Expression of type QcircuitEquiv

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, 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, QcircuitEquiv

# 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 = QcircuitEquiv(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}\right) \cong \left(\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
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

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