Expression of type Forall

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 m, n
from proveit.logic import Equals, Forall
from proveit.numbers import Abs, Exp, two
from proveit.physics.quantum import NumBra, Qmult, 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 = 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)

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())

\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)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

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