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, U, Variable, VertExprArray, s, t
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 QPE, QPE1
from proveit.physics.quantum.circuits import Gate, MultiQubitElem, Qcircuit

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(t, s)
sub_expr3 = Add(t, one)
sub_expr4 = Interval(one, sub_expr2)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE(U, t), part = sub_expr1), targets = sub_expr4)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE1(U, t), part = sub_expr1), targets = sub_expr4)
expr = ExprTuple(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr5, one, t), ExprRange(sub_expr1, sub_expr5, sub_expr3, sub_expr2)])), Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr6, one, t), ExprRange(sub_expr1, sub_expr6, sub_expr3, sub_expr2)], [ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(t), part = sub_expr1), targets = Interval(one, t)), one, t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, s)])))

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{
& \multigate{1}{\textrm{QPE}\left(U, t\right)} & { /^{t} } \qw \\
& \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \multigate{1}{\textrm{QPE}_1\left(U, t\right)} & \gate{{\mathrm {FT}}^{\dag}_{t}} & { /^{t} } \qw \\
& \ghost{\textrm{QPE}_1\left(U, t\right)} & { /^{s} } \qw & { /^{s} } \qw
} \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 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	7, 8
6	ExprTuple	9, 10
7	ExprTuple	11, 12
8	ExprTuple	13, 14
9	ExprRange	lambda_map: 15 start_index: 49 end_index: 59
10	ExprRange	lambda_map: 15 start_index: 17 end_index: 46
11	ExprRange	lambda_map: 16 start_index: 49 end_index: 59
12	ExprRange	lambda_map: 16 start_index: 17 end_index: 46
13	ExprRange	lambda_map: 18 start_index: 49 end_index: 59
14	ExprRange	lambda_map: 19 start_index: 49 end_index: 58
15	Lambda	parameter: 48 body: 20
16	Lambda	parameter: 48 body: 21
17	Operation	operator: 53 operands: 22
18	Lambda	parameter: 48 body: 23
19	Lambda	parameter: 48 body: 25
20	Operation	operator: 28 operands: 26
21	Operation	operator: 28 operands: 27
22	ExprTuple	59, 49
23	Operation	operator: 28 operands: 29
24	ExprTuple	48
25	Operation	operator: 40 operands: 30
26	NamedExprs	element: 31 targets: 33
27	NamedExprs	element: 32 targets: 33
28	Literal
29	NamedExprs	element: 34 targets: 35
30	NamedExprs	operation: 36
31	Operation	operator: 40 operands: 37
32	Operation	operator: 40 operands: 38
33	Operation	operator: 42 operands: 39
34	Operation	operator: 40 operands: 41
35	Operation	operator: 42 operands: 43
36	Literal
37	NamedExprs	operation: 44 part: 48
38	NamedExprs	operation: 45 part: 48
39	ExprTuple	49, 46
40	Literal
41	NamedExprs	operation: 47 part: 48
42	Literal
43	ExprTuple	49, 59
44	Operation	operator: 50 operands: 52
45	Operation	operator: 51 operands: 52
46	Operation	operator: 53 operands: 54
47	Operation	operator: 55 operand: 59
48	Variable
49	Literal
50	Literal
51	Literal
52	ExprTuple	57, 59
53	Literal
54	ExprTuple	59, 58
55	Literal
56	ExprTuple	59
57	Variable
58	Variable
59	Variable