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Fixed typo of C_{U} and Controlled Z gate (#1313)
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* Fixed typo of C_{U}

Fixed typo of C_{U}:
"$$C_{(jk), (lm)} = \\left(\\underset{\\text{qubit}~1}{\\left\\langle j \\right|} \\otimes \\underset{\\text{qubit}~0}{\\left\\langle k \\right|}\\right) C_{U} \\left(\\underset{\\text{qubit}~1}{\\left| l \\right\\rangle} \\otimes \\underset{\\text{qubit}~0}{\\left| k \\right\\rangle}\\right),$$\n"

It should be 

"$$C_{(jk), (lm)} = \\left(\\underset{\\text{qubit}~1}{\\left\\langle j \\right|} \\otimes \\underset{\\text{qubit}~0}{\\left\\langle k \\right|}\\right) C_{U} \\left(\\underset{\\text{qubit}~1}{\\left| l \\right\\rangle} \\otimes \\underset{\\text{qubit}~0}{\\left| m \\right\\rangle}\\right),$$\n"

* Fix typo of Controlled Z gate

Fix typo of Controlled Z gate:
"#### Controlled $Z$ (or, controlled Phase) gate\n"

It should be
"#### Controlled $Z$ (or, controlled Phase-Flip) gate\n"

ref:
Page 319
Michael A. Nielsen, Isaac L. Chuang, Quantum Computation and Quantum Information, 2010

Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
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ChihHanHuang and mergify[bot] committed May 17, 2022
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Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions tutorials/circuits/3_summary_of_quantum_operations.ipynb
Original file line number Diff line number Diff line change
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"\n",
"To work out these matrix elements, let\n",
"\n",
"$$C_{(jk), (lm)} = \\left(\\underset{\\text{qubit}~1}{\\left\\langle j \\right|} \\otimes \\underset{\\text{qubit}~0}{\\left\\langle k \\right|}\\right) C_{U} \\left(\\underset{\\text{qubit}~1}{\\left| l \\right\\rangle} \\otimes \\underset{\\text{qubit}~0}{\\left| k \\right\\rangle}\\right),$$\n",
"$$C_{(jk), (lm)} = \\left(\\underset{\\text{qubit}~1}{\\left\\langle j \\right|} \\otimes \\underset{\\text{qubit}~0}{\\left\\langle k \\right|}\\right) C_{U} \\left(\\underset{\\text{qubit}~1}{\\left| l \\right\\rangle} \\otimes \\underset{\\text{qubit}~0}{\\left| m \\right\\rangle}\\right),$$\n",
"\n",
"compute the action of $C_{U}$ (given above), and compute the inner products.\n",
"\n",
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"cell_type": "markdown",
"metadata": {},
"source": [
"#### Controlled $Z$ (or, controlled Phase) gate\n",
"#### Controlled $Z$ (or, controlled Phase-Flip) gate\n",
"\n",
"Similarly, the controlled Z gate flips the phase of the target qubit if the control qubit is $\\left|1\\right\\rangle$. The matrix looks the same regardless of whether the MSB or LSB is the control qubit:\n",
"\n",
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