Expression of type ExprTuple

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, ExprTuple, Variable, VertExprArray, m
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z
from proveit.physics.quantum.QPE import _Psi_ket, _alpha_m_sqrd, _ket_u, _s, _s_wire, _t
from proveit.physics.quantum.circuits import Input, Measure, 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)
sub_expr3 = Interval(Add(_t, one), Add(_t, _s))
expr = ExprTuple(Prob(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _Psi_ket, part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr3), one, _s)], [ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr3), one, _s)]))), _alpha_m_sqrd)

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())

\left(\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert \Psi \rangle} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert u \rangle} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right), \left|\alpha_{m}\right|^{2}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operand: 17
9	Literal
10	Literal
11	ExprTuple	14, 15, 16
12	Literal
13	ExprTuple	17
14	ExprTuple	18, 19
15	ExprTuple	20, 21
16	ExprTuple	22, 23
17	Operation	operator: 24 operand: 75
18	ExprRange	lambda_map: 26 start_index: 76 end_index: 77
19	ExprRange	lambda_map: 27 start_index: 76 end_index: 78
20	ExprRange	lambda_map: 28 start_index: 76 end_index: 77
21	ExprRange	lambda_map: 29 start_index: 76 end_index: 78
22	ExprRange	lambda_map: 30 start_index: 76 end_index: 77
23	ExprRange	lambda_map: 31 start_index: 76 end_index: 78
24	Literal
25	ExprTuple	75
26	Lambda	parameter: 67 body: 32
27	Lambda	parameter: 67 body: 33
28	Lambda	parameter: 67 body: 34
29	Lambda	parameter: 67 body: 35
30	Lambda	parameter: 67 body: 36
31	Lambda	parameter: 67 body: 38
32	Operation	operator: 46 operands: 39
33	Operation	operator: 46 operands: 40
34	Operation	operator: 41 operands: 42
35	Operation	operator: 43 operands: 44
36	Operation	operator: 46 operands: 45
37	ExprTuple	67
38	Operation	operator: 46 operands: 47
39	NamedExprs	element: 48 targets: 53
40	NamedExprs	element: 49 targets: 55
41	Literal
42	NamedExprs	basis: 50
43	Literal
44	NamedExprs	operation: 51
45	NamedExprs	element: 52 targets: 53
46	Literal
47	NamedExprs	element: 54 targets: 55
48	Operation	operator: 57 operands: 56
49	Operation	operator: 57 operands: 61
50	Literal
51	Literal
52	Operation	operator: 60 operands: 58
53	Operation	operator: 62 operands: 59
54	Operation	operator: 60 operands: 61
55	Operation	operator: 62 operands: 63
56	NamedExprs	state: 64 part: 67
57	Literal
58	NamedExprs	state: 65 part: 67
59	ExprTuple	76, 77
60	Literal
61	NamedExprs	state: 66 part: 67
62	Literal
63	ExprTuple	68, 69
64	Literal
65	Operation	operator: 70 operands: 71
66	Literal
67	Variable
68	Operation	operator: 73 operands: 72
69	Operation	operator: 73 operands: 74
70	Literal
71	ExprTuple	75, 77
72	ExprTuple	77, 76
73	Literal
74	ExprTuple	77, 78
75	Variable
76	Literal
77	Literal
78	Literal