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Fix Docs: cirq/tutorials/educators/chemistry (quantumlib#5251)
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TimoEckstein authored and tonybruguier committed Apr 19, 2022
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Showing 1 changed file with 2 additions and 11 deletions.
13 changes: 2 additions & 11 deletions docs/tutorials/educators/chemistry.ipynb
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"- Stores the Hermitian matrix $M_{pq}$ and antisymmetric matrix $\\Delta_{pq}$ describing a general quadratic Hamiltonian\n",
"\n",
"$$\n",
"\\sum_{p, q} M_{pq} a^\\dagger_p a_q\n",
"+ \\frac12 \\sum_{p, q}\n",
" (\\Delta_{pq} a^\\dagger_p a^\\dagger_q + \\text{h.c.})\n",
"\\sum_{p, q} M_{pq} a^\\dagger_p a_q + \\frac12 \\sum_{p, q} (\\Delta_{pq} a^\\dagger_p a^\\dagger_q + \\text{h.c.})\n",
"$$\n",
"\n",
"- Routines included for efficient diagonalization (can handle thousands of fermionic modes)\n",
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"- The BCS mean-field d-wave model of superconductivity has the Hamiltonian\n",
"\n",
"$$\n",
"H = - t \\sum_{\\langle i,j \\rangle} \\sum_\\sigma\n",
" (a^\\dagger_{i, \\sigma} a_{j, \\sigma} +\n",
" a^\\dagger_{j, \\sigma} a_{i, \\sigma})\n",
" - \\sum_{\\langle i,j \\rangle} \\Delta_{ij}\n",
" (a^\\dagger_{i, \\uparrow} a^\\dagger_{j, \\downarrow} -\n",
" a^\\dagger_{i, \\downarrow} a^\\dagger_{j, \\uparrow} +\n",
" a_{j, \\downarrow} a_{i, \\uparrow} -\n",
" a_{j, \\uparrow} a_{i, \\downarrow})\n",
"H = - t \\sum_{\\langle i,j \\rangle} \\sum_\\sigma (a^\\dagger_{i, \\sigma} a_{j, \\sigma} + a^\\dagger_{j, \\sigma} a_{i, \\sigma}) - \\sum_{\\langle i,j \\rangle} \\Delta_{ij} (a^\\dagger_{i, \\uparrow} a^\\dagger_{j, \\downarrow} - a^\\dagger_{i, \\downarrow} a^\\dagger_{j, \\uparrow} + a_{j, \\downarrow} a_{i, \\uparrow} - a_{j, \\uparrow} a_{i, \\downarrow})\n",
"$$\n",
"\n",
"Use the `mean_field_dwave` function to generate an instance of this model with dimensions 10x10.\n",
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