The Spectrum of Quantum Superposition: From Simple States to Entangled Qubits

Not all superpositions are created equal!

Photo by Andrew George on Unsplash

Quantum superposition is one of the most fundamental principles of quantum mechanics; it allows qubits to exist in multiple states simultaneously. Superposition is a concept that enables quantum computers to excel over classical computers. However, not all superpositions are the same.

Mathematically, when we form a superposition, we create a probability distribution over a set of qubits. This distribution depends on the gates we apply to the registers containing the qubits. These probability distributions differ in phase relationships and symmetry properties.

Let me take a step back for a second. If you are unfamiliar with quantum computing and its math, I will briefly explain how it works. Mathematically, qubit states are represented as vectors, while gates are represented using unitary matrices. When we multiply the qubit vectors with the gate unitaries, we have a new state for the qubits.

Now, we can get back to talking about the types of superposition. When we design or implement quantum algorithms, we choose a superposition that matches our desired application. Understanding these differences is crucial for quantum computing, cryptography, and sensing applications.