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 A, ExprRange, IndexedVar, Variable, VertExprArray, k, l
from proveit.numbers import Interval, one
from proveit.physics.quantum import var_ket_u, var_ket_v
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 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr3 = Interval(one, l)
expr = Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Input(state = var_ket_u, part = sub_expr1), targets = sub_expr3), one, l)], ExprRange(sub_expr2, [ExprRange(sub_expr1, IndexedVar(A, [sub_expr2, sub_expr1]), one, l)], one, k), [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = var_ket_v, part = sub_expr1), targets = sub_expr3), one, l)]))

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{
\multiqin{3}{\lvert u \rangle} & \gate{A_{1, 1}} \qwx[1] & \gate{A_{2, 1}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 1}} \qwx[1] & \multiqout{3}{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{A_{1, 2}} \qwx[1] & \gate{A_{2, 2}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 2}} \qwx[1] & \ghostqout{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} \qwx[1] & \ghostqout{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{A_{1, l}} & \gate{A_{2, l}} & \gate{\cdots} & \gate{A_{k, l}} & \ghostqout{\lvert v \rangle}
} \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: 38 end_index: 8
5	ExprTuple	9
6	ExprRange	lambda_map: 10 start_index: 38 end_index: 39
7	Lambda	parameter: 35 body: 12
8	Variable
9	ExprRange	lambda_map: 13 start_index: 38 end_index: 39
10	Lambda	parameter: 37 body: 14
11	ExprTuple	35
12	ExprTuple	15
13	Lambda	parameter: 37 body: 16
14	Operation	operator: 19 operands: 17
15	ExprRange	lambda_map: 18 start_index: 38 end_index: 39
16	Operation	operator: 19 operands: 20
17	NamedExprs	element: 21 targets: 25
18	Lambda	parameter: 37 body: 23
19	Literal
20	NamedExprs	element: 24 targets: 25
21	Operation	operator: 26 operands: 27
22	ExprTuple	37
23	IndexedVar	variable: 28 indices: 29
24	Operation	operator: 30 operands: 31
25	Operation	operator: 32 operands: 33
26	Literal
27	NamedExprs	state: 34 part: 37
28	Variable
29	ExprTuple	35, 37
30	Literal
31	NamedExprs	state: 36 part: 37
32	Literal
33	ExprTuple	38, 39
34	Variable
35	Variable
36	Variable
37	Variable
38	Literal
39	Variable