reproducibility
+)
+```
+
+### Pre-optimization Tips
+
+1. **Test with simulators first**:
+```python
+from qiskit_aer import AerSimulator
+
+sim = AerSimulator.from_backend(backend)
+qc_test = transpile(qc, sim, optimization_level=3)
+print(f"Estimated depth: {qc_test.depth()}")
+```
+
+2. **Analyze transpilation results**:
+```python
+print(f"Original gates: {qc.size()}")
+print(f"Transpiled gates: {qc_isa.size()}")
+print(f"Two-qubit gates: {qc_isa.count_ops().get('cx', 0)}")
+```
+
+3. **Consider circuit cutting** for large circuits:
+```python
+# For circuits too large for available hardware
+# Use circuit cutting techniques to split into smaller subcircuits
+```
+
+## Step 3: Execute
+
+### Goal
+Run ISA circuits on quantum hardware using primitives.
+
+### Using Sampler
+
+```python
+from qiskit_ibm_runtime import QiskitRuntimeService, SamplerV2 as Sampler
+
+service = QiskitRuntimeService()
+backend = service.backend("ibm_brisbane")
+
+# Transpile first
+qc_isa = transpile(qc, backend=backend, optimization_level=3)
+
+# Execute
+sampler = Sampler(backend)
+job = sampler.run([qc_isa], shots=10000)
+result = job.result()
+counts = result[0].data.meas.get_counts()
+```
+
+### Using Estimator
+
+```python
+from qiskit_ibm_runtime import EstimatorV2 as Estimator
+from qiskit.quantum_info import SparsePauliOp
+
+service = QiskitRuntimeService()
+backend = service.backend("ibm_brisbane")
+
+# Transpile
+qc_isa = transpile(qc, backend=backend, optimization_level=3)
+
+# Define observable
+observable = SparsePauliOp(["ZZZZ", "XXXX"])
+
+# Execute
+estimator = Estimator(backend)
+job = estimator.run([(qc_isa, observable)])
+result = job.result()
+expectation_value = result[0].data.evs
+```
+
+### Execution Modes
+
+**Session Mode (Iterative):**
+```python
+from qiskit_ibm_runtime import Session
+
+with Session(backend=backend) as session:
+    sampler = Sampler(session=session)
+
+    # Multiple iterations
+    for iteration in range(max_iterations):
+        qc_iteration = update_circuit(params[iteration])
+        qc_isa = transpile(qc_iteration, backend=backend)
+
+        job = sampler.run([qc_isa], shots=1000)
+        result = job.result()
+
+        # Update parameters
+        params[iteration + 1] = optimize_params(result)
+```
+
+**Batch Mode (Parallel):**
+```python
+from qiskit_ibm_runtime import Batch
+
+with Batch(backend=backend) as batch:
+    sampler = Sampler(session=batch)
+
+    # Submit all jobs at once
+    jobs = []
+    for qc in circuit_list:
+        qc_isa = transpile(qc, backend=backend)
+        job = sampler.run([qc_isa], shots=1000)
+        jobs.append(job)
+
+    # Collect results
+    results = [job.result() for job in jobs]
+```
+
+### Error Mitigation
+
+```python
+from qiskit_ibm_runtime import Options
+
+options = Options()
+options.resilience_level = 2  # 0=none, 1=light, 2=moderate, 3=heavy
+options.optimization_level = 3
+
+sampler = Sampler(backend, options=options)
+```
+
+## Step 4: Post-process
+
+### Goal
+Extract meaningful results from quantum measurements using classical computation.
+
+### Result Processing
+
+**For Sampler (Bitstrings):**
+```python
+counts = result[0].data.meas.get_counts()
+
+# Convert to probabilities
+total_shots = sum(counts.values())
+probabilities = {state: count/total_shots for state, count in counts.items()}
+
+# Find most probable state
+max_state = max(counts, key=counts.get)
+print(f"Most probable state: {max_state} ({counts[max_state]}/{total_shots})")
+```
+
+**For Estimator (Expectation Values):**
+```python
+expectation_value = result[0].data.evs
+std_dev = result[0].data.stds  # Standard deviation
+
+print(f"Energy: {expectation_value} ± {std_dev}")
+```
+
+### Domain-Specific Post-Processing
+
+**Chemistry: Ground State Energy**
+```python
+def post_process_chemistry(result, nuclear_repulsion):
+    """Extract ground state energy"""
+    electronic_energy = result[0].data.evs
+    total_energy = electronic_energy + nuclear_repulsion
+    return total_energy
+```
+
+**Optimization: MaxCut Solution**
+```python
+def post_process_maxcut(counts, graph):
+    """Find best cut from measurement results"""
+    def compute_cut_value(bitstring, graph):
+        cut_value = 0
+        for edge in graph.edges():
+            if bitstring[edge[0]] != bitstring[edge[1]]:
+                cut_value += 1
+        return cut_value
+
+    # Find bitstring with maximum cut
+    best_cut = 0
+    best_string = None
+
+    for bitstring, count in counts.items():
+        cut = compute_cut_value(bitstring, graph)
+        if cut > best_cut:
+            best_cut = cut
+            best_string = bitstring
+
+    return best_string, best_cut
+```
+
+### Advanced Post-Processing
+
+**Error Mitigation Post-Processing:**
+```python
+# Apply additional classical error mitigation
+from qiskit.result import marginal_counts
+
+# Marginalize to relevant qubits
+relevant_qubits = [0, 1, 2]
+marginal = marginal_counts(counts, indices=relevant_qubits)
+```
+
+**Statistical Analysis:**
+```python
+import numpy as np
+
+def analyze_results(results_list):
+    """Analyze multiple runs for statistics"""
