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Course outlineQubits and state vectors
Course Overview
States and Measurement
Qubits and state vectorsCore
Superposition and measurementCore
Wavefunction: the broader quantum idea
Operators, Evolution, and Uncertainty
Operators, eigenstates, and eigenvalues
The Schrödinger equation
The uncertainty principle
Gates, Phase, and Interference
Single-qubit gates and the Bloch sphereCore
Interference: why phase becomes visibleCore
Entanglement and Other Quantum Effects
EntanglementCore
Spin
Tunneling
Phase kickback and the road to algorithms
Course outline
Course Overview
States and Measurement
Qubits and state vectorsCore
Superposition and measurementCore
Wavefunction: the broader quantum idea
Operators, Evolution, and Uncertainty
Operators, eigenstates, and eigenvalues
The Schrödinger equation
The uncertainty principle
Gates, Phase, and Interference
Single-qubit gates and the Bloch sphereCore
Interference: why phase becomes visibleCore
Entanglement and Other Quantum Effects
EntanglementCore
Spin
Tunneling
Phase kickback and the road to algorithms
Home/Quantum Physics/Lessons/Qubits and state vectors
1

States and Measurement

The first step is to separate three ideas that beginners often mix together: the quantum state, the probabilities you predict from that state, and the measurement outcome you finally observe.

Qubits and state vectors

In one sentence: A qubit is a two-state quantum system whose state is described by amplitudes, not by an ordinary probability list.
Formula
∣ψ⟩=α∣0⟩+β∣1⟩,∣α∣2+∣β∣2=1
Simple intuition
A classical bit has one actual value at a time. A qubit is different: before measurement, it is described by a state that tells you how future measurements can turn out.
Precise explanation
The symbols alpha and beta are complex amplitudes. Their squared magnitudes give measurement probabilities in the computational basis. The amplitudes also contain phase information, which is why a qubit is richer than a classical random bit.
Example or analogy
Analogy: a recipe is not the meal. The quantum state is like the recipe for what outcomes can appear and how they interfere, while the measured 0 or 1 is the meal you finally serve.
Common misconception
A qubit is not literally a bit that is secretly both 0 and 1 in an everyday sense. The state encodes amplitudes for possible outcomes; it is not just a statement of ignorance.
Why this matters
Every gate, histogram bar, and Bloch sphere arrow in the simulator is a different view of the same state. If you understand the state, the rest of the interface becomes much easier to read.
Self-check
  • • What is the difference between an amplitude and a probability?
  • • Why can two qubits have the same measurement probabilities but still be different states?
↗ MIT OCW 8.04: lecture notes↗ Nielsen and Chuang, Quantum Computation and Quantum Information▶ See a qubit state
States and Measurement
Superposition and measurement