Expression of type Lambda ¶

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 import Lambda
from proveit.core_expr_types.expr_arrays import A11_to_Akl
from proveit.logic import Equals
from proveit.physics.quantum.circuits import circuit__u_Akl_v, circuit__u_Akl_v__psi_m
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Lambda([A11_to_Akl], Equals(Prob(circuit__u_Akl_v), Prob(circuit__u_Akl_v__psi_m)).with_wrapping_at(2))

# 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(A_{1, 1}, A_{1, 2}, \ldots, A_{1, l}, A_{2, 1}, A_{2, 2}, \ldots, A_{2, l}, \ldots\ldots, A_{k, 1}, A_{k, 2}, \ldots, A_{k, l}\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \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) =  \\ \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) \end{array} \end{array}\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Lambda	parameters: 1 body: 2
1	ExprTuple	3
2	Operation	operator: 4 operands: 5
3	ExprRange	lambda_map: 6 start_index: 82 end_index: 27
4	Literal
5	ExprTuple	7, 8
6	Lambda	parameter: 72 body: 39
7	Operation	operator: 10 operand: 12
8	Operation	operator: 10 operand: 13
9	ExprTuple	12
10	Literal
11	ExprTuple	13
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18, 19
15	Literal
16	ExprTuple	20, 21, 22
17	ExprTuple	24
18	ExprRange	lambda_map: 23 start_index: 82 end_index: 27
19	ExprTuple	28
20	ExprTuple	24, 25
21	ExprRange	lambda_map: 26 start_index: 82 end_index: 27
22	ExprTuple	28, 29
23	Lambda	parameter: 72 body: 30
24	ExprRange	lambda_map: 31 start_index: 82 end_index: 83
25	ExprRange	lambda_map: 32 start_index: 82 end_index: 84
26	Lambda	parameter: 72 body: 34
27	Variable
28	ExprRange	lambda_map: 35 start_index: 82 end_index: 83
29	ExprRange	lambda_map: 36 start_index: 82 end_index: 84
30	ExprTuple	39
31	Lambda	parameter: 76 body: 37
32	Lambda	parameter: 76 body: 38
33	ExprTuple	72
34	ExprTuple	39, 40
35	Lambda	parameter: 76 body: 41
36	Lambda	parameter: 76 body: 42
37	Operation	operator: 48 operands: 43
38	Operation	operator: 48 operands: 44
39	ExprRange	lambda_map: 45 start_index: 82 end_index: 83
40	ExprRange	lambda_map: 46 start_index: 82 end_index: 84
41	Operation	operator: 48 operands: 47
42	Operation	operator: 48 operands: 49
43	NamedExprs	element: 50 targets: 56
44	NamedExprs	element: 51 targets: 58
45	Lambda	parameter: 76 body: 52
46	Lambda	parameter: 76 body: 54
47	NamedExprs	element: 55 targets: 56
48	Literal
49	NamedExprs	element: 57 targets: 58
50	Operation	operator: 60 operands: 59
51	Operation	operator: 60 operands: 68
52	IndexedVar	variable: 61 indices: 62
53	ExprTuple	76
54	Operation	operator: 63 operands: 64
55	Operation	operator: 67 operands: 65
56	Operation	operator: 69 operands: 66
57	Operation	operator: 67 operands: 68
58	Operation	operator: 69 operands: 70
59	NamedExprs	state: 71 part: 76
60	Literal
61	Variable
62	ExprTuple	72, 76
63	Literal
64	NamedExprs	operation: 73
65	NamedExprs	state: 74 part: 76
66	ExprTuple	82, 83
67	Literal
68	NamedExprs	state: 75 part: 76
69	Literal
70	ExprTuple	77, 78
71	Variable
72	Variable
73	Literal
74	Variable
75	Variable
76	Variable
77	Operation	operator: 80 operands: 79
78	Operation	operator: 80 operands: 81
79	ExprTuple	83, 82
80	Literal
81	ExprTuple	83, 84
82	Literal
83	Variable
84	Variable

Expression of type Lambda¶

from the theory of proveit.physics.quantum.circuits¶

Expression of type Lambda ¶

from the theory of proveit.physics.quantum.circuits ¶