Qubits vs. Classical Bits: The Superposition Advantage

1. From Classical Bits to Quantum Bits

As an electronics and electrical engineering student, you're intimately familiar with the classical bit. It's the fundamental unit of information, physically realized by a transistor acting as a switch, representing either a low voltage state (0) or a high voltage state (1). It's always one or the other.

A quantum bit, or qubit, is also a binary system, but its physical basis is entirely different. It leverages the quantum properties of an object, such as the spin of an electron or two energy levels of an atom.

To explore this contrast from an engineer's perspective, let's watch a segment from a video featuring Professor Andrea Morello, a quantum engineer.

The key idea is that we designate two distinct quantum states to be our |0⟩ and |1⟩. So far, this seems like a direct analog to a classical bit. The crucial difference, however, lies in what else the qubit can do.

2. The Power of Superposition

A classical bit must be in a state of 0 or 1. A qubit, however, can be in a state of 0, 1, or a combination of both simultaneously. This is called superposition.

Mathematically, we represent a qubit's state as a linear combination (a weighted sum) of its two basis states, |0⟩ and |1⟩:
$|\psi ⟩=\alpha |0⟩+\beta |1⟩$
Here, $\alpha$ and $\beta$ are complex numbers called amplitudes. They are not probabilities themselves, but they determine the probability of what we'll find when we measure the qubit. Specifically, $|\alpha {|}^2$ is the probability of measuring 0, and $|\beta {|}^2$ is the probability of measuring 1. As we know, we must always have $|\alpha {|}^2+|\beta {|}^2=1$.

Let's return to the EEVblog video, where Prof. Morello explains why superposition isn't some strange, "counter-intuitive" idea, but a logical consequence of a symmetric quantum system.

3. Superposition vs. Classical Probability: The Coin Flip Analogy

A common analogy for measuring a superposition is flipping a coin. Before it lands, you don't know the outcome; it could be heads or tails. After it lands (the "measurement"), it's definitively one or the other.

This analogy is a useful starting point, but it's also dangerously misleading. A spinning coin's state is unknown, but it's not fundamentally in both states at once. We are simply ignorant of the definite outcome. A qubit in superposition is in a fundamentally different kind of state.

The following video and its companion article explore this analogy, first building it up and then showing its critical flaws.

To see the underlying code and mathematical notation, you can review the first part of the companion learning module from IBM Quantum.

4. The Real Difference: Phase and Interference

So, if a 50/50 superposition gives the same measurement statistics as a fair coin, what's the big deal? The difference is phase.

The amplitudes $\alpha$ and $\beta$ are complex numbers, which means they have both a magnitude and a phase. While the magnitude determines the probability, the phase is what allows quantum states to interfere with each other, like waves.

• Constructive Interference: When parts of the state are in phase, they add up.
• Destructive Interference: When parts of the state are out of phase, they cancel out.

This has no classical parallel. You can't flip a coin, do something to it mid-air, and guarantee it always lands on heads. But with a qubit, you can. The next segment of the Qiskit video demonstrates this beautifully by applying a second Hadamard gate.

The companion article walks through the mathematics of this interference, showing exactly how the |1⟩ components cancel out.

This phenomenon shows that quantum operations are not random. They are precise, deterministic rotations (as we learned from unitarity). The randomness only enters at the moment of measurement.

5. A Better Model: The Bloch Sphere

The flipping coin analogy is broken because it focuses on randomness. A better analogy is a stationary coin balanced on its edge. More formally, we visualize a single qubit's state as a vector on a 3D sphere called the Bloch Sphere.

In this model:

• The North Pole is the state |0⟩.
• The South Pole is the state |1⟩.
• Any other point on the sphere's surface is a superposition of |0⟩ and |1⟩.
• The latitude determines the amplitudes (probabilities). The equator represents a 50/50 superposition.
• The longitude determines the relative phase between |0⟩ and |1⟩.

This connects perfectly to our last lesson! A single-qubit gate is simply a rotation of the state vector on the Bloch sphere. The Hadamard gate, for example, is a specific rotation that takes a vector at the north pole (|0⟩) and moves it to the equator. Applying it a second time rotates it back to the north pole.

Conclusion

Today we've uncovered the true nature of a qubit. It's not just a classical bit with some uncertainty; it is a fundamentally different object that obeys the strange and powerful rules of quantum mechanics.

Key Takeaways:

• A classical bit is always either 0 or 1.
• A qubit can be in a superposition of |0⟩ and |1⟩, meaning it is in a combination of both states at once.
• A superposition is described by complex amplitudes which have both a magnitude and a phase.
• The squared magnitude of an amplitude gives the probability of measuring that state.
• The phase is what distinguishes quantum superposition from classical probability. It allows for interference, where parts of a quantum state can cancel each other out or reinforce each other.
• Randomness only enters the picture upon measurement, which forces the qubit to "choose" a classical state. The operations themselves (gates) are deterministic and reversible rotations on the Bloch Sphere.

Preview of the Next Lesson:
We've now conceptually introduced the qubit state |\psi⟩ = \alpha|0\rangle + \beta|1\rangle and the Bloch sphere. In our next lesson, we will formalize this. We will learn to properly use Dirac (ket) notation to represent any single-qubit state and explore the mathematics of the Bloch sphere in more detail, connecting the angles of the sphere directly to the amplitudes $\alpha$ and $\beta$.