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, t
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import ket_plus
from proveit.physics.quantum.QPE import QPE1, _U, _ket_u, _psi_t_ket, _s
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, one)
sub_expr3 = Add(t, _s)
sub_expr4 = Interval(sub_expr2, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE1(_U, t), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = Prob(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Input(state = ket_plus), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)], [ExprRange(sub_expr1, sub_expr5, one, t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _psi_t_ket, part = sub_expr1), targets = Interval(one, t)), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr4), 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{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}_1\left(U, t\right)} & \multiqout{3}{\lvert \psi_{t} \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \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: 67 end_index: 68
10	ExprRange	lambda_map: 16 start_index: 67 end_index: 69
11	ExprRange	lambda_map: 17 start_index: 67 end_index: 68
12	ExprRange	lambda_map: 17 start_index: 57 end_index: 58
13	ExprRange	lambda_map: 18 start_index: 67 end_index: 68
14	ExprRange	lambda_map: 19 start_index: 67 end_index: 69
15	Lambda	parameter: 56 body: 20
16	Lambda	parameter: 56 body: 21
17	Lambda	parameter: 56 body: 22
18	Lambda	parameter: 56 body: 23
19	Lambda	parameter: 56 body: 25
20	Operation	operator: 42 operands: 26
21	Operation	operator: 30 operands: 27
22	Operation	operator: 30 operands: 28
23	Operation	operator: 30 operands: 29
24	ExprTuple	56
25	Operation	operator: 30 operands: 31
26	NamedExprs	state: 32
27	NamedExprs	element: 33 targets: 39
28	NamedExprs	element: 34 targets: 35
29	NamedExprs	element: 36 targets: 37
30	Literal
31	NamedExprs	element: 38 targets: 39
32	Operation	operator: 40 operand: 52
33	Operation	operator: 42 operands: 49
34	Operation	operator: 43 operands: 44
35	Operation	operator: 50 operands: 45
36	Operation	operator: 48 operands: 46
37	Operation	operator: 50 operands: 47
38	Operation	operator: 48 operands: 49
39	Operation	operator: 50 operands: 51
40	Literal
41	ExprTuple	52
42	Literal
43	Literal
44	NamedExprs	operation: 53 part: 56
45	ExprTuple	67, 58
46	NamedExprs	state: 54 part: 56
47	ExprTuple	67, 68
48	Literal
49	NamedExprs	state: 55 part: 56
50	Literal
51	ExprTuple	57, 58
52	Literal
53	Operation	operator: 59 operands: 60
54	Operation	operator: 61 operand: 68
55	Literal
56	Variable
57	Operation	operator: 64 operands: 63
58	Operation	operator: 64 operands: 65
59	Literal
60	ExprTuple	66, 68
61	Literal
62	ExprTuple	68
63	ExprTuple	68, 67
64	Literal
65	ExprTuple	68, 69
66	Literal
67	Literal
68	Variable
69	Literal