from the theory of proveit.physics.quantum.algebra¶

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, Lambda, U, n
from proveit.linear_algebra import Unitary
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, var_ket_psi

In [2]:
# build up the expression from sub-expressions
sub_expr1 = CartExp(Complex, n)
expr = ExprTuple(Lambda(U, Conditional(Forall(instance_param_or_params = [var_ket_psi], instance_expr = InSet(Qmult(U, var_ket_psi), sub_expr1), domain = sub_expr1), InSet(U, Unitary(n)))))

expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(U \mapsto \left\{\forall_{\lvert \psi \rangle \in \mathbb{C}^{n}}~\left(\left(U \thinspace \lvert \psi \rangle\right) \in \mathbb{C}^{n}\right) \textrm{ if } U \in \textrm{U}\left(n\right)\right..\right)

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 26
body: 3
2ExprTuple26
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 9
5Operationoperator: 18
operands: 8
6Literal
7ExprTuple9
8ExprTuple26, 10
9Lambdaparameter: 27
body: 12
10Operationoperator: 13
operand: 29
11ExprTuple27
12Conditionalvalue: 15
condition: 16
13Literal
14ExprTuple29
15Operationoperator: 18
operands: 17
16Operationoperator: 18
operands: 19
17ExprTuple20, 21
18Literal
19ExprTuple27, 21
20Operationoperator: 22
operands: 23
21Operationoperator: 24
operands: 25
22Literal
23ExprTuple26, 27
24Literal
25ExprTuple28, 29
26Variable
27Variable
28Literal
29Variable