A is the fundamental unit of quantum information that can exist in a superposition of two basis states.

Context: Qubit vs Classical Bit

In the state α|0⟩+β|1⟩, the maps squared magnitudes of amplitudes to measurement probabilities in the standard basis.

Context: Born Rule for Measurement Probabilities

Measurement uses the to produce classical outcomes and collapses the quantum state to a basis state.

Context: Measurement collapse and Born rule

Superposition represents a qubit as a linear combination of basis states, and alters measurement probabilities through relative phases.

Context: Superposition and Quantum Interference

A valid n-qubit state lives in a -dimensional state space, which makes classical simulation resource-intensive.

Context: State Space Scaling with Qubits

Quantum computation is modeled as a network of logic gates acting on state vectors, with measurements typically deferred to the end.

Context: Unitary Gates and Quantum Logic Networks

The gate is a two-qubit gate that applies NOT to the second qubit iff the first (control) qubit is |1⟩.

Context: Controlled-NOT (CNOT) gate

CNOT|10⟩=|11⟩ because the control qubit is |1⟩, so the target qubit undergoes a operation.

Context: NOT behavior inside CNOT

Algorithm designers create procedures that amplify the probability of a desired measurement result, which leads to increasing the chance of obtaining the correct output.

Context: Cause→Effect: interference-based amplification

A quantum algorithm uses superposition to encode multiple inputs at once (quantum parallelism), which causes multiple output values to be represented in the final quantum state through a transformation.

Context: Cause→Effect: quantum parallelism via unitary encoding

Measurement at the end returns only one classical outcome, so alone is insufficient to guarantee speedup.

Context: Cause→Effect: why parallelism alone does not guarantee speedup

Fault-tolerant quantum memory and error correction target decoherence and noise, which allows systems to scale beyond the era toward reliable computation.

Context: Cause→Effect: moving beyond the NISQ era

A qubit is not sufficiently isolated from its environment, which causes to occur, introducing noise into calculations.

Context: Cause→Effect: decoherence from environmental coupling

A milestone claim that a quantum device outperforms classical computers on a narrowly defined task is called / quantum supremacy.

Context: Quantum advantage / quantum supremacy

The 2019 supremacy claim by Google AI and NASA used a -qubit machine.

Context: Experimental milestone data: 2019 54-qubit claim