Expression of type ProbOfAll ¶

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

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 ExprRange, Variable, VertExprArray, l
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z, ket_plus
from proveit.physics.quantum.QPE import ModAdd, QPE, _U, _b_floor, _ket_u, _neg_domain, _s, _s_wire, _t
from proveit.physics.quantum.circuits import Gate, Input, Measure, MultiQubitElem, Output, Qcircuit
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(_t, one)
sub_expr3 = Add(_t, _s)
sub_expr4 = Interval(sub_expr2, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = ProbOfAll(instance_param_or_params = [l], instance_element = Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Input(state = ket_plus), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)], [ExprRange(sub_expr1, sub_expr5, one, _t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(ModAdd(_b_floor, l), _t), part = sub_expr1), targets = Interval(one, _t)), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)])), domain = _neg_domain)

# 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())

\textrm{Prob}_{l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}}~\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert b_{\textit{f}} \oplus l \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 b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 109 body: 5
4	ExprTuple	109
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13, 14, 15
10	Literal
11	ExprTuple	109, 16
12	ExprTuple	17, 18
13	ExprTuple	19, 20
14	ExprTuple	21, 22
15	ExprTuple	23, 24
16	Operation	operator: 78 operands: 25
17	ExprRange	lambda_map: 26 start_index: 112 end_index: 106
18	ExprRange	lambda_map: 27 start_index: 112 end_index: 101
19	ExprRange	lambda_map: 28 start_index: 112 end_index: 106
20	ExprRange	lambda_map: 28 start_index: 87 end_index: 88
21	ExprRange	lambda_map: 29 start_index: 112 end_index: 106
22	ExprRange	lambda_map: 30 start_index: 112 end_index: 101
23	ExprRange	lambda_map: 31 start_index: 112 end_index: 106
24	ExprRange	lambda_map: 32 start_index: 112 end_index: 101
25	ExprTuple	33, 34
26	Lambda	parameter: 86 body: 35
27	Lambda	parameter: 86 body: 36
28	Lambda	parameter: 86 body: 37
29	Lambda	parameter: 86 body: 38
30	Lambda	parameter: 86 body: 39
31	Lambda	parameter: 86 body: 40
32	Lambda	parameter: 86 body: 42
33	Operation	operator: 102 operands: 43
34	Operation	operator: 110 operand: 55
35	Operation	operator: 70 operands: 45
36	Operation	operator: 52 operands: 46
37	Operation	operator: 52 operands: 47
38	Operation	operator: 48 operands: 49
39	Operation	operator: 71 operands: 50
40	Operation	operator: 52 operands: 51
41	ExprTuple	86
42	Operation	operator: 52 operands: 53
43	ExprTuple	54, 112
44	ExprTuple	55
45	NamedExprs	state: 56
46	NamedExprs	element: 57 targets: 65
47	NamedExprs	element: 58 targets: 59
48	Literal
49	NamedExprs	basis: 60
50	NamedExprs	operation: 61
51	NamedExprs	element: 62 targets: 63
52	Literal
53	NamedExprs	element: 64 targets: 65
54	Operation	operator: 110 operand: 80
55	Operation	operator: 102 operands: 67
56	Operation	operator: 68 operand: 82
57	Operation	operator: 70 operands: 77
58	Operation	operator: 71 operands: 72
59	Operation	operator: 78 operands: 73
60	Literal
61	Literal
62	Operation	operator: 76 operands: 74
63	Operation	operator: 78 operands: 75
64	Operation	operator: 76 operands: 77
65	Operation	operator: 78 operands: 79
66	ExprTuple	80
67	ExprTuple	81, 112
68	Literal
69	ExprTuple	82
70	Literal
71	Literal
72	NamedExprs	operation: 83 part: 86
73	ExprTuple	112, 88
74	NamedExprs	state: 84 part: 86
75	ExprTuple	112, 106
76	Literal
77	NamedExprs	state: 85 part: 86
78	Literal
79	ExprTuple	87, 88
80	Operation	operator: 89 operands: 90
81	Variable
82	Literal
83	Operation	operator: 91 operands: 92
84	Operation	operator: 93 operands: 94
85	Literal
86	Variable
87	Operation	operator: 102 operands: 95
88	Operation	operator: 102 operands: 96
89	Literal
90	ExprTuple	97, 98
91	Literal
92	ExprTuple	99, 106
93	Literal
94	ExprTuple	100, 106
95	ExprTuple	106, 112
96	ExprTuple	106, 101
97	Literal
98	Operation	operator: 102 operands: 103
99	Literal
100	Operation	operator: 104 operands: 105
101	Literal
102	Literal
103	ExprTuple	106, 107
104	Literal
105	ExprTuple	108, 109
106	Literal
107	Operation	operator: 110 operand: 112
108	Literal
109	Variable
110	Literal
111	ExprTuple	112
112	Literal

Expression of type ProbOfAll¶

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

Expression of type ProbOfAll ¶

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