About quantum computers
Quantum computers will use two fundamental properties of the quantum world: superposition and entanglement.
So, what is superposition? Qubits can be in the “|0⟩” state (called a zero-ket), the “|1⟩” state (called the one-ket), or a linear combination of the two (superposition). The half-angle bracket notation |⟩ is conventionally used to indicate qubits, as opposed to ordinary bits. When you measure the |0⟩ quantum state, you get a classical 0, and when you measure the |1⟩ quantum state, you get a classical 1. The |0⟩ state is sometimes called the ground state because in many physical implementations of quantum computing, including mine, it is the lowest energy state.
What’s a QBit ?
A qubit is a quantum system consisting of two energy levels, labeled |0⟩ and |1⟩. The |0⟩ state is often called the ground state because it is the lower of the two energies. Together, |0⟩ and |1⟩ make up what we call “standard basis vectors”. Like all vectors, they point in a direction and have a magnitude. Defining basis vectors is a really useful trick we have borrowed from linear algebra. The basic idea is that once you have defined these vectors, you can construct any other vector from a linear combination of the basis vectors.
Additionally, qubits also have a “phase”, which results from the fact that superpositions can be complex. To represent these superpositions, we put a coefficient such as a or b in front of the state like so: a|0⟩+b|1⟩. Here’s what the formula is saying: “The state is made up of a linear combination of |0⟩ and |1⟩, where the proportion of each depends on the coefficients a and b.” The coefficients a and b could be positive, negative, or even complex. If we take the absolute value of a or b and square it (e.g. |a|2‘or:math:‘|b|2 ), we get the probability of measuring the 0 or 1 outcome, respectively.
The basis states |0⟩ and |1⟩ and their linear combinations a|0⟩ + b|1⟩ describe the state of a single qubit. But because the coefficients a and b are not just real numbers, but can be imaginary or even complex, visualizing a qubit requires a special tool called the Bloch Sphere. The Bloch Sphere is a sphere with a radius of one and a point on its surface represents the state of a qubit. Like a globe uses longitude and latitude to describe points on the surface, the Bloch sphere can also use angles to describe the state of a qubit. This representation allows any qubit state, including those with complex coefficients, to be represented as a point on the surface of the Bloch sphere. Points on the surface of the Bloch sphere which lie along the X, Y, or Z axis correspond to special states as described below.