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, _neg_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(_neg_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~-\left(e + 1\right)\} \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: 111 body: 6
4	Operation	operator: 7 operands: 8
5	ExprTuple	111
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: 112 end_index: 104
19	ExprRange	lambda_map: 29 start_index: 112 end_index: 103
20	ExprRange	lambda_map: 30 start_index: 112 end_index: 104
21	ExprRange	lambda_map: 30 start_index: 89 end_index: 90
22	ExprRange	lambda_map: 31 start_index: 112 end_index: 104
23	ExprRange	lambda_map: 32 start_index: 112 end_index: 103
24	ExprRange	lambda_map: 33 start_index: 112 end_index: 104
25	ExprRange	lambda_map: 34 start_index: 112 end_index: 103
26	Operation	operator: 99 operands: 35
27	Operation	operator: 108 operand: 46
28	Lambda	parameter: 88 body: 37
29	Lambda	parameter: 88 body: 38
30	Lambda	parameter: 88 body: 39
31	Lambda	parameter: 88 body: 40
32	Lambda	parameter: 88 body: 41
33	Lambda	parameter: 88 body: 42
34	Lambda	parameter: 88 body: 44
35	ExprTuple	45, 112
36	ExprTuple	46
37	Operation	operator: 72 operands: 47
38	Operation	operator: 54 operands: 48
39	Operation	operator: 54 operands: 49
40	Operation	operator: 50 operands: 51
41	Operation	operator: 73 operands: 52
42	Operation	operator: 54 operands: 53
43	ExprTuple	88
44	Operation	operator: 54 operands: 55
45	Operation	operator: 108 operand: 68
46	Operation	operator: 99 operands: 57
47	NamedExprs	state: 58
48	NamedExprs	element: 59 targets: 67
49	NamedExprs	element: 60 targets: 61
50	Literal
51	NamedExprs	basis: 62
52	NamedExprs	operation: 63
53	NamedExprs	element: 64 targets: 65
54	Literal
55	NamedExprs	element: 66 targets: 67
56	ExprTuple	68
57	ExprTuple	69, 112
58	Operation	operator: 70 operand: 84
59	Operation	operator: 72 operands: 79
60	Operation	operator: 73 operands: 74
61	Operation	operator: 80 operands: 75
62	Literal
63	Literal
64	Operation	operator: 78 operands: 76
65	Operation	operator: 80 operands: 77
66	Operation	operator: 78 operands: 79
67	Operation	operator: 80 operands: 81
68	Operation	operator: 82 operands: 83
69	Variable
70	Literal
71	ExprTuple	84
72	Literal
73	Literal
74	NamedExprs	operation: 85 part: 88
75	ExprTuple	112, 90
76	NamedExprs	state: 86 part: 88
77	ExprTuple	112, 104
78	Literal
79	NamedExprs	state: 87 part: 88
80	Literal
81	ExprTuple	89, 90
82	Literal
83	ExprTuple	91, 92
84	Literal
85	Operation	operator: 93 operands: 94
86	Operation	operator: 95 operands: 96
87	Literal
88	Variable
89	Operation	operator: 99 operands: 97
90	Operation	operator: 99 operands: 98
91	Literal
92	Operation	operator: 99 operands: 100
93	Literal
94	ExprTuple	101, 104
95	Literal
96	ExprTuple	102, 104
97	ExprTuple	104, 112
98	ExprTuple	104, 103
99	Literal
100	ExprTuple	104, 105
101	Literal
102	Operation	operator: 106 operands: 107
103	Literal
104	Literal
105	Operation	operator: 108 operand: 112
106	Literal
107	ExprTuple	110, 111
108	Literal
109	ExprTuple	112
110	Literal
111	Variable
112	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 ¶