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, m
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import I, var_ket_psi, var_ket_u, var_ket_v
from proveit.physics.quantum.circuits import Gate, 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, m)
sub_expr4 = Interval(Add(m, one), Add(m, l))
expr = Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Input(state = var_ket_psi, part = sub_expr1), targets = sub_expr3), one, m), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = var_ket_u, part = sub_expr1), targets = sub_expr4), one, l)], ExprRange(sub_expr2, [ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, m), ExprRange(sub_expr1, IndexedVar(A, [sub_expr2, sub_expr1]), one, l)], one, k), [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = var_ket_psi, part = sub_expr1), targets = sub_expr3), one, m), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = var_ket_v, part = sub_expr1), targets = sub_expr4), 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{
\qin{\lvert \psi \rangle} & { /^{m} } \qw & { /^{m} } \qw & \gate{\cdots} & { /^{m} } \qw & \qout{\lvert \psi \rangle} \\
\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, 7
4	ExprRange	lambda_map: 8 start_index: 63 end_index: 9
5	ExprTuple	10, 11
6	ExprRange	lambda_map: 12 start_index: 63 end_index: 64
7	ExprRange	lambda_map: 13 start_index: 63 end_index: 65
8	Lambda	parameter: 54 body: 15
9	Variable
10	ExprRange	lambda_map: 16 start_index: 63 end_index: 64
11	ExprRange	lambda_map: 17 start_index: 63 end_index: 65
12	Lambda	parameter: 57 body: 18
13	Lambda	parameter: 57 body: 19
14	ExprTuple	54
15	ExprTuple	20, 21
16	Lambda	parameter: 57 body: 22
17	Lambda	parameter: 57 body: 23
18	Operation	operator: 29 operands: 24
19	Operation	operator: 29 operands: 25
20	ExprRange	lambda_map: 26 start_index: 63 end_index: 64
21	ExprRange	lambda_map: 27 start_index: 63 end_index: 65
22	Operation	operator: 29 operands: 28
23	Operation	operator: 29 operands: 30
24	NamedExprs	element: 31 targets: 37
25	NamedExprs	element: 32 targets: 39
26	Lambda	parameter: 57 body: 33
27	Lambda	parameter: 57 body: 35
28	NamedExprs	element: 36 targets: 37
29	Literal
30	NamedExprs	element: 38 targets: 39
31	Operation	operator: 40 operands: 46
32	Operation	operator: 40 operands: 41
33	Operation	operator: 42 operands: 43
34	ExprTuple	57
35	IndexedVar	variable: 44 indices: 45
36	Operation	operator: 48 operands: 46
37	Operation	operator: 50 operands: 47
38	Operation	operator: 48 operands: 49
39	Operation	operator: 50 operands: 51
40	Literal
41	NamedExprs	state: 52 part: 57
42	Literal
43	NamedExprs	operation: 53
44	Variable
45	ExprTuple	54, 57
46	NamedExprs	state: 55 part: 57
47	ExprTuple	63, 64
48	Literal
49	NamedExprs	state: 56 part: 57
50	Literal
51	ExprTuple	58, 59
52	Variable
53	Literal
54	Variable
55	Variable
56	Variable
57	Variable
58	Operation	operator: 61 operands: 60
59	Operation	operator: 61 operands: 62
60	ExprTuple	64, 63
61	Literal
62	ExprTuple	64, 65
63	Literal
64	Variable
65	Variable