Expression of type InSet ¶

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 Conditional, ExprRange, Lambda, Variable, VertExprArray, l
from proveit.logic import Bijections, InSet
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z, ket_plus
from proveit.physics.quantum.QPE import ModAdd, QPE, _Omega, _U, _b_floor, _full_domain, _ket_u, _s, _s_wire, _t
from proveit.physics.quantum.circuits import Gate, Input, Measure, MultiQubitElem, Output, Qcircuit

# 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 = InSet(Lambda(l, Conditional(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)])), InSet(l, _full_domain))), Bijections(_full_domain, _Omega))

# 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())

\left[l \mapsto \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} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\}\right..\right] \in \left[\{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\} \xrightarrow[\text{onto}]{\text{1-to-1}} \Omega\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',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

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