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https://github.com/K-Dense-AI/claude-scientific-skills.git
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198 lines
3.4 KiB
Markdown
198 lines
3.4 KiB
Markdown
# Quantum Circuit Building
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## Creating a Quantum Circuit
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Create circuits using the `QuantumCircuit` class:
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```python
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from qiskit import QuantumCircuit
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# Create a circuit with 3 qubits
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qc = QuantumCircuit(3)
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# Create a circuit with 3 qubits and 3 classical bits
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qc = QuantumCircuit(3, 3)
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```
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## Single-Qubit Gates
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### Pauli Gates
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```python
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qc.x(0) # NOT/Pauli-X gate on qubit 0
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qc.y(1) # Pauli-Y gate on qubit 1
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qc.z(2) # Pauli-Z gate on qubit 2
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```
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### Hadamard Gate
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Creates superposition:
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```python
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qc.h(0) # Hadamard gate on qubit 0
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```
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### Phase Gates
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```python
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qc.s(0) # S gate (√Z)
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qc.t(0) # T gate (√S)
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qc.p(π/4, 0) # Phase gate with custom angle
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```
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### Rotation Gates
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```python
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from math import pi
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qc.rx(pi/2, 0) # Rotation around X-axis
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qc.ry(pi/4, 1) # Rotation around Y-axis
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qc.rz(pi/3, 2) # Rotation around Z-axis
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```
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## Multi-Qubit Gates
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### CNOT (Controlled-NOT)
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```python
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qc.cx(0, 1) # CNOT with control=0, target=1
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```
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### Controlled Gates
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```python
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qc.cy(0, 1) # Controlled-Y
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qc.cz(0, 1) # Controlled-Z
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qc.ch(0, 1) # Controlled-Hadamard
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```
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### SWAP Gate
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```python
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qc.swap(0, 1) # Swap qubits 0 and 1
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```
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### Toffoli (CCX) Gate
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```python
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qc.ccx(0, 1, 2) # Toffoli with controls=0,1 and target=2
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```
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## Measurements
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Add measurements to read qubit states:
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```python
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# Measure all qubits
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qc.measure_all()
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# Measure specific qubits to specific classical bits
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qc.measure(0, 0) # Measure qubit 0 to classical bit 0
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qc.measure([0, 1], [0, 1]) # Measure qubits 0,1 to bits 0,1
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```
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## Circuit Composition
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### Combining Circuits
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```python
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qc1 = QuantumCircuit(2)
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qc1.h(0)
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qc2 = QuantumCircuit(2)
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qc2.cx(0, 1)
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# Compose circuits
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qc_combined = qc1.compose(qc2)
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```
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### Tensor Product
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```python
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qc1 = QuantumCircuit(1)
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qc1.h(0)
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qc2 = QuantumCircuit(1)
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qc2.x(0)
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# Create larger circuit from smaller ones
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qc_tensor = qc1.tensor(qc2) # Results in 2-qubit circuit
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```
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## Barriers and Labels
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```python
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qc.barrier() # Add visual barrier in circuit
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qc.barrier([0, 1]) # Barrier on specific qubits
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# Add labels for clarity
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qc.barrier(label="Initialization")
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```
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## Circuit Properties
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```python
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print(qc.num_qubits) # Number of qubits
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print(qc.num_clbits) # Number of classical bits
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print(qc.depth()) # Circuit depth
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print(qc.size()) # Total gate count
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print(qc.count_ops()) # Dictionary of gate counts
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```
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## Example: Bell State
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Create entanglement between two qubits:
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```python
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qc = QuantumCircuit(2)
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qc.h(0) # Superposition on qubit 0
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qc.cx(0, 1) # Entangle qubit 0 and 1
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qc.measure_all() # Measure both qubits
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```
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## Example: Quantum Fourier Transform (QFT)
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```python
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from math import pi
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def qft(n):
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qc = QuantumCircuit(n)
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for j in range(n):
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qc.h(j)
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for k in range(j+1, n):
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qc.cp(pi/2**(k-j), k, j)
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return qc
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# Create 3-qubit QFT
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qc_qft = qft(3)
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```
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## Parameterized Circuits
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Create circuits with parameters for variational algorithms:
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```python
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from qiskit.circuit import Parameter
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theta = Parameter('θ')
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qc = QuantumCircuit(1)
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qc.ry(theta, 0)
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# Bind parameter value
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qc_bound = qc.assign_parameters({theta: pi/4})
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```
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## Circuit Operations
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```python
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# Inverse of a circuit
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qc_inverse = qc.inverse()
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# Decompose gates to basis gates
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qc_decomposed = qc.decompose()
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# Draw circuit (returns string or diagram)
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print(qc.draw())
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print(qc.draw('mpl')) # Matplotlib figure
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```
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