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__psi_m
from proveit.statistics import Prob

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

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} \\
\qin{\lvert \psi \rangle} & { /^{m} } \qw & { /^{m} } \qw & \gate{\cdots} & { /^{m} } \qw & \qout{\lvert \psi \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, 10
7	ExprRange	lambda_map: 11 start_index: 66 end_index: 12
8	ExprTuple	13, 14
9	ExprRange	lambda_map: 15 start_index: 66 end_index: 67
10	ExprRange	lambda_map: 16 start_index: 66 end_index: 68
11	Lambda	parameter: 56 body: 18
12	Variable
13	ExprRange	lambda_map: 19 start_index: 66 end_index: 67
14	ExprRange	lambda_map: 20 start_index: 66 end_index: 68
15	Lambda	parameter: 60 body: 21
16	Lambda	parameter: 60 body: 22
17	ExprTuple	56
18	ExprTuple	23, 24
19	Lambda	parameter: 60 body: 25
20	Lambda	parameter: 60 body: 26
21	Operation	operator: 32 operands: 27
22	Operation	operator: 32 operands: 28
23	ExprRange	lambda_map: 29 start_index: 66 end_index: 67
24	ExprRange	lambda_map: 30 start_index: 66 end_index: 68
25	Operation	operator: 32 operands: 31
26	Operation	operator: 32 operands: 33
27	NamedExprs	element: 34 targets: 40
28	NamedExprs	element: 35 targets: 42
29	Lambda	parameter: 60 body: 36
30	Lambda	parameter: 60 body: 38
31	NamedExprs	element: 39 targets: 40
32	Literal
33	NamedExprs	element: 41 targets: 42
34	Operation	operator: 44 operands: 43
35	Operation	operator: 44 operands: 52
36	IndexedVar	variable: 45 indices: 46
37	ExprTuple	60
38	Operation	operator: 47 operands: 48
39	Operation	operator: 51 operands: 49
40	Operation	operator: 53 operands: 50
41	Operation	operator: 51 operands: 52
42	Operation	operator: 53 operands: 54
43	NamedExprs	state: 55 part: 60
44	Literal
45	Variable
46	ExprTuple	56, 60
47	Literal
48	NamedExprs	operation: 57
49	NamedExprs	state: 58 part: 60
50	ExprTuple	66, 67
51	Literal
52	NamedExprs	state: 59 part: 60
53	Literal
54	ExprTuple	61, 62
55	Variable
56	Variable
57	Literal
58	Variable
59	Variable
60	Variable
61	Operation	operator: 64 operands: 63
62	Operation	operator: 64 operands: 65
63	ExprTuple	67, 66
64	Literal
65	ExprTuple	67, 68
66	Literal
67	Variable
68	Variable