Expression of type Qcircuit

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, Qcircuit

# build up the expression from sub-expressions
sub_expr1 = Variable("_c", latex_format = r"{_{-}c}")
sub_expr2 = Variable("_b", latex_format = r"{_{-}b}")
expr = Qcircuit(vert_expr_array = 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} \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}

stored_expr.style_options()

name	description	default	current value	related methods
spacing	change the spacing of a circuit using the format '@C=1em @R=.7em' where C is the column spacing and R is the row spacing	@C=1em @R=.7em	@C=1em @R=.7em

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	ExprTuple	4
4	ExprRange	lambda_map: 5 start_index: 41 end_index: 40
5	Lambda	parameter: 34 body: 6
6	ExprRange	lambda_map: 7 start_index: 8 end_index: 9
7	Lambda	parameter: 26 body: 11
8	Operation	operator: 28 operands: 12
9	IndexedVar	variable: 32 index: 34
10	ExprTuple	26
11	Operation	operator: 14 operands: 15
12	ExprTuple	16, 41
13	ExprTuple	34
14	Literal
15	NamedExprs	element: 17 targets: 18
16	IndexedVar	variable: 32 index: 24
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprTuple	24
20	Literal
21	NamedExprs	state: 25 part: 26
22	Literal
23	ExprTuple	41, 27
24	Operation	operator: 28 operands: 29
25	Operation	operator: 30 operands: 31
26	Variable
27	IndexedVar	variable: 32 index: 40
28	Literal
29	ExprTuple	34, 35
30	Literal
31	ExprTuple	36
32	Variable
33	ExprTuple	40
34	Variable
35	Operation	operator: 37 operand: 41
36	ExprRange	lambda_map: 39 start_index: 41 end_index: 40
37	Literal
38	ExprTuple	41
39	Lambda	parameter: 45 body: 42
40	Variable
41	Literal
42	IndexedVar	variable: 43 index: 45
43	Variable
44	ExprTuple	45
45	Variable