Step 03 of 12 · 20 min
Basic quantum vocabulary
The words for one Bell state. The workshop lesson is Quantum from Zero to One, by Andrew Chen of Qolour. The full definition list is the glossary.
Qubi and Qolour
The workshop lesson is Quantum from Zero to One. Andrew Chen, Qolour (andrew@qolour.com), wrote this 0-to-1 introduction. It uses Qolour’s handheld Qubi. Open the PDF from the lesson page, then come back for the words the Bell lab needs.
The educator course stays on Qolour’s site. This page does not copy it.
Words for the lab
Read the plain sentence and the technical sentence. The glossary holds the rest of the list, including gates that this lab does not use.
Qubit
A qubit is the basic unit of quantum information. Before measurement it is described by a quantum state, not by a single stored 0 or 1.
A qubit’s pure state is a normalized vector in a two-dimensional complex vector space, spanned by the basis states |0⟩ and |1⟩.
State
The state is the complete description of what we know about the qubits before we measure them.
For an isolated pure state of n qubits, the state is a normalized vector with 2ⁿ amplitudes, one for each computational basis string.
Superposition
A superposition is a state that is a combination of basis states, with amplitudes, before measurement.
A state is a superposition when more than one computational-basis amplitude is nonzero. Measurement in that basis yields one basis state, with probability given by the squared magnitudes.
Entanglement
Entanglement is a correlation between qubits that cannot be written as each qubit having its own separate state.
A multi-qubit pure state is entangled when it cannot be factored into a tensor product of single-qubit states. The Bell state (|00⟩ + |11⟩)/√2 is entangled.
Hadamard gate
The Hadamard gate, written H, takes |0⟩ into an equal superposition of |0⟩ and |1⟩.
H|0⟩ = (|0⟩ + |1⟩)/√2 and H|1⟩ = (|0⟩ − |1⟩)/√2. Applying H twice returns the original basis state.
CNOT or CX gate
CNOT, also called CX, flips the target qubit when the control qubit is |1⟩.
CX|00⟩ = |00⟩, CX|01⟩ = |01⟩, CX|10⟩ = |11⟩, CX|11⟩ = |10⟩, with the control written first in this sentence. In Qiskit’s little-endian bitstrings, read the rightmost bit as qubit 0.
Measurement
Measurement asks a qubit for a classical result. You get one basis outcome, not the full list of amplitudes.
A computational-basis measurement samples a bit string x with probability |αₓ|² and leaves the system in the corresponding basis state.
Shot
A shot is one run of the circuit that ends in one measurement result.
The shots argument tells a sampler how many times to sample the measured circuit.
Counts
Counts are how many shots produced each bitstring.
A counts dictionary maps bitstrings to integers. The values sum to the number of shots.