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 Conditional, ExprTuple, Lambda, m, n
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Abs, Exp, two
from proveit.physics.quantum import NumBra, Qmult, m_bit_interval, m_ket_domain, normalized_var_ket_psi, var_ket_psi
from proveit.physics.quantum.circuits import register_meas
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [var_ket_psi], instance_expr = Equals(Prob(register_meas), Exp(Abs(Qmult(NumBra(n, m), var_ket_psi)), two)), domain = m_ket_domain, condition = normalized_var_ket_psi), InSet(n, m_bit_interval))))

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(n \mapsto \left\{\forall_{\lvert \psi \rangle \in \mathbb{C}^{2^{m}}~|~\left \|\lvert \psi \rangle\right \| = 1}~\left(\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert \psi \rangle} & \meter & \multiqout{3}{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \measure{\begin{array}{c}:\\ \left(m - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}}
} \end{array}\right) = \left|{_{m}}\langle n \rvert \thinspace \lvert \psi \rangle\right|^{2}\right) \textrm{ if } n \in \{0~\ldotp \ldotp~2^{m} - 1\}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 92 body: 3
2	ExprTuple	92
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 30 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	92, 10
9	Lambda	parameter: 86 body: 11
10	Operation	operator: 84 operands: 12
11	Conditional	value: 13 condition: 14
12	ExprTuple	15, 16
13	Operation	operator: 32 operands: 17
14	Operation	operator: 18 operands: 19
15	Literal
16	Operation	operator: 20 operands: 21
17	ExprTuple	22, 23
18	Literal
19	ExprTuple	24, 25
20	Literal
21	ExprTuple	53, 26
22	Operation	operator: 27 operand: 36
23	Operation	operator: 59 operands: 29
24	Operation	operator: 30 operands: 31
25	Operation	operator: 32 operands: 33
26	Operation	operator: 34 operand: 89
27	Literal
28	ExprTuple	36
29	ExprTuple	37, 65
30	Literal
31	ExprTuple	86, 38
32	Literal
33	ExprTuple	39, 89
34	Literal
35	ExprTuple	89
36	Operation	operator: 40 operands: 41
37	Operation	operator: 42 operand: 51
38	Operation	operator: 44 operands: 45
39	Operation	operator: 46 operand: 86
40	Literal
41	ExprTuple	48, 49, 50
42	Literal
43	ExprTuple	51
44	Literal
45	ExprTuple	52, 53
46	Literal
47	ExprTuple	86
48	ExprTuple	54
49	ExprTuple	55
50	ExprTuple	56
51	Operation	operator: 57 operands: 58
52	Literal
53	Operation	operator: 59 operands: 60
54	ExprRange	lambda_map: 61 start_index: 89 end_index: 93
55	ExprRange	lambda_map: 62 start_index: 89 end_index: 93
56	ExprRange	lambda_map: 63 start_index: 89 end_index: 93
57	Literal
58	ExprTuple	64, 86
59	Literal
60	ExprTuple	65, 93
61	Lambda	parameter: 88 body: 66
62	Lambda	parameter: 88 body: 67
63	Lambda	parameter: 88 body: 69
64	Operation	operator: 70 operands: 91
65	Literal
66	Operation	operator: 74 operands: 71
67	Operation	operator: 72 operands: 73
68	ExprTuple	88
69	Operation	operator: 74 operands: 75
70	Literal
71	NamedExprs	element: 76 targets: 79
72	Literal
73	NamedExprs	basis: 77
74	Literal
75	NamedExprs	element: 78 targets: 79
76	Operation	operator: 80 operands: 81
77	Literal
78	Operation	operator: 82 operands: 83
79	Operation	operator: 84 operands: 85
80	Literal
81	NamedExprs	state: 86 part: 88
82	Literal
83	NamedExprs	state: 87 part: 88
84	Literal
85	ExprTuple	89, 93
86	Variable
87	Operation	operator: 90 operands: 91
88	Variable
89	Literal
90	Literal
91	ExprTuple	92, 93
92	Variable
93	Variable