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, _pos_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 = _pos_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 \{e + 1~\ldotp \ldotp~2^{t - 1}\}}~\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: 106 body: 5
4	ExprTuple	106
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	106, 16
12	ExprTuple	17, 18
13	ExprTuple	19, 20
14	ExprTuple	21, 22
15	ExprTuple	23, 24
16	Operation	operator: 79 operands: 25
17	ExprRange	lambda_map: 26 start_index: 100 end_index: 101
18	ExprRange	lambda_map: 27 start_index: 100 end_index: 102
19	ExprRange	lambda_map: 28 start_index: 100 end_index: 101
20	ExprRange	lambda_map: 28 start_index: 87 end_index: 88
21	ExprRange	lambda_map: 29 start_index: 100 end_index: 101
22	ExprRange	lambda_map: 30 start_index: 100 end_index: 102
23	ExprRange	lambda_map: 31 start_index: 100 end_index: 101
24	ExprRange	lambda_map: 32 start_index: 100 end_index: 102
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: 96 operands: 43
34	Operation	operator: 44 operands: 45
35	Operation	operator: 71 operands: 46
36	Operation	operator: 53 operands: 47
37	Operation	operator: 53 operands: 48
38	Operation	operator: 49 operands: 50
39	Operation	operator: 72 operands: 51
40	Operation	operator: 53 operands: 52
41	ExprTuple	86
42	Operation	operator: 53 operands: 54
43	ExprTuple	55, 100
44	Literal
45	ExprTuple	56, 57
46	NamedExprs	state: 58
47	NamedExprs	element: 59 targets: 67
48	NamedExprs	element: 60 targets: 61
49	Literal
50	NamedExprs	basis: 62
51	NamedExprs	operation: 63
52	NamedExprs	element: 64 targets: 65
53	Literal
54	NamedExprs	element: 66 targets: 67
55	Variable
56	Literal
57	Operation	operator: 96 operands: 68
58	Operation	operator: 69 operand: 82
59	Operation	operator: 71 operands: 78
60	Operation	operator: 72 operands: 73
61	Operation	operator: 79 operands: 74
62	Literal
63	Literal
64	Operation	operator: 77 operands: 75
65	Operation	operator: 79 operands: 76
66	Operation	operator: 77 operands: 78
67	Operation	operator: 79 operands: 80
68	ExprTuple	101, 81
69	Literal
70	ExprTuple	82
71	Literal
72	Literal
73	NamedExprs	operation: 83 part: 86
74	ExprTuple	100, 88
75	NamedExprs	state: 84 part: 86
76	ExprTuple	100, 101
77	Literal
78	NamedExprs	state: 85 part: 86
79	Literal
80	ExprTuple	87, 88
81	Operation	operator: 89 operand: 100
82	Literal
83	Operation	operator: 91 operands: 92
84	Operation	operator: 93 operands: 94
85	Literal
86	Variable
87	Operation	operator: 96 operands: 95
88	Operation	operator: 96 operands: 97
89	Literal
90	ExprTuple	100
91	Literal
92	ExprTuple	98, 101
93	Literal
94	ExprTuple	99, 101
95	ExprTuple	101, 100
96	Literal
97	ExprTuple	101, 102
98	Literal
99	Operation	operator: 103 operands: 104
100	Literal
101	Literal
102	Literal
103	Literal
104	ExprTuple	105, 106
105	Literal
106	Variable

Expression of type ProbOfAll¶

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

Expression of type ProbOfAll ¶

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