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 A, Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, N, Variable, VertExprArray, m, n
from proveit.core_expr_types import A_1_to_m, n_1_to_m
from proveit.linear_algebra import TensorProd
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Add, Complex, Exp, Interval, Natural, NaturalPos, one, subtract, two
from proveit.physics.quantum.circuits import MultiQubitElem, N_0_to_m, N_m, Output, Qcircuit, QcircuitEquiv, each_Nk_is_partial_sum

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr3 = Variable("_c", latex_format = r"{_{-}c}")
expr = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [n_1_to_m], instance_expr = Forall(instance_param_or_params = [A_1_to_m], instance_expr = Forall(instance_param_or_params = [N_0_to_m], instance_expr = QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, ExprRange(sub_expr2, MultiQubitElem(element = Output(state = IndexedVar(A, sub_expr1), part = sub_expr2), targets = Interval(Add(IndexedVar(N, subtract(sub_expr1, one)), one), IndexedVar(N, sub_expr1))), one, IndexedVar(n, sub_expr1)).with_wrapping_at(2,6), one, m)])), Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr3, ExprRange(sub_expr1, MultiQubitElem(element = Output(state = TensorProd(A_1_to_m), part = sub_expr1), targets = Interval(one, N_m)), Add(IndexedVar(N, subtract(sub_expr3, one)), one), IndexedVar(N, sub_expr3)).with_wrapping_at(2,6), one, m)]))), domain = Natural, condition = each_Nk_is_partial_sum).with_wrapping(), domains = [ExprRange(sub_expr2, CartExp(Complex, Exp(two, IndexedVar(n, sub_expr2))), one, m)]).with_wrapping(), domain = NaturalPos).with_wrapping(), 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(m \mapsto \left\{\begin{array}{l}\forall_{n_{1}, n_{2}, \ldots, n_{m} \in \mathbb{N}^+}~\\
\left[\begin{array}{l}\forall_{\left(A_{1} \in \mathbb{C}^{2^{n_{1}}}\right), \left(A_{2} \in \mathbb{C}^{2^{n_{2}}}\right), \ldots, \left(A_{m} \in \mathbb{C}^{2^{n_{m}}}\right)}~\\
\left[\begin{array}{l}\forall_{N_{0}, N_{1}, \ldots, N_{m} \in \mathbb{N}~|~\left(N_{0} = 0\right)\land \left(N_{1} = \left(N_{1 - 1} + n_{1}\right)\right) \land  \left(N_{2} = \left(N_{2 - 1} + n_{2}\right)\right) \land  \ldots \land  \left(N_{m} = \left(N_{m - 1} + n_{m}\right)\right)}~\\
\left(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qout{A_{1}~\mbox{part}~1~\mbox{on}~\{N_{1 - 1} + 1~\ldotp \ldotp~N_{1}\}} \\
& \qout{A_{1}~\mbox{part}~2~\mbox{on}~\{N_{1 - 1} + 1~\ldotp \ldotp~N_{1}\}} \\
& \qout{\vdots} \\
& \qout{A_{1}~\mbox{part}~n_{1}~\mbox{on}~\{N_{1 - 1} + 1~\ldotp \ldotp~N_{1}\}} \\
& \qout{A_{2}~\mbox{part}~1~\mbox{on}~\{N_{2 - 1} + 1~\ldotp \ldotp~N_{2}\}} \\
& \qout{A_{2}~\mbox{part}~2~\mbox{on}~\{N_{2 - 1} + 1~\ldotp \ldotp~N_{2}\}} \\
& \qout{\vdots} \\
& \qout{A_{2}~\mbox{part}~n_{2}~\mbox{on}~\{N_{2 - 1} + 1~\ldotp \ldotp~N_{2}\}} \\
& \qout{\begin{array}{c}\vdots\\ \vdots\end{array}} \\
& \qout{A_{m}~\mbox{part}~1~\mbox{on}~\{N_{m - 1} + 1~\ldotp \ldotp~N_{m}\}} \\
& \qout{A_{m}~\mbox{part}~2~\mbox{on}~\{N_{m - 1} + 1~\ldotp \ldotp~N_{m}\}} \\
& \qout{\vdots} \\
& \qout{A_{m}~\mbox{part}~n_{m}~\mbox{on}~\{N_{m - 1} + 1~\ldotp \ldotp~N_{m}\}}
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qout{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{1 - 1} + 1~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} \\
& \qout{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{1 - 1} + 2~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} \\
& \qout{\vdots} \\
& \qout{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{1}~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} \\
& \qout{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{2 - 1} + 1~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} \\
& \qout{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{2 - 1} + 2~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} \\
& \qout{\vdots} \\
& \qout{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{2}~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} \\
& \qout{\begin{array}{c}\vdots\\ \vdots\end{array}} \\
& \qout{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{m - 1} + 1~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} \\
& \qout{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{m - 1} + 2~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} \\
& \qout{\vdots} \\
& \qout{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{m}~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}}
