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Expression of type ExprTuple

from the theory of proveit.physics.quantum.circuits

In [1]:
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, ExprRange, ExprTuple, IndexedVar, N, Variable, VertExprArray, m, n
from proveit.core_expr_types import A_1_to_m
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one, subtract
from proveit.physics.quantum.circuits import Input, MultiQubitElem, N_m, Qcircuit
In [2]:
# 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(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, ExprRange(sub_expr2, MultiQubitElem(element = Input(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 = Input(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)])))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{A_{1}~\mbox{part}~1~\mbox{on}~\{N_{1 - 1} + 1~\ldotp \ldotp~N_{1}\}} & \qw \\
\qin{A_{1}~\mbox{part}~2~\mbox{on}~\{N_{1 - 1} + 1~\ldotp \ldotp~N_{1}\}} & \qw \\
\qin{\vdots} & \qw \\
\qin{A_{1}~\mbox{part}~n_{1}~\mbox{on}~\{N_{1 - 1} + 1~\ldotp \ldotp~N_{1}\}} & \qw \\
\qin{A_{2}~\mbox{part}~1~\mbox{on}~\{N_{2 - 1} + 1~\ldotp \ldotp~N_{2}\}} & \qw \\
\qin{A_{2}~\mbox{part}~2~\mbox{on}~\{N_{2 - 1} + 1~\ldotp \ldotp~N_{2}\}} & \qw \\
\qin{\vdots} & \qw \\
\qin{A_{2}~\mbox{part}~n_{2}~\mbox{on}~\{N_{2 - 1} + 1~\ldotp \ldotp~N_{2}\}} & \qw \\
\qin{\begin{array}{c}\vdots\\ \vdots\end{array}} & \qw \\
\qin{A_{m}~\mbox{part}~1~\mbox{on}~\{N_{m - 1} + 1~\ldotp \ldotp~N_{m}\}} & \qw \\
\qin{A_{m}~\mbox{part}~2~\mbox{on}~\{N_{m - 1} + 1~\ldotp \ldotp~N_{m}\}} & \qw \\
\qin{\vdots} & \qw \\
\qin{A_{m}~\mbox{part}~n_{m}~\mbox{on}~\{N_{m - 1} + 1~\ldotp \ldotp~N_{m}\}} & \qw
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{1 - 1} + 1~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw \\
\qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{1 - 1} + 2~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw \\
\qin{\vdots} & \qw \\
\qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{1}~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw \\
\qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{2 - 1} + 1~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw \\
\qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{2 - 1} + 2~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw \\
\qin{\vdots} & \qw \\
\qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{2}~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw \\
\qin{\begin{array}{c}\vdots\\ \vdots\end{array}} & \qw \\
\qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{m - 1} + 1~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw \\
\qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{m - 1} + 2~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw \\
\qin{\vdots} & \qw \\
\qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{m}~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw
} \end{array}\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 4
operand: 6
2Operationoperator: 4
operand: 7
3ExprTuple6
4Literal
5ExprTuple7
6ExprTuple8
7ExprTuple9
8ExprRangelambda_map: 10
start_index: 69
end_index: 57
9ExprRangelambda_map: 11
start_index: 69
end_index: 57
10Lambdaparameter: 64
body: 12
11Lambdaparameter: 51
body: 13
12ExprRangelambda_map: 14
start_index: 69
end_index: 15
13ExprRangelambda_map: 16
start_index: 17
end_index: 18
14Lambdaparameter: 66
body: 19
15IndexedVarvariable: 20
index: 64
16Lambdaparameter: 64
body: 21
17Operationoperator: 60
operands: 22
18IndexedVarvariable: 54
index: 51
19Operationoperator: 25
operands: 24
20Variable
21Operationoperator: 25
operands: 26
22ExprTuple27, 69
23ExprTuple51
24NamedExprselement: 28
targets: 29
25Literal
26NamedExprselement: 30
targets: 31
27IndexedVarvariable: 54
index: 39
28Operationoperator: 35
operands: 33
29Operationoperator: 37
operands: 34
30Operationoperator: 35
operands: 36
31Operationoperator: 37
operands: 38
32ExprTuple39
33NamedExprsstate: 40
part: 66
34ExprTuple41, 42
35Literal
36NamedExprsstate: 43
part: 64
37Literal
38ExprTuple69, 44
39Operationoperator: 60
operands: 45
40IndexedVarvariable: 62
index: 64
41Operationoperator: 60
operands: 46
42IndexedVarvariable: 54
index: 64
43Operationoperator: 48
operands: 49
44IndexedVarvariable: 54
index: 57
45ExprTuple51, 65
46ExprTuple52, 69
47ExprTuple64
48Literal
49ExprTuple53
50ExprTuple57
51Variable
52IndexedVarvariable: 54
index: 58
53ExprRangelambda_map: 56
start_index: 69
end_index: 57
54Variable
55ExprTuple58
56Lambdaparameter: 66
body: 59
57Variable
58Operationoperator: 60
operands: 61
59IndexedVarvariable: 62
index: 66
60Literal
61ExprTuple64, 65
62Variable
63ExprTuple66
64Variable
65Operationoperator: 67
operand: 69
66Variable
67Literal
68ExprTuple69
69Literal