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.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import I
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _psi__t_ket, _s, _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 = Add(_t, _s)
sub_expr3 = Add(_t, one)
sub_expr4 = Interval(one, _t)
sub_expr5 = MultiQubitElem(element = Input(state = TensorProd(_psi__t_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr2))
expr = Prob(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr5, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr5, sub_expr3, sub_expr2).with_wrapping_at(2,6)], [ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr4), one, _t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, _s)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _Psi_ket, part = sub_expr1), targets = sub_expr4), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(sub_expr3, sub_expr2)), one, _s)])))

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{
\multiqin{1}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} & \gate{{\mathrm {FT}}^{\dag}_{t}} & \qout{\lvert \Psi \rangle} \\
\ghostqin{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} & { /^{s} } \qw & \qout{\lvert u \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, 10
7	ExprTuple	11, 12
8	ExprTuple	13, 14
9	ExprRange	lambda_map: 15 start_index: 65 end_index: 69
10	ExprRange	lambda_map: 15 start_index: 55 end_index: 56
11	ExprRange	lambda_map: 16 start_index: 65 end_index: 69
12	ExprRange	lambda_map: 17 start_index: 65 end_index: 66
13	ExprRange	lambda_map: 18 start_index: 65 end_index: 69
14	ExprRange	lambda_map: 19 start_index: 65 end_index: 66
15	Lambda	parameter: 54 body: 20
16	Lambda	parameter: 54 body: 21
17	Lambda	parameter: 54 body: 22
18	Lambda	parameter: 54 body: 23
19	Lambda	parameter: 54 body: 25
20	Operation	operator: 30 operands: 26
21	Operation	operator: 30 operands: 27
22	Operation	operator: 43 operands: 28
23	Operation	operator: 30 operands: 29
24	ExprTuple	54
25	Operation	operator: 30 operands: 31
26	NamedExprs	element: 32 targets: 33
27	NamedExprs	element: 34 targets: 37
28	NamedExprs	operation: 35
29	NamedExprs	element: 36 targets: 37
30	Literal
31	NamedExprs	element: 38 targets: 39
32	Operation	operator: 40 operands: 41
33	Operation	operator: 49 operands: 42
34	Operation	operator: 43 operands: 44
35	Literal
36	Operation	operator: 47 operands: 45
37	Operation	operator: 49 operands: 46
38	Operation	operator: 47 operands: 48
39	Operation	operator: 49 operands: 50
40	Literal
41	NamedExprs	state: 51 part: 54
42	ExprTuple	65, 56
43	Literal
44	NamedExprs	operation: 52 part: 54
45	NamedExprs	state: 53 part: 54
46	ExprTuple	65, 69
47	Literal
48	NamedExprs	state: 64 part: 54
49	Literal
50	ExprTuple	55, 56
51	Operation	operator: 57 operands: 58
52	Operation	operator: 59 operand: 69
53	Literal
54	Variable
55	Operation	operator: 61 operands: 60
56	Operation	operator: 61 operands: 62
57	Literal
58	ExprTuple	63, 64
59	Literal
60	ExprTuple	69, 65
61	Literal
62	ExprTuple	69, 66
63	Operation	operator: 67 operand: 69
64	Literal
65	Literal
66	Literal
67	Literal
68	ExprTuple	69
69	Literal