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, U, Variable, VertExprArray, m
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import Set
from proveit.numbers import Add, Exp, Interval, Mult, e, frac, i, one, pi, sqrt, two
from proveit.physics.quantum import CONTROL, ket0, ket1, ket_plus, var_ket_u, varphi
from proveit.physics.quantum.circuits import Gate, Input, MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(m, one)
sub_expr3 = Interval(two, Add(m, two))
expr = VertExprArray([Input(state = ket_plus), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = var_ket_u, part = sub_expr1), targets = sub_expr3), one, sub_expr2)], [MultiQubitElem(element = CONTROL, targets = Set(two)), ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = U, part = sub_expr1), targets = sub_expr3), one, sub_expr2)], [Output(state = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, varphi)), ket1)))), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = var_ket_u, part = sub_expr1), targets = sub_expr3), one, sub_expr2)])

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}{ccc} 
 \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert + \rangle} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{2\right\}} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array} \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{2~\ldotp \ldotp~m + 2\}} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U~\mbox{part}~1~\mbox{on}~\{2~\ldotp \ldotp~m + 2\}} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{2~\ldotp \ldotp~m + 2\}} 
} \end{array} \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{2~\ldotp \ldotp~m + 2\}} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U~\mbox{part}~2~\mbox{on}~\{2~\ldotp \ldotp~m + 2\}} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{2~\ldotp \ldotp~m + 2\}} 
} \end{array} \\
\vdots & \vdots & \vdots \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~m + 1~\mbox{on}~\{2~\ldotp \ldotp~m + 2\}} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U~\mbox{part}~m + 1~\mbox{on}~\{2~\ldotp \ldotp~m + 2\}} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~m + 1~\mbox{on}~\{2~\ldotp \ldotp~m + 2\}} 
} \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, 2, 3
1	ExprTuple	4, 5
2	ExprTuple	6, 7
3	ExprTuple	8, 9
4	Operation	operator: 41 operands: 10
5	ExprRange	lambda_map: 11 start_index: 77 end_index: 16
6	Operation	operator: 32 operands: 12
7	ExprRange	lambda_map: 13 start_index: 77 end_index: 16
8	Operation	operator: 47 operands: 14
9	ExprRange	lambda_map: 15 start_index: 77 end_index: 16
10	NamedExprs	state: 17
11	Lambda	parameter: 56 body: 18
12	NamedExprs	element: 19 targets: 20
13	Lambda	parameter: 56 body: 21
14	NamedExprs	state: 22
15	Lambda	parameter: 56 body: 24
16	Operation	operator: 62 operands: 25
17	Operation	operator: 73 operand: 34
18	Operation	operator: 32 operands: 27
19	Literal
20	Operation	operator: 28 operand: 80
21	Operation	operator: 32 operands: 30
22	Operation	operator: 60 operands: 31
23	ExprTuple	56
24	Operation	operator: 32 operands: 33
25	ExprTuple	68, 77
26	ExprTuple	34
27	NamedExprs	element: 35 targets: 40
28	Literal
29	ExprTuple	80
30	NamedExprs	element: 36 targets: 40
31	ExprTuple	37, 38
32	Literal
33	NamedExprs	element: 39 targets: 40
34	Literal
35	Operation	operator: 41 operands: 48
36	Operation	operator: 42 operands: 43
37	Operation	operator: 69 operands: 44
38	Operation	operator: 45 operands: 46
39	Operation	operator: 47 operands: 48
40	Operation	operator: 49 operands: 50
41	Literal
42	Literal
43	NamedExprs	operation: 51 part: 56
44	ExprTuple	77, 52
45	Literal
46	ExprTuple	53, 54
47	Literal
48	NamedExprs	state: 55 part: 56
49	Literal
50	ExprTuple	80, 57
51	Variable
52	Operation	operator: 71 operands: 58
53	Operation	operator: 73 operand: 65
54	Operation	operator: 60 operands: 61
55	Variable
56	Variable
57	Operation	operator: 62 operands: 63
58	ExprTuple	80, 64
59	ExprTuple	65
60	Literal
61	ExprTuple	66, 67
62	Literal
63	ExprTuple	68, 80
64	Operation	operator: 69 operands: 70
65	Literal
66	Operation	operator: 71 operands: 72
67	Operation	operator: 73 operand: 77
68	Variable
69	Literal
70	ExprTuple	77, 80
71	Literal
72	ExprTuple	75, 76
73	Literal
74	ExprTuple	77
75	Literal
76	Operation	operator: 78 operands: 79
77	Literal
78	Literal
79	ExprTuple	80, 81, 82, 83
80	Literal
81	Literal
82	Literal
83	Variable