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
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import I, ket_plus
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import QPE1, _Psi_ket, _U, _ket_u, _s, _t
from proveit.physics.quantum.circuits import Gate, Input, MultiQubitElem, Output, Qcircuit
from proveit.statistics import Prob

# 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(one, _t)
sub_expr5 = Interval(sub_expr2, sub_expr3)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE1(_U, _t), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = ExprTuple(Prob(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_expr5), one, _s)], [ExprRange(sub_expr1, sub_expr6, one, _t), ExprRange(sub_expr1, sub_expr6, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr4), one, _t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, _s)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _Psi_ket, part = sub_expr1), targets = sub_expr4), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr5), one, _s)]))), one)

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(\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}_1\left(U, t\right)} & \multigate{3}{{\mathrm {FT}}^{\dag}_{t}} & \multiqout{3}{\lvert \Psi \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghost{{\mathrm {FT}}^{\dag}_{t}} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghost{{\mathrm {FT}}^{\dag}_{t}} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghost{{\mathrm {FT}}^{\dag}_{t}} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right), 1\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 81
1	Operation	operator: 2 operand: 4
2	Literal
3	ExprTuple	4
4	Operation	operator: 5 operands: 6
5	Literal
6	ExprTuple	7, 8, 9, 10
7	ExprTuple	11, 12
8	ExprTuple	13, 14
9	ExprTuple	15, 16
10	ExprTuple	17, 18
11	ExprRange	lambda_map: 19 start_index: 81 end_index: 82
12	ExprRange	lambda_map: 20 start_index: 81 end_index: 83
13	ExprRange	lambda_map: 21 start_index: 81 end_index: 82
14	ExprRange	lambda_map: 21 start_index: 71 end_index: 72
15	ExprRange	lambda_map: 22 start_index: 81 end_index: 82
16	ExprRange	lambda_map: 23 start_index: 81 end_index: 83
17	ExprRange	lambda_map: 24 start_index: 81 end_index: 82
18	ExprRange	lambda_map: 25 start_index: 81 end_index: 83
19	Lambda	parameter: 70 body: 26
20	Lambda	parameter: 70 body: 27
21	Lambda	parameter: 70 body: 28
22	Lambda	parameter: 70 body: 29
23	Lambda	parameter: 70 body: 30
24	Lambda	parameter: 70 body: 31
25	Lambda	parameter: 70 body: 33
26	Operation	operator: 54 operands: 34
27	Operation	operator: 40 operands: 35
28	Operation	operator: 40 operands: 36
29	Operation	operator: 40 operands: 37
30	Operation	operator: 57 operands: 38
31	Operation	operator: 40 operands: 39
32	ExprTuple	70
33	Operation	operator: 40 operands: 41
34	NamedExprs	state: 42
35	NamedExprs	element: 43 targets: 51
36	NamedExprs	element: 44 targets: 45
37	NamedExprs	element: 46 targets: 49
38	NamedExprs	operation: 47
39	NamedExprs	element: 48 targets: 49
40	Literal
41	NamedExprs	element: 50 targets: 51
42	Operation	operator: 52 operand: 65
43	Operation	operator: 54 operands: 62
44	Operation	operator: 57 operands: 55
45	Operation	operator: 63 operands: 56
46	Operation	operator: 57 operands: 58
47	Literal
48	Operation	operator: 61 operands: 59
49	Operation	operator: 63 operands: 60
50	Operation	operator: 61 operands: 62
51	Operation	operator: 63 operands: 64
52	Literal
53	ExprTuple	65
54	Literal
55	NamedExprs	operation: 66 part: 70
56	ExprTuple	81, 72
57	Literal
58	NamedExprs	operation: 67 part: 70
59	NamedExprs	state: 68 part: 70
60	ExprTuple	81, 82
61	Literal
62	NamedExprs	state: 69 part: 70
63	Literal
64	ExprTuple	71, 72
65	Literal
66	Operation	operator: 73 operands: 74
67	Operation	operator: 75 operand: 82
68	Literal
69	Literal
70	Variable
71	Operation	operator: 78 operands: 77
72	Operation	operator: 78 operands: 79
73	Literal
74	ExprTuple	80, 82
75	Literal
76	ExprTuple	82
77	ExprTuple	82, 81
78	Literal
79	ExprTuple	82, 83
80	Literal
81	Literal
82	Literal
83	Literal