Expression of type ExprTuple

from the theory of proveit.physics.quantum.circuits

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 ExprTuple
from proveit.numbers import one
from proveit.physics.quantum.circuits import phase_kickback_on_register_circuit
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = ExprTuple(Prob(phase_kickback_on_register_circuit), one)

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{
\qin{\lvert + \rangle} & \control{} \qw \qwx[1] & \qw & \gate{\cdots} \qwx[1] & \qw & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{1}} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\lvert + \rangle} & \qw \qwx[1] & \control{} \qw \qwx[1] & \gate{\cdots} \qwx[1] & \qw & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{2}} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} & \qout{\vdots} \\
\qin{\lvert + \rangle} & \qw \qwx[1] & \qw \qwx[1] & \gate{\cdots} \qwx[1] & \control{} \qw \qwx[1] & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{t}} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\lvert u \rangle} & \gate{U_{1}} & \gate{U_{2}} & \gate{\cdots} & \gate{U_{t}} & \qout{\lvert u \rangle}
} \end{array}\right), 1\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, 106
1	Operation	operator: 2 operand: 4
2	Literal
3	ExprTuple	4
4	Operation	operator: 5 operands: 6
5	Literal
6	ExprTuple	7, 8, 9
7	ExprTuple	10, 11
8	ExprRange	lambda_map: 12 start_index: 106 end_index: 105
9	ExprTuple	13, 14
10	ExprRange	lambda_map: 15 start_index: 106 end_index: 105
11	ExprRange	lambda_map: 16 start_index: 106 end_index: 89
12	Lambda	parameter: 88 body: 17
13	ExprRange	lambda_map: 18 start_index: 106 end_index: 105
14	ExprRange	lambda_map: 19 start_index: 106 end_index: 89
15	Lambda	parameter: 115 body: 20
16	Lambda	parameter: 115 body: 21
17	ExprTuple	22, 23
18	Lambda	parameter: 115 body: 24
19	Lambda	parameter: 115 body: 25
20	Operation	operator: 39 operands: 26
21	Operation	operator: 64 operands: 27
22	ExprRange	lambda_map: 28 start_index: 106 end_index: 105
23	ExprRange	lambda_map: 29 start_index: 106 end_index: 89
24	Operation	operator: 44 operands: 30
25	Operation	operator: 64 operands: 31
26	NamedExprs	state: 32
27	NamedExprs	element: 33 targets: 50
28	Lambda	parameter: 115 body: 34
29	Lambda	parameter: 115 body: 35
30	NamedExprs	state: 36
31	NamedExprs	element: 37 targets: 50
32	Operation	operator: 99 operand: 46
33	Operation	operator: 39 operands: 45
34	Operation	operator: 40 operands: 41
35	Operation	operator: 64 operands: 42
36	Operation	operator: 84 operands: 43
37	Operation	operator: 44 operands: 45
38	ExprTuple	46
39	Literal
40	Literal
41	ExprTuple	47, 48
42	NamedExprs	element: 49 targets: 50
43	ExprTuple	51, 52
44	Literal
45	NamedExprs	state: 53 part: 115
46	Literal
47	Conditional	value: 54 condition: 55
48	Conditional	value: 56 condition: 57
49	Operation	operator: 67 operands: 58
50	Operation	operator: 59 operands: 60
51	Operation	operator: 95 operands: 61
52	Operation	operator: 62 operands: 63
53	Variable
54	Operation	operator: 64 operands: 65
55	Operation	operator: 66 operands: 70
56	Operation	operator: 67 operands: 68
57	Operation	operator: 69 operands: 70
58	NamedExprs	operation: 71 part: 115
59	Literal
60	ExprTuple	94, 72
61	ExprTuple	106, 73
62	Literal
63	ExprTuple	74, 75
64	Literal
65	NamedExprs	element: 76 targets: 77
66	Literal
67	Literal
68	NamedExprs	operation: 78
69	Literal
70	ExprTuple	88, 115
71	IndexedVar	variable: 79 index: 88
72	Operation	operator: 101 operands: 81
73	Operation	operator: 97 operands: 82
74	Operation	operator: 99 operand: 91
75	Operation	operator: 84 operands: 85
76	Literal
77	Operation	operator: 86 operand: 94
78	Literal
79	Variable
80	ExprTuple	88
81	ExprTuple	105, 89
82	ExprTuple	109, 90
83	ExprTuple	91
84	Literal
85	ExprTuple	92, 93
86	Literal
87	ExprTuple	94
88	Variable
89	Variable
90	Operation	operator: 95 operands: 96
91	Literal
92	Operation	operator: 97 operands: 98
93	Operation	operator: 99 operand: 106
94	Operation	operator: 101 operands: 102
95	Literal
96	ExprTuple	106, 109
97	Literal
98	ExprTuple	103, 104
99	Literal
100	ExprTuple	106
101	Literal
102	ExprTuple	105, 106
103	Literal
104	Operation	operator: 107 operands: 108
105	Variable
106	Literal
107	Literal
108	ExprTuple	109, 110, 111, 112
109	Literal
110	Literal
111	Literal
112	IndexedVar	variable: 113 index: 115
113	Variable
114	ExprTuple	115
115	Variable