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 ExprRange, ExprTuple, Variable, VertExprArray, m
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _s, _s_wire, _t
from proveit.physics.quantum.circuits import Input, Measure, MultiQubitElem, Output, Qcircuit

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Interval(one, _t)
sub_expr3 = Add(_t, one)
sub_expr4 = Add(_t, _s)
sub_expr5 = Interval(sub_expr3, sub_expr4)
sub_expr6 = [ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire]
sub_expr7 = MultiQubitElem(element = Input(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr4))
sub_expr8 = [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr5), one, _s)]
expr = ExprTuple(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _Psi_ket, part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr5), one, _s)], sub_expr6, sub_expr8)), Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr7, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr7, sub_expr3, sub_expr4).with_wrapping_at(2,6)], sub_expr6, sub_expr8)))

expr:

# 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{
\multiqin{3}{\lvert \Psi \rangle} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert u \rangle} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{4}{\lvert \Psi \rangle {\otimes} \lvert u \rangle} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle {\otimes} \lvert u \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle {\otimes} \lvert u \rangle} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle {\otimes} \lvert u \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle {\otimes} \lvert u \rangle} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right)

stored_expr.style_options()

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',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 8, 9
4	Literal
5	ExprTuple	7, 8, 9
6	ExprTuple	10, 11
7	ExprTuple	12, 13
8	ExprTuple	14, 15
9	ExprTuple	16, 17
10	ExprRange	lambda_map: 18 start_index: 78 end_index: 79
11	ExprRange	lambda_map: 19 start_index: 78 end_index: 80
12	ExprRange	lambda_map: 20 start_index: 78 end_index: 79
13	ExprRange	lambda_map: 20 start_index: 66 end_index: 67
14	ExprRange	lambda_map: 21 start_index: 78 end_index: 79
15	ExprRange	lambda_map: 22 start_index: 78 end_index: 80
16	ExprRange	lambda_map: 23 start_index: 78 end_index: 79
17	ExprRange	lambda_map: 24 start_index: 78 end_index: 80
18	Lambda	parameter: 65 body: 25
19	Lambda	parameter: 65 body: 26
20	Lambda	parameter: 65 body: 27
21	Lambda	parameter: 65 body: 28
22	Lambda	parameter: 65 body: 29
23	Lambda	parameter: 65 body: 30
24	Lambda	parameter: 65 body: 32
25	Operation	operator: 41 operands: 33
26	Operation	operator: 41 operands: 34
27	Operation	operator: 41 operands: 35
28	Operation	operator: 36 operands: 37
29	Operation	operator: 38 operands: 39
30	Operation	operator: 41 operands: 40
31	ExprTuple	65
32	Operation	operator: 41 operands: 42
33	NamedExprs	element: 43 targets: 50
34	NamedExprs	element: 44 targets: 52
35	NamedExprs	element: 45 targets: 46
36	Literal
37	NamedExprs	basis: 47
38	Literal
39	NamedExprs	operation: 48
40	NamedExprs	element: 49 targets: 50
41	Literal
42	NamedExprs	element: 51 targets: 52
43	Operation	operator: 54 operands: 53
44	Operation	operator: 54 operands: 60
45	Operation	operator: 54 operands: 55
46	Operation	operator: 61 operands: 56
47	Literal
48	Literal
49	Operation	operator: 59 operands: 57
50	Operation	operator: 61 operands: 58
51	Operation	operator: 59 operands: 60
52	Operation	operator: 61 operands: 62
53	NamedExprs	state: 75 part: 65
54	Literal
55	NamedExprs	state: 63 part: 65
56	ExprTuple	78, 67
57	NamedExprs	state: 64 part: 65
58	ExprTuple	78, 79
59	Literal
60	NamedExprs	state: 76 part: 65
61	Literal
62	ExprTuple	66, 67
63	Operation	operator: 68 operands: 69
64	Operation	operator: 70 operands: 71
65	Variable
66	Operation	operator: 73 operands: 72
67	Operation	operator: 73 operands: 74
68	Literal
69	ExprTuple	75, 76
70	Literal
71	ExprTuple	77, 79
72	ExprTuple	79, 78
73	Literal
74	ExprTuple	79, 80
75	Literal
76	Literal
77	Variable
78	Literal
79	Literal
80	Literal