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, k, l, m
from proveit.core_expr_types.expr_arrays import A11_to_Akl
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import NaturalPos
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__u_Akl_v, circuit__u_Akl_v__psi_m
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([k, l, m], Conditional(Forall(instance_param_or_params = [var_ket_u, var_ket_v], instance_expr = 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__u_Akl_v__psi_m)).with_wrapping_at(2)).with_wrapping(), domain = m_ket_domain), domain = l_ket_domain), And(InSet(k, NaturalPos), InSet(l, NaturalPos), InSet(m, NaturalPos)))))

# 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(k, l, m\right) \mapsto \left\{\forall_{\lvert u \rangle, \lvert v \rangle \in \mathbb{C}^{2^{l}}}~\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{
\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)\end{array}\right]\right] \textrm{ if } k \in \mathbb{N}^+ ,  l \in \mathbb{N}^+ ,  m \in \mathbb{N}^+\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	75, 131, 132
3	Conditional	value: 4 condition: 5
4	Operation	operator: 33 operand: 8
5	Operation	operator: 21 operands: 7
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameters: 12 body: 13
9	Operation	operator: 35 operands: 14
10	Operation	operator: 35 operands: 15
11	Operation	operator: 35 operands: 16
12	ExprTuple	119, 122
13	Conditional	value: 17 condition: 18
14	ExprTuple	75, 19
15	ExprTuple	131, 19
16	ExprTuple	132, 19
17	Operation	operator: 33 operand: 23
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23
21	Literal
22	ExprTuple	24, 25
23	Lambda	parameter: 123 body: 27
24	Operation	operator: 35 operands: 28
25	Operation	operator: 35 operands: 29
26	ExprTuple	123
27	Conditional	value: 30 condition: 31
28	ExprTuple	119, 32
29	ExprTuple	122, 32
30	Operation	operator: 33 operand: 38
31	Operation	operator: 35 operands: 36
32	Operation	operator: 43 operands: 37
33	Literal
34	ExprTuple	38
35	Literal
36	ExprTuple	123, 39
37	ExprTuple	49, 40
38	Lambda	parameters: 41 body: 42
39	Operation	operator: 43 operands: 44
40	Operation	operator: 54 operands: 45
41	ExprTuple	46
42	Operation	operator: 47 operands: 48
43	Literal
44	ExprTuple	49, 50
45	ExprTuple	59, 131
46	ExprRange	lambda_map: 51 start_index: 130 end_index: 75
47	Literal
48	ExprTuple	52, 53
49	Literal
50	Operation	operator: 54 operands: 55
51	Lambda	parameter: 120 body: 87
52	Operation	operator: 57 operand: 60
53	Operation	operator: 57 operand: 61
54	Literal
55	ExprTuple	59, 132
56	ExprTuple	60
57	Literal
58	ExprTuple	61
59	Literal
60	Operation	operator: 63 operands: 62
61	Operation	operator: 63 operands: 64
62	ExprTuple	65, 66, 67
63	Literal
64	ExprTuple	68, 69, 70
65	ExprTuple	72
66	ExprRange	lambda_map: 71 start_index: 130 end_index: 75
67	ExprTuple	76
68	ExprTuple	72, 73
69	ExprRange	lambda_map: 74 start_index: 130 end_index: 75
70	ExprTuple	76, 77
71	Lambda	parameter: 120 body: 78
72	ExprRange	lambda_map: 79 start_index: 130 end_index: 131
73	ExprRange	lambda_map: 80 start_index: 130 end_index: 132
74	Lambda	parameter: 120 body: 82
75	Variable
76	ExprRange	lambda_map: 83 start_index: 130 end_index: 131
77	ExprRange	lambda_map: 84 start_index: 130 end_index: 132
78	ExprTuple	87
79	Lambda	parameter: 124 body: 85
80	Lambda	parameter: 124 body: 86
81	ExprTuple	120
82	ExprTuple	87, 88
83	Lambda	parameter: 124 body: 89
84	Lambda	parameter: 124 body: 90
85	Operation	operator: 96 operands: 91
86	Operation	operator: 96 operands: 92
87	ExprRange	lambda_map: 93 start_index: 130 end_index: 131
88	ExprRange	lambda_map: 94 start_index: 130 end_index: 132
89	Operation	operator: 96 operands: 95
90	Operation	operator: 96 operands: 97
91	NamedExprs	element: 98 targets: 104
92	NamedExprs	element: 99 targets: 106
93	Lambda	parameter: 124 body: 100
94	Lambda	parameter: 124 body: 102
95	NamedExprs	element: 103 targets: 104
96	Literal
97	NamedExprs	element: 105 targets: 106
98	Operation	operator: 108 operands: 107
99	Operation	operator: 108 operands: 116
100	IndexedVar	variable: 109 indices: 110
101	ExprTuple	124
102	Operation	operator: 111 operands: 112
103	Operation	operator: 115 operands: 113
104	Operation	operator: 117 operands: 114
105	Operation	operator: 115 operands: 116
106	Operation	operator: 117 operands: 118
107	NamedExprs	state: 119 part: 124
108	Literal
109	Variable
110	ExprTuple	120, 124
111	Literal
112	NamedExprs	operation: 121
113	NamedExprs	state: 122 part: 124
114	ExprTuple	130, 131
115	Literal
116	NamedExprs	state: 123 part: 124
117	Literal
118	ExprTuple	125, 126
119	Variable
120	Variable
121	Literal
122	Variable
123	Variable
124	Variable
125	Operation	operator: 128 operands: 127
126	Operation	operator: 128 operands: 129
127	ExprTuple	131, 130
128	Literal
129	ExprTuple	131, 132
130	Literal
131	Variable
132	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 ¶