+    energies = [r[0].data.evs for r in results_list]
+
+    mean_energy = np.mean(energies)
+    std_energy = np.std(energies)
+    confidence_interval = 1.96 * std_energy / np.sqrt(len(energies))
+
+    return {
+        'mean': mean_energy,
+        'std': std_energy,
+        '95% CI': (mean_energy - confidence_interval, mean_energy + confidence_interval)
+    }
+```
+
+**Visualization:**
+```python
+from qiskit.visualization import plot_histogram
+import matplotlib.pyplot as plt
+
+# Visualize results
+plot_histogram(counts, figsize=(12, 6))
+plt.title("Measurement Results")
+plt.show()
+```
+
+## Complete Example: VQE for Chemistry
+
+```python
+from qiskit import QuantumCircuit, transpile
+from qiskit_ibm_runtime import QiskitRuntimeService, EstimatorV2 as Estimator, Session
+from qiskit.quantum_info import SparsePauliOp
+from scipy.optimize import minimize
+import numpy as np
+
+# 1. MAP: Create parameterized circuit
+def create_ansatz(num_qubits):
+    qc = QuantumCircuit(num_qubits)
+    params = []
+
+    for i in range(num_qubits):
+        theta = f'θ_{i}'
+        params.append(theta)
+        qc.ry(theta, i)
+
+    for i in range(num_qubits - 1):
+        qc.cx(i, i + 1)
+
+    return qc, params
+
+# Define Hamiltonian (example: H2 molecule)
+hamiltonian = SparsePauliOp(["IIZZ", "ZZII", "XXII", "IIXX"], coeffs=[0.3, 0.3, 0.1, 0.1])
+
+# 2. OPTIMIZE: Connect and prepare
+service = QiskitRuntimeService()
+backend = service.backend("ibm_brisbane")
+
+ansatz, param_names = create_ansatz(num_qubits=4)
+
+# 3. EXECUTE: Run VQE
+def cost_function(params):
+    # Bind parameters
+    bound_circuit = ansatz.assign_parameters({param_names[i]: params[i] for i in range(len(params))})
+
+    # Transpile
+    qc_isa = transpile(bound_circuit, backend=backend, optimization_level=3)
+
+    # Execute
+    job = estimator.run([(qc_isa, hamiltonian)])
+    result = job.result()
+    energy = result[0].data.evs
+
+    return energy
+
+with Session(backend=backend) as session:
+    estimator = Estimator(session=session)
+
+    # Classical optimization loop
+    initial_params = np.random.random(len(param_names)) * 2 * np.pi
+    result = minimize(cost_function, initial_params, method='COBYLA')
+
+# 4. POST-PROCESS: Extract ground state energy
+ground_state_energy = result.fun
+optimized_params = result.x
+
+print(f"Ground state energy: {ground_state_energy}")
+print(f"Optimized parameters: {optimized_params}")
+```
+
+## Best Practices
+
+### 1. Iterate Locally First
+Test the full workflow with simulators before using hardware:
+```python
+from qiskit.primitives import StatevectorEstimator
+
+estimator = StatevectorEstimator()
+# Test workflow locally
+```
+
+### 2. Use Sessions for Iterative Algorithms
+VQE, QAOA, and other variational algorithms benefit from sessions.
+
+### 3. Choose Appropriate Shots
+- Development/testing: 100-1000 shots
+- Production: 10,000+ shots
+
+### 4. Monitor Convergence
+```python
+energies = []
+
+def cost_function_with_tracking(params):
+    energy = cost_function(params)
+    energies.append(energy)
+    print(f"Iteration {len(energies)}: E = {energy}")
+    return energy
+```
+
+### 5. Save Results
+```python
+import json
+
+results_data = {
+    'energy': float(ground_state_energy),
+    'parameters': optimized_params.tolist(),
+    'iterations': len(energies),
+    'backend': backend.name
+}
+
+with open('vqe_results.json', 'w') as f:
+    json.dump(results_data, f, indent=2)
+```
+
+## Qiskit Serverless
+
+For large-scale workflows, use Qiskit Serverless for distributed computation:
+
+```python
+from qiskit_serverless import ServerlessClient, QiskitFunction
+
+client = ServerlessClient()
+
+# Define serverless function
+@QiskitFunction()
+def run_vqe_serverless(hamiltonian, ansatz):
+    # Your VQE implementation
+    pass
+
+# Execute remotely
+job = run_vqe_serverless(hamiltonian, ansatz)
+result = job.result()
+```
+
+## Common Workflow Patterns
+
+### Pattern 1: Parameter Sweep
+```python
+# Map → Optimize once → Execute many → Post-process
+qc_isa = transpile(parameterized_circuit, backend=backend)
+
+with Batch(backend=backend) as batch:
+    sampler = Sampler(session=batch)
+    results = []
+
+    for param_set in parameter_sweep:
+        bound_qc = qc_isa.assign_parameters(param_set)
+        job = sampler.run([bound_qc], shots=1000)
+        results.append(job.result())
+```
+
+### Pattern 2: Iterative Refinement
+```python
+# Map → (Optimize → Execute → Post-process) repeated
+with Session(backend=backend) as session:
+    estimator = Estimator(session=session)
+
+    for iteration in range(max_iter):
+        qc = update_circuit(params)
+        qc_isa = transpile(qc, backend=backend)
+
+        result = estimator.run([(qc_isa, observable)]).result()
+        params = update_params(result)
+```
+
+### Pattern 3: Ensemble Measurement
+```python
+# Map → Optimize → Execute many observables → Post-process
+qc_isa = transpile(qc, backend=backend)
+
+observables = [obs1, obs2, obs3, obs4]
+jobs = [(qc_isa, obs) for obs in observables]
+
+estimator = Estimator(backend)
+result = estimator.run(jobs).result()
+expectation_values = [r.data.evs for r in result]
+```