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cleanup connection files on notebook shutdown Kernels would not linger, but the KernelManagers are not garbage-collected on shutdown. This means that connection files for kernels still running at notebook shutdown would not be removed. Also disable the unnecessary (and actively unhelpful) SIGINT handler inherited from the original copy/paste from the qt app.
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Basic Symbolic Quantum Mechanics with SymPy

We first load the IPython extensions that enable LaTeX-based mathematical printing of SymPy objects, and then import the quantum computing libraries from SymPy.

In [1]:
%load_ext sympyprinting
In [2]:
from sympy import sqrt, symbols, Rational
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

Bras and Kets

Create symbolic states

In [3]:
phi, psi = Ket('phi'), Ket('psi')
alpha, beta = symbols('alpha beta', complex=True)

Create a superposition

In [4]:
state = alpha*psi + beta*phi; state
Out[4]:
$$\alpha {\left|\psi\right\rangle } + \beta {\left|\phi\right\rangle }$$

Dagger the superposition and multiply the original

In [5]:
ip = Dagger(state)*state; ip
Out[5]:
$$\left(\overline{\alpha} {\left\langle \psi\right|} + \overline{\beta} {\left\langle \phi\right|}\right) \left(\alpha {\left|\psi\right\rangle } + \beta {\left|\phi\right\rangle }\right)$$

Distribute

In [6]:
qapply(expand(ip))
Out[6]:
$$\alpha \overline{\alpha} \left\langle \psi \right. {\left|\psi\right\rangle } + \alpha \overline{\beta} \left\langle \phi \right. {\left|\psi\right\rangle } + \beta \overline{\alpha} \left\langle \psi \right. {\left|\phi\right\rangle } + \beta \overline{\beta} \left\langle \phi \right. {\left|\phi\right\rangle }$$

Operators

Create symbolic operators

In [7]:
A = Operator('A')
B = Operator('B')
C = Operator('C')

Test commutativity

In [8]:
A*B == B*A
Out[8]:
False

Distribute A+B squared

In [9]:
expand((A+B)**2)
Out[9]:
$$A B + \left(A\right)^{2} + B A + \left(B\right)^{2}$$

Create a commutator

In [10]:
comm = Commutator(A,B); comm
Out[10]:
$$\left[A,B\right]$$

Carry out the commutator

In [11]:
comm.doit()
Out[11]:
$$A B - B A$$

Create a more fancy commutator

In [12]:
comm = Commutator(A*B,B+C); comm
Out[12]:
$$\left[A B,B + C\right]$$

Expand the commutator

In [13]:
comm.expand(commutator=True)
Out[13]:
$$\left[A,B\right] B + \left[A,C\right] B + A \left[B,C\right]$$

Carry out and expand the commutators

In [14]:
_.doit().expand()
Out[14]:
$$A B C + A \left(B\right)^{2} - B A B - C A B$$

Take the dagger

In [15]:
Dagger(_)
Out[15]:
$$- B^{\dagger} A^{\dagger} B^{\dagger} - B^{\dagger} A^{\dagger} C^{\dagger} + \left(B^{\dagger}\right)^{2} A^{\dagger} + C^{\dagger} B^{\dagger} A^{\dagger}$$