Expression of type QcircuitEquiv

from the theory of proveit.physics.quantum.circuits

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.physics.quantum.circuits import QcircuitEquiv, circuit_aU, circuit_b

# build up the expression from sub-expressions
expr = QcircuitEquiv(circuit_aU, circuit_b)

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{a} & \gate{\begin{array}{c} \uparrow \\U_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\U_{2} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\U_{m} \\ \downarrow\end{array}} & { /^{k} } \qw
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{b} & { /^{k} } \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
9	ExprRange	lambda_map: 12 start_index: 36 end_index: 13
10	ExprTuple	14
11	ExprRange	lambda_map: 15 start_index: 36 end_index: 37
12	Lambda	parameter: 35 body: 16
13	Variable
14	ExprRange	lambda_map: 17 start_index: 36 end_index: 37
15	Lambda	parameter: 35 body: 18
16	IndexedVar	variable: 19 index: 35
17	Lambda	parameter: 35 body: 21
18	Operation	operator: 23 operands: 22
19	Variable
20	ExprTuple	35
21	Operation	operator: 23 operands: 24
22	NamedExprs	element: 25 targets: 27
23	Literal
24	NamedExprs	element: 26 targets: 27
25	Operation	operator: 29 operands: 28
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operands: 32
28	NamedExprs	state: 33 part: 35
29	Literal
30	NamedExprs	state: 34 part: 35
31	Literal
32	ExprTuple	36, 37
33	Variable
34	Variable
35	Variable
36	Literal
37	Variable