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Expression of type QcircuitEquiv

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, 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, QcircuitEquiv
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 = QcircuitEquiv(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}\right) \cong \left(\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
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 6
operand: 8
4Operationoperator: 6
operand: 9
5ExprTuple8
6Literal
7ExprTuple9
8ExprTuple10
9ExprTuple11
10ExprRangelambda_map: 12
start_index: 71
end_index: 59
11ExprRangelambda_map: 13
start_index: 71
end_index: 59
12Lambdaparameter: 66
body: 14
13Lambdaparameter: 53
body: 15
14ExprRangelambda_map: 16
start_index: 71
end_index: 17
15ExprRangelambda_map: 18
start_index: 19
end_index: 20
16Lambdaparameter: 68
body: 21
17IndexedVarvariable: 22
index: 66
18Lambdaparameter: 66
body: 23
19Operationoperator: 62
operands: 24
20IndexedVarvariable: 56
index: 53
21Operationoperator: 27
operands: 26
22Variable
23Operationoperator: 27
operands: 28
24ExprTuple29, 71
25ExprTuple53
26NamedExprselement: 30
targets: 31
27Literal
28NamedExprselement: 32
targets: 33
29IndexedVarvariable: 56
index: 41
30Operationoperator: 37
operands: 35
31Operationoperator: 39
operands: 36
32Operationoperator: 37
operands: 38
33Operationoperator: 39
operands: 40
34ExprTuple41
35NamedExprsstate: 42
part: 68
36ExprTuple43, 44
37Literal
38NamedExprsstate: 45
part: 66
39Literal
40ExprTuple71, 46
41Operationoperator: 62
operands: 47
42IndexedVarvariable: 64
index: 66
43Operationoperator: 62
operands: 48
44IndexedVarvariable: 56
index: 66
45Operationoperator: 50
operands: 51
46IndexedVarvariable: 56
index: 59
47ExprTuple53, 67
48ExprTuple54, 71
49ExprTuple66
50Literal
51ExprTuple55
52ExprTuple59
53Variable
54IndexedVarvariable: 56
index: 60
55ExprRangelambda_map: 58
start_index: 71
end_index: 59
56Variable
57ExprTuple60
58Lambdaparameter: 68
body: 61
59Variable
60Operationoperator: 62
operands: 63
61IndexedVarvariable: 64
index: 68
62Literal
63ExprTuple66, 67
64Variable
65ExprTuple68
66Variable
67Operationoperator: 69
operand: 71
68Variable
69Literal
70ExprTuple71
71Literal