### Algoritmo de Shor   --- <!-- _backgroundImage: url(static/bg/bg2.svg) -- $$ \ket{0}\ket1 \xrightarrow{H} \begin{matrix} \ket{00}\ket1\\ \ket{01}\ket1\\ \ket{02}\ket1\\ \ket{03}\ket1\\ \ket{04}\ket1\\ \vdots\\ \ket{11}\ket1\\ \ket{12}\ket1\\ \ket{13}\ket1\\ \ket{14}\ket1\\ \ket{15}\ket1 \end{matrix} \xrightarrow{8^x \text{ mod } 15} \begin{matrix} \ket{00}\ket1\\ \ket{01}\ket8\\ \ket{02}\ket4\\ \ket{03}\ket2\\ \ket{04}\ket1\\ \vdots\\ \ket{11}\ket2\\ \ket{12}\ket1\\ \ket{13}\ket8\\ \ket{14}\ket4\\ \ket{15}\ket2 \end{matrix} \xRightarrow{\text{Medida}} \begin{matrix} \ket{03}\ket2\\ \ket{07}\ket2\\ \ket{11}\ket2\\ \ket{15}\ket2\\ \end{matrix} \xrightarrow{\text{QFT}^\dagger} \begin{matrix} \ket{00} \equiv 0\times4\\ \ket{04} \equiv 1\times4\\ \ket{08} \equiv 2\times4\\ \ket{12} \equiv 3\times4 \end{matrix} \Rightarrow 4 $$ --- ```py from ket import * from ket.plugins import pown from math import pi def qft(qubits: quant, inverter: bool = True) -> quant: if len(qubits) == 1: H(qubits) else: head, *tail = qubits H(head) for i, c in enumerate(reversed(tail)): ctrl(c, phase(pi / 2**(i + 1)), head) qft(tail, inverter=False) if inverter: for i in range(len(qubits) // 2): swap(qubits[i], qubits[- i - 1]) N = 15 a = 8 qubits_de_entrada = quant(N.bit_length()) H(qubits_de_entrada) qubits_de_saída = pown(a, qubits_de_entrada, N) measure(qubits_de_saída) adj(qft, qubits_de_entrada) r = measure(qubits_de_entrada) ```

### Algoritmo de Grover   --- ```py from ket import * from math import pi, sqrt def grover(n, oraculo): qubits = quant(n) H(qubits) for _ in range(int((pi/4)*sqrt(2**n/m))): oraculo(qubits) with around([H, X], qubits): ctrl(qubits[1:], Z, qubits[0]) return measure(qubits) ``` Exemplo: [Execução do Algoritmo de Grover](static/grover.html)