density_matrix.ipynb
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Symbolic Density Matrices
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%load_ext sympyprinting
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from sympy import sqrt, symbols, Rational, S
from sympy import expand, Eq, Symbol, simplify, exp, sin
from sympy.physics.quantum import *
from sympy.physics.quantum.qubit import *
from sympy.physics.quantum.gate import *
from sympy.physics.quantum.grover import *
from sympy.physics.quantum.qft import QFT, IQFT, Fourier
from sympy.physics.quantum.circuitplot import circuit_plot
from sympy.physics.quantum.densityOp import *
Density Operators are used to represent systems which has both classical mixtures as well as quantum superpositions.
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state = Density([Qubit('00'),0.5],[(Qubit('00')+Qubit('11'))/sqrt(2),0.5]); state
In addition to Dirac notation, code can represent the state as a matrix.
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represent(state, nqubits=2)
Gate operators can be applied to density operators.
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qapply(state.operate_on(HadamardGate(0)))
Von Neumann Entropy can be calculated.
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state.entropy(nqubits=2)
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Density([Qubit('00'),1]).entropy(nqubits=2)
We can also create symbolic states.
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genState = Density([Ket('psi'),.5],[Ket('phi'),.5]); genState
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%notebook save density_matrix.ipynb
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%notebook load qerror.ipynb