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.QPE import QPE1, QPE1_U_t_circuit
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 = MultiQubitElem(element = Gate(operation = QPE1(U, t), part = sub_expr1), targets = Interval(one, sub_expr2))
expr = QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr3, one, t), ExprRange(sub_expr1, sub_expr3, Add(t, one), sub_expr2)])), QPE1_U_t_circuit)

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)} & { /^{t} } \qw \\
& \ghost{\textrm{QPE}_1\left(U, t\right)} & { /^{s} } \qw
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \control{} \qw \qwx[1] & \qw & \gate{\cdots} \qwx[1] & \qw & \qw \\
& \qw \qwx[1] & \control{} \qw \qwx[1] & \gate{\cdots} \qwx[1] & \qw & \qw \\
& \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} & \qw \\
& \qw \qwx[1] & \qw \qwx[1] & \gate{\cdots} \qwx[1] & \control{} \qw \qwx[1] & \qw \\
& \gate{U^{2^{t - 1}}} & \gate{U^{2^{t - 2}}} & \gate{\cdots} & \gate{U^{2^{0}}} & { /^{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
8	ExprTuple	10, 11
9	ExprRange	lambda_map: 12 start_index: 13 end_index: 14
10	ExprRange	lambda_map: 15 start_index: 81 end_index: 80
11	ExprRange	lambda_map: 15 start_index: 73 end_index: 58
12	Lambda	parameter: 84 body: 16
13	Operation	operator: 76 operands: 17
14	Literal
15	Lambda	parameter: 63 body: 18
16	ExprTuple	19, 20
17	ExprTuple	21, 81
18	Operation	operator: 50 operands: 22
19	ExprRange	lambda_map: 23 start_index: 81 end_index: 80
20	ExprRange	lambda_map: 24 start_index: 81 end_index: 72
21	Operation	operator: 82 operand: 80
22	NamedExprs	element: 26 targets: 27
23	Lambda	parameter: 63 body: 28
24	Lambda	parameter: 63 body: 30
25	ExprTuple	80
26	Operation	operator: 53 operands: 31
27	Operation	operator: 48 operands: 32
28	Operation	operator: 33 operands: 34
29	ExprTuple	63
30	Operation	operator: 50 operands: 35
31	NamedExprs	operation: 36 part: 63
32	ExprTuple	81, 58
33	Literal
34	ExprTuple	37, 38
35	NamedExprs	element: 39 targets: 40
36	Operation	operator: 41 operands: 42
37	Conditional	value: 43 condition: 44
38	Conditional	value: 45 condition: 46
39	Operation	operator: 53 operands: 47
40	Operation	operator: 48 operands: 49
41	Literal
42	ExprTuple	70, 80
43	Operation	operator: 50 operands: 51
44	Operation	operator: 52 operands: 56
45	Operation	operator: 53 operands: 54
46	Operation	operator: 55 operands: 56
47	NamedExprs	operation: 57 part: 63
48	Literal
49	ExprTuple	73, 58
50	Literal
51	NamedExprs	element: 59 targets: 60
52	Literal
53	Literal
54	NamedExprs	operation: 61
55	Literal
56	ExprTuple	62, 63
57	Operation	operator: 64 operands: 65
58	Operation	operator: 76 operands: 66
59	Literal
60	Operation	operator: 67 operand: 73
61	Literal
62	Operation	operator: 76 operands: 69
63	Variable
64	Literal
65	ExprTuple	70, 71
66	ExprTuple	80, 72
67	Literal
68	ExprTuple	73
69	ExprTuple	84, 80
70	Variable
71	Operation	operator: 74 operands: 75
72	Variable
73	Operation	operator: 76 operands: 77
74	Literal
75	ExprTuple	78, 79
76	Literal
77	ExprTuple	80, 81
78	Literal
79	Operation	operator: 82 operand: 84
80	Variable
81	Literal
82	Literal
83	ExprTuple	84
84	Variable