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 InSet, Injections
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, _ket_u, _pos_domain, _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)]))), Injections(_pos_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[\{e + 1~\ldotp \ldotp~2^{t - 1}\} \xrightarrow[]{\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: 80 operands: 17
12	Literal
13	ExprTuple	18, 19
14	ExprTuple	20, 21
15	ExprTuple	22, 23
16	ExprTuple	24, 25
17	ExprTuple	26, 27
18	ExprRange	lambda_map: 28 start_index: 100 end_index: 101
19	ExprRange	lambda_map: 29 start_index: 100 end_index: 102
20	ExprRange	lambda_map: 30 start_index: 100 end_index: 101
21	ExprRange	lambda_map: 30 start_index: 89 end_index: 90
22	ExprRange	lambda_map: 31 start_index: 100 end_index: 101
23	ExprRange	lambda_map: 32 start_index: 100 end_index: 102
24	ExprRange	lambda_map: 33 start_index: 100 end_index: 101
25	ExprRange	lambda_map: 34 start_index: 100 end_index: 102
26	Operation	operator: 96 operands: 35
27	Operation	operator: 36 operands: 37
28	Lambda	parameter: 88 body: 38
29	Lambda	parameter: 88 body: 39
30	Lambda	parameter: 88 body: 40
31	Lambda	parameter: 88 body: 41
32	Lambda	parameter: 88 body: 42
33	Lambda	parameter: 88 body: 43
34	Lambda	parameter: 88 body: 45
35	ExprTuple	46, 100
36	Literal
37	ExprTuple	47, 48
38	Operation	operator: 72 operands: 49
39	Operation	operator: 56 operands: 50
40	Operation	operator: 56 operands: 51
41	Operation	operator: 52 operands: 53
42	Operation	operator: 73 operands: 54
43	Operation	operator: 56 operands: 55
44	ExprTuple	88
45	Operation	operator: 56 operands: 57
46	Variable
47	Literal
48	Operation	operator: 96 operands: 58
49	NamedExprs	state: 59
50	NamedExprs	element: 60 targets: 68
51	NamedExprs	element: 61 targets: 62
52	Literal
53	NamedExprs	basis: 63
54	NamedExprs	operation: 64
55	NamedExprs	element: 65 targets: 66
56	Literal
57	NamedExprs	element: 67 targets: 68
58	ExprTuple	101, 69
59	Operation	operator: 70 operand: 84
60	Operation	operator: 72 operands: 79
61	Operation	operator: 73 operands: 74
62	Operation	operator: 80 operands: 75
63	Literal
64	Literal
65	Operation	operator: 78 operands: 76
66	Operation	operator: 80 operands: 77
67	Operation	operator: 78 operands: 79
68	Operation	operator: 80 operands: 81
69	Operation	operator: 82 operand: 100
70	Literal
71	ExprTuple	84
72	Literal
73	Literal
74	NamedExprs	operation: 85 part: 88
75	ExprTuple	100, 90
76	NamedExprs	state: 86 part: 88
77	ExprTuple	100, 101
78	Literal
79	NamedExprs	state: 87 part: 88
80	Literal
81	ExprTuple	89, 90
82	Literal
83	ExprTuple	100
84	Literal
85	Operation	operator: 91 operands: 92
86	Operation	operator: 93 operands: 94
87	Literal
88	Variable
89	Operation	operator: 96 operands: 95
90	Operation	operator: 96 operands: 97
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 InSet¶

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

Expression of type InSet ¶

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