Expression of type Prob

from the theory of proveit.physics.quantum.QPE

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprRange, Variable, VertExprArray
from proveit.numbers import Interval, one
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _Psi_ket, _psi__t_ket, _t
from proveit.physics.quantum.circuits import Gate, Input, MultiQubitElem, Output, Qcircuit
from proveit.statistics import Prob

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Interval(one, _t)
expr = Prob(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _psi__t_ket, part = sub_expr1), targets = sub_expr2), one, _t)], [ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr2), one, _t)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _Psi_ket, part = sub_expr1), targets = sub_expr2), one, _t)])))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi_{t} \rangle} & \gate{{\mathrm {FT}}^{\dag}_{t}} & \qout{\lvert \Psi \rangle}
} \end{array}\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7, 8
6	ExprTuple	9
7	ExprTuple	10
8	ExprTuple	11
9	ExprRange	lambda_map: 12 start_index: 39 end_index: 43
10	ExprRange	lambda_map: 13 start_index: 39 end_index: 43
11	ExprRange	lambda_map: 14 start_index: 39 end_index: 43
12	Lambda	parameter: 38 body: 15
13	Lambda	parameter: 38 body: 16
14	Lambda	parameter: 38 body: 18
15	Operation	operator: 21 operands: 19
16	Operation	operator: 21 operands: 20
17	ExprTuple	38
18	Operation	operator: 21 operands: 22
19	NamedExprs	element: 23 targets: 26
20	NamedExprs	element: 24 targets: 26
21	Literal
22	NamedExprs	element: 25 targets: 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 29 operands: 30
25	Operation	operator: 31 operands: 32
26	Operation	operator: 33 operands: 34
27	Literal
28	NamedExprs	state: 35 part: 38
29	Literal
30	NamedExprs	operation: 36 part: 38
31	Literal
32	NamedExprs	state: 37 part: 38
33	Literal
34	ExprTuple	39, 43
35	Operation	operator: 40 operand: 43
36	Operation	operator: 41 operand: 43
37	Literal
38	Variable
39	Literal
40	Literal
41	Literal
42	ExprTuple	43
43	Literal