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 Equals, Forall, InSet
from proveit.physics.quantum import m_ket_domain, var_ket_psi
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(var_ket_psi, Conditional(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(), InSet(var_ket_psi, m_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(\lvert \psi \rangle \mapsto \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} \textrm{ if } \lvert \psi \rangle \in \mathbb{C}^{2^{m}}\right..\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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