Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

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, ExprTuple, Variable, VertExprArray, t
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import ket_plus
from proveit.physics.quantum.QPE import QPE1, _U, _ket_u, _psi_t_ket, _s
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 = Add(t, one)
sub_expr3 = Add(t, _s)
sub_expr4 = Interval(sub_expr2, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE1(_U, t), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = ExprTuple(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Input(state = ket_plus), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)], [ExprRange(sub_expr1, sub_expr5, one, t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _psi_t_ket, part = sub_expr1), targets = Interval(one, t)), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)])))

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())

\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}_1\left(U, t\right)} & \multiqout{3}{\lvert \psi_{t} \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \qout{\lvert u \rangle}
} \end{array}\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Operation	operator: 2 operands: 3
2	Literal
3	ExprTuple	4, 5, 6
4	ExprTuple	7, 8
5	ExprTuple	9, 10
6	ExprTuple	11, 12
7	ExprRange	lambda_map: 13 start_index: 65 end_index: 66
8	ExprRange	lambda_map: 14 start_index: 65 end_index: 67
9	ExprRange	lambda_map: 15 start_index: 65 end_index: 66
10	ExprRange	lambda_map: 15 start_index: 55 end_index: 56
11	ExprRange	lambda_map: 16 start_index: 65 end_index: 66
12	ExprRange	lambda_map: 17 start_index: 65 end_index: 67
13	Lambda	parameter: 54 body: 18
14	Lambda	parameter: 54 body: 19
15	Lambda	parameter: 54 body: 20
16	Lambda	parameter: 54 body: 21
17	Lambda	parameter: 54 body: 23
18	Operation	operator: 40 operands: 24
19	Operation	operator: 28 operands: 25
20	Operation	operator: 28 operands: 26
21	Operation	operator: 28 operands: 27
22	ExprTuple	54
23	Operation	operator: 28 operands: 29
24	NamedExprs	state: 30
25	NamedExprs	element: 31 targets: 37
26	NamedExprs	element: 32 targets: 33
27	NamedExprs	element: 34 targets: 35
28	Literal
29	NamedExprs	element: 36 targets: 37
30	Operation	operator: 38 operand: 50
31	Operation	operator: 40 operands: 47
32	Operation	operator: 41 operands: 42
33	Operation	operator: 48 operands: 43
34	Operation	operator: 46 operands: 44
35	Operation	operator: 48 operands: 45
36	Operation	operator: 46 operands: 47
37	Operation	operator: 48 operands: 49
38	Literal
39	ExprTuple	50
40	Literal
41	Literal
42	NamedExprs	operation: 51 part: 54
43	ExprTuple	65, 56
44	NamedExprs	state: 52 part: 54
45	ExprTuple	65, 66
46	Literal
47	NamedExprs	state: 53 part: 54
48	Literal
49	ExprTuple	55, 56
50	Literal
51	Operation	operator: 57 operands: 58
52	Operation	operator: 59 operand: 66
53	Literal
54	Variable
55	Operation	operator: 62 operands: 61
56	Operation	operator: 62 operands: 63
57	Literal
58	ExprTuple	64, 66
59	Literal
60	ExprTuple	66
61	ExprTuple	66, 65
62	Literal
63	ExprTuple	66, 67
64	Literal
65	Literal
66	Variable
67	Literal