Expression of type Prob

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 circuit__u_Akl_v
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Prob(circuit__u_Akl_v)

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())

\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert u \rangle} & \gate{A_{1, 1}} \qwx[1] & \gate{A_{2, 1}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 1}} \qwx[1] & \multiqout{3}{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{A_{1, 2}} \qwx[1] & \gate{A_{2, 2}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 2}} \qwx[1] & \ghostqout{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} \qwx[1] & \ghostqout{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{A_{1, l}} & \gate{A_{2, l}} & \gate{\cdots} & \gate{A_{k, l}} & \ghostqout{\lvert v \rangle}
} \end{array}\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7, 8
6	ExprTuple	9
7	ExprRange	lambda_map: 10 start_index: 41 end_index: 11
8	ExprTuple	12
9	ExprRange	lambda_map: 13 start_index: 41 end_index: 42
10	Lambda	parameter: 38 body: 15
11	Variable
12	ExprRange	lambda_map: 16 start_index: 41 end_index: 42
13	Lambda	parameter: 40 body: 17
14	ExprTuple	38
15	ExprTuple	18
16	Lambda	parameter: 40 body: 19
17	Operation	operator: 22 operands: 20
18	ExprRange	lambda_map: 21 start_index: 41 end_index: 42
19	Operation	operator: 22 operands: 23
20	NamedExprs	element: 24 targets: 28
21	Lambda	parameter: 40 body: 26
22	Literal
23	NamedExprs	element: 27 targets: 28
24	Operation	operator: 29 operands: 30
25	ExprTuple	40
26	IndexedVar	variable: 31 indices: 32
27	Operation	operator: 33 operands: 34
28	Operation	operator: 35 operands: 36
29	Literal
30	NamedExprs	state: 37 part: 40
31	Variable
32	ExprTuple	38, 40
33	Literal
34	NamedExprs	state: 39 part: 40
35	Literal
36	ExprTuple	41, 42
37	Variable
38	Variable
39	Variable
40	Variable
41	Literal
42	Variable