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_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 = Forall(instance_param_or_params = [n], instance_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), domain = m_bit_interval)

# 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_{n \in \{0~\ldotp \ldotp~2^{m} - 1\}}~\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)\right]

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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',)

	core type	sub-expressions
0	Operation	operator: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 93 body: 4
3	ExprTuple	93
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 31 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	93, 11
10	Lambda	parameter: 87 body: 12
11	Operation	operator: 85 operands: 13
12	Conditional	value: 14 condition: 15
13	ExprTuple	16, 17
14	Operation	operator: 33 operands: 18
15	Operation	operator: 19 operands: 20
16	Literal
17	Operation	operator: 21 operands: 22
18	ExprTuple	23, 24
19	Literal
20	ExprTuple	25, 26
21	Literal
22	ExprTuple	54, 27
23	Operation	operator: 28 operand: 37
24	Operation	operator: 60 operands: 30
25	Operation	operator: 31 operands: 32
26	Operation	operator: 33 operands: 34
27	Operation	operator: 35 operand: 90
28	Literal
29	ExprTuple	37
30	ExprTuple	38, 66
31	Literal
32	ExprTuple	87, 39
33	Literal
34	ExprTuple	40, 90
35	Literal
36	ExprTuple	90
37	Operation	operator: 41 operands: 42
38	Operation	operator: 43 operand: 52
39	Operation	operator: 45 operands: 46
40	Operation	operator: 47 operand: 87
41	Literal
42	ExprTuple	49, 50, 51
43	Literal
44	ExprTuple	52
45	Literal
46	ExprTuple	53, 54
47	Literal
48	ExprTuple	87
49	ExprTuple	55
50	ExprTuple	56
51	ExprTuple	57
52	Operation	operator: 58 operands: 59
53	Literal
54	Operation	operator: 60 operands: 61
55	ExprRange	lambda_map: 62 start_index: 90 end_index: 94
56	ExprRange	lambda_map: 63 start_index: 90 end_index: 94
57	ExprRange	lambda_map: 64 start_index: 90 end_index: 94
58	Literal
59	ExprTuple	65, 87
60	Literal
61	ExprTuple	66, 94
62	Lambda	parameter: 89 body: 67
63	Lambda	parameter: 89 body: 68
64	Lambda	parameter: 89 body: 70
65	Operation	operator: 71 operands: 92
66	Literal
67	Operation	operator: 75 operands: 72
68	Operation	operator: 73 operands: 74
69	ExprTuple	89
70	Operation	operator: 75 operands: 76
71	Literal
72	NamedExprs	element: 77 targets: 80
73	Literal
74	NamedExprs	basis: 78
75	Literal
76	NamedExprs	element: 79 targets: 80
77	Operation	operator: 81 operands: 82
78	Literal
79	Operation	operator: 83 operands: 84
80	Operation	operator: 85 operands: 86
81	Literal
82	NamedExprs	state: 87 part: 89
83	Literal
84	NamedExprs	state: 88 part: 89
85	Literal
86	ExprTuple	90, 94
87	Variable
88	Operation	operator: 91 operands: 92
89	Variable
90	Literal
91	Literal
92	ExprTuple	93, 94
93	Variable
94	Variable

Expression of type Forall¶

from the theory of proveit.physics.quantum.circuits¶

Expression of type Forall ¶

from the theory of proveit.physics.quantum.circuits ¶