Lilly Tech Systems
Quantum Computing Basics
Understanding qubits, quantum gates, and measurement is essential before building quantum ML models. This lesson covers the fundamentals you need.
Qubits: The Quantum Bit
A classical bit is either 0 or 1. A qubit can be in a superposition of both states simultaneously, represented as: |ψ⟩ = α|0⟩ + β|1⟩, where α and β are complex probability amplitudes satisfying |α|² + |β|² = 1.
When measured, a qubit collapses to |0⟩ with probability |α|² or |1⟩ with probability |β|². This probabilistic nature is what gives quantum computing its unique power.
Key Quantum Phenomena
| Phenomenon | Description | ML Relevance |
|---|---|---|
| Superposition | A qubit exists in multiple states at once | Enables parallel evaluation of many inputs |
| Entanglement | Qubits become correlated; measuring one affects the other | Creates complex feature correlations |
| Interference | Quantum amplitudes can add or cancel | Amplifies correct solutions, cancels wrong ones |
Quantum Gates
Quantum gates are unitary operations that transform qubit states. Think of them as the quantum equivalent of classical logic gates.
- Pauli-X (NOT gate): Flips |0⟩ to |1⟩ and vice versa. The quantum bit-flip.
- Hadamard (H): Creates equal superposition. Maps |0⟩ to (|0⟩ + |1⟩)/√2. Essential for QML.
- CNOT: Controlled-NOT. Entangles two qubits. If control qubit is |1⟩, flips the target.
- Rotation Gates (RX, RY, RZ): Parameterized rotations around X, Y, Z axes. These are the trainable parameters in QML.
- Phase Gate (S, T): Adds a phase to the |1⟩ component. Used for interference patterns.
Quantum Circuits
A quantum circuit is a sequence of quantum gates applied to qubits, followed by measurement. This is the quantum equivalent of a computational graph:
Initialize Qubits
Start with qubits in the |0⟩ state (or encode your data into qubit states).
Apply Gates
Apply a sequence of single-qubit and multi-qubit gates to transform the quantum state.
Measure
Measure the qubits to collapse them into classical bit values. Repeat many times to estimate probabilities.
The Bloch Sphere
A single qubit state can be visualized on a Bloch sphere — a unit sphere where the north pole is |0⟩ and the south pole is |1⟩. Rotation gates (RX, RY, RZ) rotate the state vector around the corresponding axis. This geometric picture is essential for understanding parameterized quantum circuits in QML.
Multiple Qubits and Entanglement
With n qubits, the quantum state lives in a 2^n-dimensional Hilbert space. For example, 2 qubits span: |00⟩, |01⟩, |10⟩, |11⟩. When qubits are entangled, their joint state cannot be described as a product of individual qubit states. This exponential state space is the source of potential quantum advantage for ML.