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Closes #1189 Replacing 'state matrix' by 'density matrix' (#1196)
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### Summary
As described in issue #1189, "state matrix" has been replaced by
"density matrix" in `plot_state_city` and
`plot_state_hinton` fotutorials/circuits/2_plotting_data_in_qiskit.html.
Additionally I have also changed it at other plot functions.


### Details and comments
"State matrix" has a different physical meaning and doesn't go with the
definition given in the documentation. Hence "density matrix" seems like
a better option to use instead of "state matrix".

Co-authored-by: Eric Arellano <14852634+Eric-Arellano@users.noreply.github.com>
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shil-m and Eric-Arellano authored Aug 16, 2023
1 parent 10b7cb5 commit 5a1dc9b
Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions tutorials/circuits/2_plotting_data_in_qiskit.ipynb
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Expand Up @@ -194,7 +194,7 @@
"plot_bloch_multivector(quantum_state)\n",
"```\n",
"\n",
"A quantum state is either a state matrix $\\rho$ (Hermitian matrix) or statevector $|\\psi\\rangle$ (complex vector). The state matrix is related to the statevector by \n",
"A quantum state is either a density matrix $\\rho$ (Hermitian matrix) or statevector $|\\psi\\rangle$ (complex vector). The density matrix is related to the statevector by \n",
"\n",
"$$\\rho = |\\psi\\rangle\\langle \\psi|,$$\n",
"\n",
Expand All @@ -204,11 +204,11 @@
"\n",
"The visualizations generated by the functions are:\n",
"\n",
"- `'plot_state_city'`: The standard view for quantum states where the real and imaginary (imag) parts of the state matrix are plotted like a city.\n",
"- `'plot_state_city'`: The standard view for quantum states where the real and imaginary (imag) parts of the density matrix are plotted like a city.\n",
"\n",
"- `'plot_state_qsphere'`: The Qiskit unique view of a quantum state where the amplitude and phase of the state vector are plotted in a spherical ball. The amplitude is the thickness of the arrow and the phase is the color. For mixed states it will show different `'qsphere'` for each component.\n",
"\n",
"- `'plot_state_paulivec'`: The representation of the state matrix using Pauli operators as the basis $\\rho=\\sum_{q=0}^{d^2-1}p_jP_j/d$.\n",
"- `'plot_state_paulivec'`: The representation of the density matrix using Pauli operators as the basis $\\rho=\\sum_{q=0}^{d^2-1}p_jP_j/d$.\n",
"\n",
"- `'plot_state_hinton'`: Same as `'city'` but where the size of the element represents the value of the matrix element.\n",
"\n",
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"\n",
"A standard way of plotting a quantum system is using the Bloch vector. This only works for a single qubit and takes as input the Bloch vector. \n",
"\n",
"The Bloch vector is defined as $[x = \\mathrm{Tr}[X \\rho], y = \\mathrm{Tr}[Y \\rho], z = \\mathrm{Tr}[Z \\rho]]$, where $X$, $Y$, and $Z$ are the Pauli operators for a single qubit and $\\rho$ is the state matrix.\n"
"The Bloch vector is defined as $[x = \\mathrm{Tr}[X \\rho], y = \\mathrm{Tr}[Y \\rho], z = \\mathrm{Tr}[Z \\rho]]$, where $X$, $Y$, and $Z$ are the Pauli operators for a single qubit and $\\rho$ is the density matrix.\n"
]
},
{
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