吾輩は量子プログラミング言語である。名前はまだ無い。 Microsoftで生れ量子テレポーテーションした事だけは記憶している。 ref: https://qiita.com/piyo7/items/0c80181c567b3075c00f

file0.txt

\newcommand{\ket}[1]{\left| #1 \right\rangle}
\frac{1}{\sqrt{2}}\ket{00} + \frac{1}{\sqrt{2}}\ket{11}

file1.txt

\begin{align}
\mathrm{X}\ket{0} &= \ket{1} \\
\mathrm{X}\ket{1} &= \ket{0} \\
\end{align}

file10.txt

CNOT (q1, q2)

file11.txt

\frac{1}{\sqrt{2}}(\mathrm{CNOT} \ket{00}) + \frac{1}{\sqrt{2}}(\mathrm{CNOT} \ket{10}) = \frac{1}{\sqrt{2}}\ket{00} + \frac{1}{\sqrt{2}}\ket{11}

file12.txt

operation() Teleport (Qubit msg, Qubit here, Qubit there) {
    Body {
        EPR (here, there)
        CNOT (msg, here)
        H (msg)

        let m_here = M (here)
        if (m_here == One) {
           X (there)
        }

        let m_msg = M (msg)
        if (m_msg == One) {
           Z (there)
        }
    }
}

file13.txt

operation() Teleport (Qubit msg, Qubit here, Qubit there) {

file14.txt

EPR (here, there)

file15.txt

\begin{align}
&a\ket{0}(\mathrm{EPR} \ket{00}) + b\ket{1}(\mathrm{EPR} \ket{00}) \\
=\quad &\frac{a}{\sqrt{2}}\ket{000} + \frac{a}{\sqrt{2}}\ket{011} + \frac{b}{\sqrt{2}}\ket{100} + \frac{b}{\sqrt{2}}\ket{111}
\end{align}

file16.txt

CNOT (msg, here)

file17.txt

\begin{align}
&\frac{a}{\sqrt{2}}(\mathrm{CNOT} \ket{00})\ket{0} + \frac{a}{\sqrt{2}}(\mathrm{CNOT} \ket{01})\ket{1} \\
&+ \frac{b}{\sqrt{2}}(\mathrm{CNOT} \ket{10})\ket{0} + \frac{b}{\sqrt{2}}(\mathrm{CNOT} \ket{11})\ket{1} \\
=\quad &\frac{a}{\sqrt{2}}\ket{000} + \frac{a}{\sqrt{2}}\ket{011} + \frac{b}{\sqrt{2}}\ket{110} + \frac{b}{\sqrt{2}}\ket{101}
\end{align}

file18.txt

H (msg)

file19.txt

\begin{align}
&\frac{a}{\sqrt{2}}(\mathrm{H}\ket{0})\ket{00} + \frac{a}{\sqrt{2}}(\mathrm{H}\ket{0})\ket{11} \\
&+ \frac{b}{\sqrt{2}}(\mathrm{H}\ket{1})\ket{10} + \frac{b}{\sqrt{2}}(\mathrm{H}\ket{1})\ket{01} \\
=\quad &\frac{a}{2}\ket{000} + \frac{a}{2}\ket{100} + \frac{a}{2}\ket{011} + \frac{a}{2}\ket{111} \\
&+ \frac{b}{2}\ket{010} - \frac{b}{2}\ket{110} + \frac{b}{2}\ket{001} - \frac{b}{2}\ket{101}
\end{align}

file2.txt

\begin{align}
\mathrm{Z}\ket{0} &= \ket{0} \\
\mathrm{Z}\ket{1} &= -\ket{1} \\
\end{align}

file20.txt

let m_here = M (here)
if (m_here == One) {
    X (there)
}

file21.txt

\begin{align}
&\sqrt{2}(\frac{a}{2}\ket{000} + \frac{a}{2}\ket{100} + \frac{b}{2}\ket{001} - \frac{b}{2}\ket{101}) \\
=\quad & \frac{a}{\sqrt{2}}\ket{000} + \frac{a}{\sqrt{2}}\ket{100} + \frac{b}{\sqrt{2}}\ket{001} - \frac{b}{\sqrt{2}}\ket{101}
\end{align}

