Quantum Computing Fundamentals

Introduction

• Learn quantum computing
• What you should know
• Qiskit and GitHub Codespaces
• Why quantum computing?

1. Quantum Bits

• Classical bits vs. quantum bits
• Measuring a qubit
• Measure a qubit with Qiskit
• Overview of vectors
• Overview of complex numbers
• Represent qubits as vectors
• Represent qubits on the Bloch sphere
• State vectors and Bloch spheres with Qiskit
• Build a model Bloch sphere
• Global and relative phase
• Challenge: Create a quantum circuit
• Solution: Create a quantum circuit

2. Multiple Quantum Bits

• Represent multiple qubits
• Represent multiple qubits with Qiskit
• How much information is in a qubit?

3. Single-Qubit Pauli Gates

• Overview of matrix operations
• Quantum logic gates
• Pauli-X gate
• Pauli-X gate with Qiskit
• Pauli-Y gate
• Pauli-Y gate with Qiskit
• Pauli-Z gate
• Pauli-Z gate with Qiskit
• Challenge: Binary numbers
• Solution: Binary numbers

4. Single-Qubit Superposition Gates

• Hadamard gate
• Hadamard gate with Qiskit
• Measurement on an arbitrary basis
• Phase shift gates
• Phase shift gates with Qiskit
• Parameterized rotation gates
• Parameterized rotation gates with Qiskit
• Single-qubit gates on multi-qubit states
• Challenge: Random numbers
• Solution: Random numbers

5. Multi-Qubit Gates

• Controlled-NOT (CNOT) gate
• Controlled-NOT (CNOT) gate with Qiskit
• Toffoli gate
• Toffoli gate with Qiskit
• Swap and Fredkin gates
• Swap and Fredkin gates with Qiskit
• Challenge: Classical two-bit adder
• Solution: Classical two-bit adder

6. Quantum Entanglement

• What is quantum entanglement?
• Represent entangled qubits
• Simulate a bell state with Qiskit
• Challenge: Entangle three qubits
• Solution: Entangle three qubits

7. Real Quantum Hardware

• Access IBM quantum computers
• Use Qiskit with real quantum hardware
• Mitigate quantum measurement errors

8. Quantum Algorithms

• Superdense coding
• Superdense coding with Qiskit
• Quantum teleportation
• Quantum teleportation with Qiskit
• Challenge: Real quantum teleportation
• Solution: Real quantum teleportation

Conclusion

• Your next quantum steps