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, Variable, VertExprArray, a, b, k
from proveit.core_expr_types import U_1_to_m
from proveit.numbers import Interval, one
from proveit.physics.quantum.circuits import Input, MultiQubitElem, Output, Qcircuit

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Interval(one, k)
expr = Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Input(state = a, part = sub_expr1), targets = sub_expr2), one, k)], U_1_to_m, [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = b, part = sub_expr1), targets = sub_expr2), one, k)]))

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} & \gate{\begin{array}{c} \uparrow \\U_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\U_{2} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\U_{m} \\ \downarrow\end{array}} & \qout{b}
} \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 operands: 2
1	Literal
2	ExprTuple	3, 4, 5
3	ExprTuple	6
4	ExprRange	lambda_map: 7 start_index: 32 end_index: 8
5	ExprTuple	9
6	ExprRange	lambda_map: 10 start_index: 32 end_index: 33
7	Lambda	parameter: 31 body: 11
8	Variable
9	ExprRange	lambda_map: 12 start_index: 32 end_index: 33
10	Lambda	parameter: 31 body: 13
11	IndexedVar	variable: 14 index: 31
12	Lambda	parameter: 31 body: 16
13	Operation	operator: 18 operands: 17
14	Variable
15	ExprTuple	31
16	Operation	operator: 18 operands: 19
17	NamedExprs	element: 20 targets: 22
18	Literal
19	NamedExprs	element: 21 targets: 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	Operation	operator: 27 operands: 28
23	Literal
24	NamedExprs	state: 29 part: 31
25	Literal
26	NamedExprs	state: 30 part: 31
27	Literal
28	ExprTuple	32, 33
29	Variable
30	Variable
31	Variable
32	Literal
33	Variable