The canonical two-qubit controlled operation used to create correlation and entanglement.
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Controlled-X is the bridge between a single-qubit operation and a multi-qubit circuit contract.
Takes a 2-qubit register and states no assumption about what is on it. That is the whole condition: anything returning 2 qubits can feed it.
16 entries meet this end. Named below.
Returns a 2-qubit register a next stage can take. This is the end that joins.
11 entries meet this end. Named below.
A unitary. The same register goes in and comes out, and this entry states no assumption about what is on it — which is what lets anything of the same width feed it. See all 29 →
Controlled- (CNOT) acts on two qubits as : the target flips exactly when the control is , the truth table this record checks directly against the four computational-basis inputs. In matrix form, , a permutation matrix that is its own inverse, . Applied after a Hadamard on the control, , the Bell state this catalog's entangling-action check reproduces — the second half of the verification claim. CNOT is a maximally entangling two-qubit gate: together with arbitrary single-qubit rotations it forms a universal gate set, and physically it is the standard native (or compiled) two-qubit interaction most hardware backends expose, making it the workhorse for building larger controlled operations.
OPENQASM 3.0;
include "stdgates.inc";
qubit[2] q;
cx q[0], q[1];Use a classical state-vector or matrix simulation at the same width, precision, and measurement objective.
The quantum record demonstrates a state or operator behavior; it does not make classical simulation or communication costs disappear.
Compare fidelity, samples, gate depth, noise, memory, and the cost of preparing and reading the state.
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Standard graduate textbook covering the single- and two-qubit gate definitions, matrix identities, and circuit primitives this record states.
doi.org/10.1017/cbo9780511976667 ↗