Expression of type ExprTuple ¶

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 Conditional, ExprTuple, Lambda
from proveit.core_expr_types.expr_arrays import A11_to_Akl
from proveit.logic import And, Equals, Forall, InSet
from proveit.physics.quantum import l_ket_domain, m_ket_domain, var_ket_psi, var_ket_u, var_ket_v
from proveit.physics.quantum.circuits import circuit__psi_m__u_Akl_v, circuit__u_Akl_v
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([var_ket_u, var_ket_v], Conditional(Forall(instance_param_or_params = [var_ket_psi], instance_expr = Forall(instance_param_or_params = [A11_to_Akl], instance_expr = Equals(Prob(circuit__u_Akl_v), Prob(circuit__psi_m__u_Akl_v)).with_wrapping_at(2)).with_wrapping(), domain = m_ket_domain), And(InSet(var_ket_u, l_ket_domain), InSet(var_ket_v, l_ket_domain)))))

# 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(\left(\lvert u \rangle, \lvert v \rangle\right) \mapsto \left\{\forall_{\lvert \psi \rangle \in \mathbb{C}^{2^{m}}}~\left[\begin{array}{l}\forall_{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}}~\\
\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{
\qin{\lvert \psi \rangle} & { /^{m} } \qw & { /^{m} } \qw & \gate{\cdots} & { /^{m} } \qw & \qout{\lvert \psi \rangle} \\
\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) \end{array} \end{array}\right)\end{array}\right] \textrm{ if } \lvert u \rangle \in \mathbb{C}^{2^{l}} ,  \lvert v \rangle \in \mathbb{C}^{2^{l}}\right..\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	115, 119
3	Conditional	value: 4 condition: 5
4	Operation	operator: 19 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Lambda	parameter: 118 body: 13
10	Operation	operator: 21 operands: 14
11	Operation	operator: 21 operands: 15
12	ExprTuple	118
13	Conditional	value: 16 condition: 17
14	ExprTuple	115, 18
15	ExprTuple	119, 18
16	Operation	operator: 19 operand: 24
17	Operation	operator: 21 operands: 22
18	Operation	operator: 29 operands: 23
19	Literal
20	ExprTuple	24
21	Literal
22	ExprTuple	118, 25
23	ExprTuple	35, 26
24	Lambda	parameters: 27 body: 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 40 operands: 31
27	ExprTuple	32
28	Operation	operator: 33 operands: 34
29	Literal
30	ExprTuple	35, 36
31	ExprTuple	45, 128
32	ExprRange	lambda_map: 37 start_index: 126 end_index: 63
33	Literal
34	ExprTuple	38, 39
35	Literal
36	Operation	operator: 40 operands: 41
37	Lambda	parameter: 117 body: 80
38	Operation	operator: 43 operand: 46
39	Operation	operator: 43 operand: 47
40	Literal
41	ExprTuple	45, 127
42	ExprTuple	46
43	Literal
44	ExprTuple	47
45	Literal
46	Operation	operator: 49 operands: 48
47	Operation	operator: 49 operands: 50
48	ExprTuple	51, 52, 53
49	Literal
50	ExprTuple	54, 55, 56
51	ExprTuple	57
52	ExprRange	lambda_map: 58 start_index: 126 end_index: 63
53	ExprTuple	59
54	ExprTuple	60, 61
55	ExprRange	lambda_map: 62 start_index: 126 end_index: 63
56	ExprTuple	64, 65
57	ExprRange	lambda_map: 66 start_index: 126 end_index: 128
58	Lambda	parameter: 117 body: 67
59	ExprRange	lambda_map: 68 start_index: 126 end_index: 128
60	ExprRange	lambda_map: 69 start_index: 126 end_index: 127
61	ExprRange	lambda_map: 70 start_index: 126 end_index: 128
62	Lambda	parameter: 117 body: 72
63	Variable
64	ExprRange	lambda_map: 73 start_index: 126 end_index: 127
65	ExprRange	lambda_map: 74 start_index: 126 end_index: 128
66	Lambda	parameter: 120 body: 75
67	ExprTuple	80
68	Lambda	parameter: 120 body: 76
69	Lambda	parameter: 120 body: 77
70	Lambda	parameter: 120 body: 78
71	ExprTuple	117
72	ExprTuple	79, 80
73	Lambda	parameter: 120 body: 81
74	Lambda	parameter: 120 body: 82
75	Operation	operator: 90 operands: 83
76	Operation	operator: 90 operands: 84
77	Operation	operator: 90 operands: 85
78	Operation	operator: 90 operands: 86
79	ExprRange	lambda_map: 87 start_index: 126 end_index: 127
80	ExprRange	lambda_map: 88 start_index: 126 end_index: 128
81	Operation	operator: 90 operands: 89
82	Operation	operator: 90 operands: 91
83	NamedExprs	element: 94 targets: 92
84	NamedExprs	element: 100 targets: 92
85	NamedExprs	element: 93 targets: 99
86	NamedExprs	element: 94 targets: 101
87	Lambda	parameter: 120 body: 95
88	Lambda	parameter: 120 body: 97
89	NamedExprs	element: 98 targets: 99
90	Literal
91	NamedExprs	element: 100 targets: 101
92	Operation	operator: 113 operands: 102
93	Operation	operator: 103 operands: 109
94	Operation	operator: 103 operands: 104
95	Operation	operator: 105 operands: 106
96	ExprTuple	120
97	IndexedVar	variable: 107 indices: 108
98	Operation	operator: 111 operands: 109
99	Operation	operator: 113 operands: 110
100	Operation	operator: 111 operands: 112
101	Operation	operator: 113 operands: 114
102	ExprTuple	126, 128
103	Literal
104	NamedExprs	state: 115 part: 120
105	Literal
106	NamedExprs	operation: 116
107	Variable
108	ExprTuple	117, 120
109	NamedExprs	state: 118 part: 120
110	ExprTuple	126, 127
111	Literal
112	NamedExprs	state: 119 part: 120
113	Literal
114	ExprTuple	121, 122
115	Variable
116	Literal
117	Variable
118	Variable
119	Variable
120	Variable
121	Operation	operator: 124 operands: 123
122	Operation	operator: 124 operands: 125
123	ExprTuple	127, 126
124	Literal
125	ExprTuple	127, 128
126	Literal
127	Variable
128	Variable

Expression of type ExprTuple¶

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

Expression of type ExprTuple ¶

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