exercise6.ipynb

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    "# Effects of garbage in quantum circuits\n",
    "\n",
    "The CX gate performs the mapping $(i,j) \\rightarrow (i,i+j \\mod 2)$ from an input on two bits to an output on two bits It is interesting to note (though not relevant to the problem) that this mapping is not of the form $(z,0) \\rightarrow (z,f(z))$, as considered last week, since the function $f(i,j) = i+j \\mod 2$ does not require the whole input to be present for reversibility.\n",
    "\n",
    "Here are two circuits with a CX gate."
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    "![](circuits.png)"
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    "* (a) The first circuit is composed of both a quantum part and an irreversible classical part. Determine the final output bit $b$.\n",
    "\n",
    "* (b) Show that the second circuit effectively acts as a CX between the first and third qubits, but with the additional effect of producting a garbage qubit on the second.\n",
    "\n",
    "* (c) Replace the true CX in the first circuit with the garbage producing one from the second. Show that this changes the output bit.\n",
    "\n",
    "* (d) Show how the garbage producing CX can be corrected by uncomputation."
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