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
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import I
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _psi__t_ket, _s, _t
from proveit.physics.quantum.circuits import Gate, Input, 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 = MultiQubitElem(element = Input(state = TensorProd(_psi__t_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr4))
sub_expr7 = [ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, _s)]
sub_expr8 = [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _Psi_ket, 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__t_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_expr7, sub_expr8)), Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr6, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr6, sub_expr3, sub_expr4).with_wrapping_at(2,6)], sub_expr7, 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{
\qin{\lvert \psi_{t} \rangle} & \gate{{\mathrm {FT}}^{\dag}_{t}} & \qout{\lvert \Psi \rangle} \\
\qin{\lvert u \rangle} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{1}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} & \gate{{\mathrm {FT}}^{\dag}_{t}} & \qout{\lvert \Psi \rangle} \\
\ghostqin{\lvert \psi_{t} \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: 77 end_index: 81
11	ExprRange	lambda_map: 19 start_index: 77 end_index: 78
12	ExprRange	lambda_map: 20 start_index: 77 end_index: 81
13	ExprRange	lambda_map: 20 start_index: 67 end_index: 68
14	ExprRange	lambda_map: 21 start_index: 77 end_index: 81
15	ExprRange	lambda_map: 22 start_index: 77 end_index: 78
16	ExprRange	lambda_map: 23 start_index: 77 end_index: 81
17	ExprRange	lambda_map: 24 start_index: 77 end_index: 78
18	Lambda	parameter: 66 body: 25
19	Lambda	parameter: 66 body: 26
20	Lambda	parameter: 66 body: 27
21	Lambda	parameter: 66 body: 28
22	Lambda	parameter: 66 body: 29
23	Lambda	parameter: 66 body: 30
24	Lambda	parameter: 66 body: 32
25	Operation	operator: 39 operands: 33
26	Operation	operator: 39 operands: 34
27	Operation	operator: 39 operands: 35
28	Operation	operator: 39 operands: 36
29	Operation	operator: 55 operands: 37
30	Operation	operator: 39 operands: 38
31	ExprTuple	66
32	Operation	operator: 39 operands: 40
33	NamedExprs	element: 41 targets: 48
34	NamedExprs	element: 42 targets: 50
35	NamedExprs	element: 43 targets: 44
36	NamedExprs	element: 45 targets: 48
37	NamedExprs	operation: 46
38	NamedExprs	element: 47 targets: 48
39	Literal
40	NamedExprs	element: 49 targets: 50
41	Operation	operator: 52 operands: 51
42	Operation	operator: 52 operands: 60
43	Operation	operator: 52 operands: 53
44	Operation	operator: 61 operands: 54
45	Operation	operator: 55 operands: 56
46	Literal
47	Operation	operator: 59 operands: 57
48	Operation	operator: 61 operands: 58
49	Operation	operator: 59 operands: 60
50	Operation	operator: 61 operands: 62
51	NamedExprs	state: 75 part: 66
52	Literal
53	NamedExprs	state: 63 part: 66
54	ExprTuple	77, 68
55	Literal
56	NamedExprs	operation: 64 part: 66
57	NamedExprs	state: 65 part: 66
58	ExprTuple	77, 81
59	Literal
60	NamedExprs	state: 76 part: 66
61	Literal
62	ExprTuple	67, 68
63	Operation	operator: 69 operands: 70
64	Operation	operator: 71 operand: 81
65	Literal
66	Variable
67	Operation	operator: 73 operands: 72
68	Operation	operator: 73 operands: 74
69	Literal
70	ExprTuple	75, 76
71	Literal
72	ExprTuple	81, 77
73	Literal
74	ExprTuple	81, 78
75	Operation	operator: 79 operand: 81
76	Literal
77	Literal
78	Literal
79	Literal
80	ExprTuple	81
81	Literal