Expression of type VertExprArray

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 ExprRange, IndexedVar, N, Variable, VertExprArray, m
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

# build up the expression from sub-expressions
sub_expr1 = Variable("_c", latex_format = r"{_{-}c}")
sub_expr2 = Variable("_b", latex_format = r"{_{-}b}")
expr = VertExprArray([ExprRange(sub_expr1, ExprRange(sub_expr2, MultiQubitElem(element = Input(state = TensorProd(A_1_to_m), part = sub_expr2), targets = Interval(one, N_m)), Add(IndexedVar(N, subtract(sub_expr1, one)), one), IndexedVar(N, sub_expr1)).with_wrapping_at(2,6), one, m)])

expr:

# 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())

\begin{array}{c} 
 \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 
} \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} + 2~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw 
} \end{array} \\
\vdots \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{1}~\mbox{on}~\{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_{2 - 1} + 1~\mbox{on}~\{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_{2 - 1} + 2~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw 
} \end{array} \\
\vdots \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{2}~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw 
} \end{array} \\
\begin{array}{c}\vdots\\ \vdots\end{array} \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \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 
} \end{array} \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \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 
} \end{array} \\
\vdots \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \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} \\
\end{array}

stored_expr.style_options()

name	description	default	current value	related methods
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	with_justification

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	ExprTuple	2
2	ExprRange	lambda_map: 3 start_index: 39 end_index: 38
3	Lambda	parameter: 32 body: 4
4	ExprRange	lambda_map: 5 start_index: 6 end_index: 7
5	Lambda	parameter: 24 body: 9
6	Operation	operator: 26 operands: 10
7	IndexedVar	variable: 30 index: 32
8	ExprTuple	24
9	Operation	operator: 12 operands: 13
10	ExprTuple	14, 39
11	ExprTuple	32
12	Literal
13	NamedExprs	element: 15 targets: 16
14	IndexedVar	variable: 30 index: 22
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	ExprTuple	22
18	Literal
19	NamedExprs	state: 23 part: 24
20	Literal
21	ExprTuple	39, 25
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operands: 29
24	Variable
25	IndexedVar	variable: 30 index: 38
26	Literal
27	ExprTuple	32, 33
28	Literal
29	ExprTuple	34
30	Variable
31	ExprTuple	38
32	Variable
33	Operation	operator: 35 operand: 39
34	ExprRange	lambda_map: 37 start_index: 39 end_index: 38
35	Literal
36	ExprTuple	39
37	Lambda	parameter: 43 body: 40
38	Variable
39	Literal
40	IndexedVar	variable: 41 index: 43
41	Variable
42	ExprTuple	43
43	Variable