file22.txt

\begin{align}
&\sqrt{2}(\frac{a}{2}\ket{01}(\mathrm{X} \ket{1}) + \frac{a}{2}\ket{11}(\mathrm{X} \ket{1}) + \frac{b}{2}\ket{01}(\mathrm{X} \ket{0}) - \frac{b}{2}\ket{11}(\mathrm{X} \ket{0})) \\
=\quad &\frac{a}{\sqrt{2}}\ket{010} + \frac{a}{\sqrt{2}}\ket{110} + \frac{b}{\sqrt{2}}\ket{011} - \frac{b}{\sqrt{2}}\ket{111}
\end{align}

file23.txt

let m_msg = M (msg)
if (m_msg == One) {
    Z (there)
}

file24.txt

\begin{align}
&\sqrt{2}(\frac{a}{\sqrt{2}}\ket{000} + \frac{b}{\sqrt{2}}\ket{001}) \\
=\quad &a\ket{000} + b\ket{001} \\
=\quad &\ket{00}(a\ket{0} + b\ket{1})
\end{align}

file25.txt

\begin{align}
&\sqrt{2}(\frac{a}{\sqrt{2}}\ket{10}(\mathrm{Z} \ket{0}) - \frac{b}{\sqrt{2}}\ket{10}(\mathrm{Z} \ket{1})) \\
=\quad &a\ket{100} + b\ket{101} \\
=\quad &\ket{10}(a\ket{0} + b\ket{1})
\end{align}

file26.txt

\begin{align}
&\sqrt{2}(\frac{a}{\sqrt{2}}\ket{010} + \frac{b}{\sqrt{2}}\ket{011}) \\
=\quad &a\ket{010} + b\ket{011} \\
=\quad &\ket{01}(a\ket{0} + b\ket{1})
\end{align}

file27.txt

\begin{align}
&\sqrt{2}(\frac{a}{\sqrt{2}}\ket{11}(\mathrm{Z} \ket{0}) - \frac{b}{\sqrt{2}}\ket{11}(\mathrm{Z} \ket{1})) \\
=\quad &a\ket{110} + b\ket{111} \\
=\quad &\ket{11}(a\ket{0} + b\ket{1})
\end{align}

file28.txt

operation (Result) TeleportTest (Result msg) {
    Body {
        mutable res = Zero
        using (qubits = Qubit[3]) {
            let msgQ = qubits[0]

            // Set msgQ to message state
            SetQubit (msg, msgQ)

            Teleport (msgQ, qubits[1], qubits[2])

            set res = M(qubits[2])
        }
        return res
    }
}

file29.txt

operation (Result) TeleportTest (Result msg) {

file3.txt

\begin{align}
\mathrm{H}\ket{0} &= \frac{1}{\sqrt{2}}\ket{0} + \frac{1}{\sqrt{2}}\ket{1} \\
\mathrm{H}\ket{1} &= \frac{1}{\sqrt{2}}\ket{0} - \frac{1}{\sqrt{2}}\ket{1}
\end{align}

file30.txt

using (qubits = Qubit[3]) {

file31.txt

let msgQ = qubits[0]

file32.txt

SetQubit (msg, msgQ)
Teleport (msgQ, qubits[1], qubits[2])
set res = M(qubits[2])

file33.txt

return res

file34.txt

OPENQASM 2.0;
include "qelib1.inc";

qreg q[3];
creg c[1];

h q[1];
cx q[1],q[2];
cx q[0],q[1];
h q[0];
measure q[1] -> c[0];
if(c==1) x q[2];
measure q[0] -> c[0];
if(c==1) z q[2];

file4.txt

\begin{align}
\mathrm{CNOT}\ket{00} &= \ket{00} \\
\mathrm{CNOT}\ket{01} &= \ket{01} \\
\mathrm{CNOT}\ket{10} &= \ket{11} \\
\mathrm{CNOT}\ket{11} &= \ket{10}
\end{align}

file5.txt

operation () EPR (Qubit q1, Qubit q2) {
    Body {
        H (q1)
        CNOT (q1, q2)
    }
}

file6.txt

operation () EPR (Qubit q1, Qubit q2) {

file7.txt

\ket{00}

file8.txt

H (q1)

file9.txt

(\mathrm{H}\ket{0})\ket{0} = \frac{1}{\sqrt{2}}\ket{00} + \frac{1}{\sqrt{2}}\ket{10}