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, QcircuitEquiv

# 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 = 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_expr9 = [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_expr10 = [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(QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray(sub_expr8)), Qcircuit(vert_expr_array = VertExprArray(sub_expr9))), QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray(sub_expr8, sub_expr6, sub_expr10)), Qcircuit(vert_expr_array = VertExprArray(sub_expr9, sub_expr6, sub_expr10))).with_wrapping_at(1))

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(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \Psi \rangle} & { /^{t} } \qw \\
\qin{\lvert u \rangle} & { /^{s} } \qw
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{1}{\lvert \Psi \rangle {\otimes} \lvert u \rangle} & { /^{t} } \qw \\
\ghostqin{\lvert \Psi \rangle {\otimes} \lvert u \rangle} & { /^{s} } \qw
} \end{array}\right), \begin{array}{c} \begin{array}{l} \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}\right) \\  \cong \left(\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) \end{array} \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, 7
4	Literal
5	ExprTuple	8, 9
6	Operation	operator: 13 operand: 15
7	Operation	operator: 13 operand: 16
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	15
11	ExprTuple	16
12	ExprTuple	15, 17, 18
13	Literal
14	ExprTuple	16, 17, 18
15	ExprTuple	19, 20
16	ExprTuple	21, 22
17	ExprTuple	23, 24
18	ExprTuple	25, 26
19	ExprRange	lambda_map: 27 start_index: 87 end_index: 88
20	ExprRange	lambda_map: 28 start_index: 87 end_index: 89
21	ExprRange	lambda_map: 29 start_index: 87 end_index: 88
22	ExprRange	lambda_map: 29 start_index: 75 end_index: 76
23	ExprRange	lambda_map: 30 start_index: 87 end_index: 88
24	ExprRange	lambda_map: 31 start_index: 87 end_index: 89
25	ExprRange	lambda_map: 32 start_index: 87 end_index: 88
26	ExprRange	lambda_map: 33 start_index: 87 end_index: 89
27	Lambda	parameter: 74 body: 34
28	Lambda	parameter: 74 body: 35
29	Lambda	parameter: 74 body: 36
30	Lambda	parameter: 74 body: 37
31	Lambda	parameter: 74 body: 38
32	Lambda	parameter: 74 body: 39
33	Lambda	parameter: 74 body: 41
34	Operation	operator: 50 operands: 42
35	Operation	operator: 50 operands: 43
36	Operation	operator: 50 operands: 44
37	Operation	operator: 45 operands: 46
38	Operation	operator: 47 operands: 48
39	Operation	operator: 50 operands: 49
40	ExprTuple	74
41	Operation	operator: 50 operands: 51
42	NamedExprs	element: 52 targets: 59
43	NamedExprs	element: 53 targets: 61
44	NamedExprs	element: 54 targets: 55
45	Literal
46	NamedExprs	basis: 56
47	Literal
48	NamedExprs	operation: 57
49	NamedExprs	element: 58 targets: 59
50	Literal
51	NamedExprs	element: 60 targets: 61
52	Operation	operator: 63 operands: 62
53	Operation	operator: 63 operands: 69
54	Operation	operator: 63 operands: 64
55	Operation	operator: 70 operands: 65
56	Literal
57	Literal
58	Operation	operator: 68 operands: 66
59	Operation	operator: 70 operands: 67
60	Operation	operator: 68 operands: 69
61	Operation	operator: 70 operands: 71
62	NamedExprs	state: 84 part: 74
63	Literal
64	NamedExprs	state: 72 part: 74
65	ExprTuple	87, 76
66	NamedExprs	state: 73 part: 74
67	ExprTuple	87, 88
68	Literal
69	NamedExprs	state: 85 part: 74
70	Literal
71	ExprTuple	75, 76
72	Operation	operator: 77 operands: 78
73	Operation	operator: 79 operands: 80
74	Variable
75	Operation	operator: 82 operands: 81
76	Operation	operator: 82 operands: 83
77	Literal
78	ExprTuple	84, 85
79	Literal
80	ExprTuple	86, 88
81	ExprTuple	88, 87
82	Literal
83	ExprTuple	88, 89
84	Literal
85	Literal
86	Variable
87	Literal
88	Literal
89	Literal