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, Variable, VertExprArray
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, _U, _s, _t
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 = QPE1(_U, _t), part = sub_expr1), targets = sub_expr4)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE(_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)], [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)])), Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr6, one, _t), ExprRange(sub_expr1, sub_expr6, sub_expr3, sub_expr2)])))

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}_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) \cong \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)

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