Expression of type InSet ¶

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

In [1]:

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 e, m
from proveit.logic import InSet, SetOfAll
from proveit.numbers import ModAbs, greater, subtract
from proveit.physics.quantum.QPE import _b_floor, _m_domain, _phase_est_circuit, _two_pow_t
from proveit.statistics import Prob, prob_domain

In [2]:

# build up the expression from sub-expressions
expr = InSet(Prob(SetOfAll(instance_param_or_params = [m], instance_element = _phase_est_circuit, domain = _m_domain, condition = greater(ModAbs(subtract(m, _b_floor), _two_pow_t), e))), prob_domain)

expr:

In [3]:

# 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

In [4]:

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\textrm{Pr}\left(\left\{\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right)~|~\left|m - b_{\textit{f}}\right|_{\textup{mod}\thinspace 2^{t}} > e\right\}_{m \in \{0~\ldotp \ldotp~2^{t} - 1\}}\right) \in \left[0,1\right]

In [5]:

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

In [6]:

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Operation	operator: 34 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operand: 8
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8
6	Literal
7	ExprTuple	68, 121
8	Operation	operator: 9 operand: 11
9	Literal
10	ExprTuple	11
11	Lambda	parameter: 120 body: 13
12	ExprTuple	120
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20, 21, 22, 23
18	Literal
19	ExprTuple	24, 25
20	ExprTuple	26, 27
21	ExprTuple	28, 29
22	ExprTuple	30, 31
23	ExprTuple	32, 33
24	Operation	operator: 34 operands: 35
25	Operation	operator: 36 operands: 37
26	ExprRange	lambda_map: 38 start_index: 121 end_index: 122
27	ExprRange	lambda_map: 39 start_index: 121 end_index: 123
28	ExprRange	lambda_map: 40 start_index: 121 end_index: 122
29	ExprRange	lambda_map: 40 start_index: 103 end_index: 104
30	ExprRange	lambda_map: 41 start_index: 121 end_index: 122
31	ExprRange	lambda_map: 42 start_index: 121 end_index: 123
32	ExprRange	lambda_map: 43 start_index: 121 end_index: 122
33	ExprRange	lambda_map: 44 start_index: 121 end_index: 123
34	Literal
35	ExprTuple	120, 45
36	Literal
37	ExprTuple	46, 47
38	Lambda	parameter: 102 body: 48
39	Lambda	parameter: 102 body: 49
40	Lambda	parameter: 102 body: 50
41	Lambda	parameter: 102 body: 51
42	Lambda	parameter: 102 body: 52
43	Lambda	parameter: 102 body: 53
44	Lambda	parameter: 102 body: 55
45	Operation	operator: 93 operands: 56
46	Variable
47	Operation	operator: 57 operands: 58
48	Operation	operator: 85 operands: 59
49	Operation	operator: 66 operands: 60
50	Operation	operator: 66 operands: 61
51	Operation	operator: 62 operands: 63
52	Operation	operator: 86 operands: 64
53	Operation	operator: 66 operands: 65
54	ExprTuple	102
55	Operation	operator: 66 operands: 67
56	ExprTuple	68, 69
57	Literal
58	ExprTuple	70, 95
59	NamedExprs	state: 71
60	NamedExprs	element: 72 targets: 80
61	NamedExprs	element: 73 targets: 74
62	Literal
63	NamedExprs	basis: 75
64	NamedExprs	operation: 76
65	NamedExprs	element: 77 targets: 78
66	Literal
67	NamedExprs	element: 79 targets: 80
68	Literal
69	Operation	operator: 115 operands: 81
70	Operation	operator: 115 operands: 82
71	Operation	operator: 83 operand: 98
72	Operation	operator: 85 operands: 92
73	Operation	operator: 86 operands: 87
74	Operation	operator: 93 operands: 88
75	Literal
76	Literal
77	Operation	operator: 91 operands: 89
78	Operation	operator: 93 operands: 90
79	Operation	operator: 91 operands: 92
80	Operation	operator: 93 operands: 94
81	ExprTuple	95, 96
82	ExprTuple	120, 97
83	Literal
84	ExprTuple	98
85	Literal
86	Literal
87	NamedExprs	operation: 99 part: 102
88	ExprTuple	121, 104
89	NamedExprs	state: 100 part: 102
90	ExprTuple	121, 122
91	Literal
92	NamedExprs	state: 101 part: 102
93	Literal
94	ExprTuple	103, 104
95	Operation	operator: 105 operands: 106
96	Operation	operator: 108 operand: 121
97	Operation	operator: 108 operand: 118
98	Literal
99	Operation	operator: 110 operands: 111
100	Operation	operator: 112 operands: 113
101	Literal
102	Variable
103	Operation	operator: 115 operands: 114
104	Operation	operator: 115 operands: 116
105	Literal
106	ExprTuple	117, 122
107	ExprTuple	121
108	Literal
109	ExprTuple	118
110	Literal
111	ExprTuple	119, 122
112	Literal
113	ExprTuple	120, 122
114	ExprTuple	122, 121
115	Literal
116	ExprTuple	122, 123
117	Literal
118	Literal
119	Literal
120	Variable
121	Literal
122	Literal
123	Literal

Expression of type InSet¶

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

Expression of type InSet ¶

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