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