Expression of type Add ¶

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 = Add(Variable("_b", latex_format = r"{_{-}b}"), 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())

{_{-}b} + \left[\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)\right]

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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',)

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

Expression of type Add¶

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

Expression of type Add ¶

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