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, Variable, VertExprArray, l
from proveit.logic import And, InSet, TRUE
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z, ket_plus
from proveit.physics.quantum.QPE import ModAdd, QPE, _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))
sub_expr6 = InSet(l, _pos_domain)
sub_expr7 = 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)]))
expr = ExprTuple(Conditional(sub_expr7, And(sub_expr6, TRUE)), Conditional(sub_expr7, sub_expr6))

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

Expression of type ExprTuple¶

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

Expression of type ExprTuple ¶

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