} \end{array}\right)\right)\end{array}\right]\end{array}\right]\end{array} \textrm{ if } 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	parameter: 133 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 23 operand: 7
4	Operation	operator: 64 operands: 6
5	ExprTuple	7
6	ExprTuple	133, 29
7	Lambda	parameters: 8 body: 9
8	ExprTuple	10
9	Conditional	value: 11 condition: 12
10	ExprRange	lambda_map: 13 start_index: 145 end_index: 133
11	Operation	operator: 23 operand: 16
12	Operation	operator: 51 operands: 15
13	Lambda	parameter: 142 body: 99
14	ExprTuple	16
15	ExprTuple	17
16	Lambda	parameters: 125 body: 18
17	ExprRange	lambda_map: 19 start_index: 145 end_index: 133
18	Conditional	value: 20 condition: 21
19	Lambda	parameter: 142 body: 22
20	Operation	operator: 23 operand: 27
21	Operation	operator: 51 operands: 25
22	Operation	operator: 64 operands: 26
23	Literal
24	ExprTuple	27
25	ExprTuple	28
26	ExprTuple	99, 29
27	Lambda	parameters: 30 body: 31
28	ExprRange	lambda_map: 32 start_index: 145 end_index: 133
29	Literal
30	ExprTuple	33
31	Conditional	value: 34 condition: 35
32	Lambda	parameter: 142 body: 36
33	ExprRange	lambda_map: 37 start_index: 86 end_index: 133
34	Operation	operator: 38 operands: 39
35	Operation	operator: 51 operands: 40
36	Operation	operator: 64 operands: 41
37	Lambda	parameter: 142 body: 87
38	Literal
39	ExprTuple	42, 43
40	ExprTuple	44, 45
41	ExprTuple	135, 46
42	Operation	operator: 48 operand: 55
43	Operation	operator: 48 operand: 56
44	ExprRange	lambda_map: 50 start_index: 86 end_index: 133
45	Operation	operator: 51 operands: 52
46	Operation	operator: 53 operands: 54
47	ExprTuple	55
48	Literal
49	ExprTuple	56
50	Lambda	parameter: 142 body: 57
51	Literal
52	ExprTuple	58, 59
53	Literal
54	ExprTuple	60, 61
55	ExprTuple	62
56	ExprTuple	63
57	Operation	operator: 64 operands: 65
58	Operation	operator: 79 operands: 66
59	ExprRange	lambda_map: 67 start_index: 145 end_index: 133
60	Literal
61	Operation	operator: 68 operands: 69
62	ExprRange	lambda_map: 70 start_index: 145 end_index: 133
63	ExprRange	lambda_map: 71 start_index: 145 end_index: 133
64	Literal
65	ExprTuple	87, 72
66	ExprTuple	73, 86
67	Lambda	parameter: 142 body: 74
68	Literal
69	ExprTuple	75, 99
70	Lambda	parameter: 140 body: 76
71	Lambda	parameter: 127 body: 77
72	Literal
73	IndexedVar	variable: 130 index: 86
74	Operation	operator: 79 operands: 80
75	Literal
76	ExprRange	lambda_map: 81 start_index: 145 end_index: 82
77	ExprRange	lambda_map: 83 start_index: 84 end_index: 85
78	ExprTuple	86
79	Literal
80	ExprTuple	87, 88
81	Lambda	parameter: 142 body: 89
82	IndexedVar	variable: 106 index: 140
83	Lambda	parameter: 140 body: 90
84	Operation	operator: 136 operands: 91
85	IndexedVar	variable: 130 index: 127
86	Literal
87	IndexedVar	variable: 130 index: 142
88	Operation	operator: 136 operands: 93
89	Operation	operator: 95 operands: 94
90	Operation	operator: 95 operands: 96
91	ExprTuple	97, 145
92	ExprTuple	127
93	ExprTuple	98, 99
94	NamedExprs	element: 100 targets: 101
95	Literal
96	NamedExprs	element: 102 targets: 103
97	IndexedVar	variable: 130 index: 113
98	IndexedVar	variable: 130 index: 114
99	IndexedVar	variable: 106 index: 142
100	Operation	operator: 109 operands: 107
101	Operation	operator: 111 operands: 108
102	Operation	operator: 109 operands: 110
103	Operation	operator: 111 operands: 112
104	ExprTuple	113
105	ExprTuple	114
106	Variable
107	NamedExprs	state: 115 part: 142
108	ExprTuple	116, 117
109	Literal
110	NamedExprs	state: 118 part: 140
111	Literal
112	ExprTuple	145, 119
113	Operation	operator: 136 operands: 120
114	Operation	operator: 136 operands: 121
115	IndexedVar	variable: 138 index: 140
116	Operation	operator: 136 operands: 122
117	IndexedVar	variable: 130 index: 140
118	Operation	operator: 124 operands: 125
119	IndexedVar	variable: 130 index: 133
120	ExprTuple	127, 141
121	ExprTuple	142, 141
122	ExprTuple	128, 145
123	ExprTuple	140
124	Literal
125	ExprTuple	129
126	ExprTuple	133
127	Variable
128	IndexedVar	variable: 130 index: 134
129	ExprRange	lambda_map: 132 start_index: 145 end_index: 133
130	Variable
131	ExprTuple	134
132	Lambda	parameter: 142 body: 135
133	Variable
134	Operation	operator: 136 operands: 137
135	IndexedVar	variable: 138 index: 142
136	Literal
137	ExprTuple	140, 141
138	Variable
139	ExprTuple	142
140	Variable
141	Operation	operator: 143 operand: 145
142	Variable
143	Literal
144	ExprTuple	145
145	Literal

Expression of type ExprTuple¶

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

Expression of type ExprTuple ¶

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