quantum-gate-ccx
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| quantum-gate-ccx [August 26, 2026 at 16:50] – created - external edit 127.0.0.1 | quantum-gate-ccx [August 26, 2026 at 17:04] (current) – external edit 127.0.0.1 | ||
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| - | # CCX (Toffoli | + | # CCX gate (Toffoli) |
| **CCX** (also Toffoli or Controlled-Controlled-X) is a three-qubit gate: flips the target qubit if both control qubits are $|1\rangle$. The quantum AND gate and is universal for reversible classical computation. | **CCX** (also Toffoli or Controlled-Controlled-X) is a three-qubit gate: flips the target qubit if both control qubits are $|1\rangle$. The quantum AND gate and is universal for reversible classical computation. | ||
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| Action: $|c_1 c_2 t\rangle \to |c_1 c_2 (t \oplus c_1 c_2)\rangle$ where $c_1, c_2$ are controls and $t$ is target. Flips target only if both controls are 1. | Action: $|c_1 c_2 t\rangle \to |c_1 c_2 (t \oplus c_1 c_2)\rangle$ where $c_1, c_2$ are controls and $t$ is target. Flips target only if both controls are 1. | ||
| - | $$\text{CCX} = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \end{pmatrix}$$ | + | $$\text{CCX} = \text{Toffoli} = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \end{pmatrix}$$ |
| Basis state mapping: $|abc\rangle \to |ab(c \oplus (a \wedge b))\rangle$. Swaps $|110\rangle \leftrightarrow |111\rangle$. | Basis state mapping: $|abc\rangle \to |ab(c \oplus (a \wedge b))\rangle$. Swaps $|110\rangle \leftrightarrow |111\rangle$. | ||
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| ## Dual gate | ## Dual gate | ||
| - | - **Fredkin (CSWAP)**: swaps two qubits if third is $|1\rangle$; | + | - **CSWAP |
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