Expression of type ExprTuple ¶

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, ExprTuple, 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 = ExprTuple(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.., \left[\{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\} \xrightarrow[\text{onto}]{\text{1-to-1}} \Omega\right]\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

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

Expression of type ExprTuple¶

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

Expression of type ExprTuple ¶

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