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
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(sub_expr2, sub_expr3)
sub_expr5 = 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_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)]))), 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)} & \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), 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, 68
1	Operation	operator: 2 operand: 4
2	Literal
3	ExprTuple	4
4	Operation	operator: 5 operands: 6
5	Literal
6	ExprTuple	7, 8, 9
7	ExprTuple	10, 11
8	ExprTuple	12, 13
9	ExprTuple	14, 15
10	ExprRange	lambda_map: 16 start_index: 68 end_index: 69
11	ExprRange	lambda_map: 17 start_index: 68 end_index: 70
12	ExprRange	lambda_map: 18 start_index: 68 end_index: 69
13	ExprRange	lambda_map: 18 start_index: 58 end_index: 59
14	ExprRange	lambda_map: 19 start_index: 68 end_index: 69
15	ExprRange	lambda_map: 20 start_index: 68 end_index: 70
16	Lambda	parameter: 57 body: 21
17	Lambda	parameter: 57 body: 22
18	Lambda	parameter: 57 body: 23
19	Lambda	parameter: 57 body: 24
20	Lambda	parameter: 57 body: 26
21	Operation	operator: 43 operands: 27
22	Operation	operator: 31 operands: 28
23	Operation	operator: 31 operands: 29
24	Operation	operator: 31 operands: 30
25	ExprTuple	57
26	Operation	operator: 31 operands: 32
27	NamedExprs	state: 33
28	NamedExprs	element: 34 targets: 40
29	NamedExprs	element: 35 targets: 36
30	NamedExprs	element: 37 targets: 38
31	Literal
32	NamedExprs	element: 39 targets: 40
33	Operation	operator: 41 operand: 53
34	Operation	operator: 43 operands: 50
35	Operation	operator: 44 operands: 45
36	Operation	operator: 51 operands: 46
37	Operation	operator: 49 operands: 47
38	Operation	operator: 51 operands: 48
39	Operation	operator: 49 operands: 50
40	Operation	operator: 51 operands: 52
41	Literal
42	ExprTuple	53
43	Literal
44	Literal
45	NamedExprs	operation: 54 part: 57
46	ExprTuple	68, 59
47	NamedExprs	state: 55 part: 57
48	ExprTuple	68, 69
49	Literal
50	NamedExprs	state: 56 part: 57
51	Literal
52	ExprTuple	58, 59
53	Literal
54	Operation	operator: 60 operands: 61
55	Operation	operator: 62 operand: 69
56	Literal
57	Variable
58	Operation	operator: 65 operands: 64
59	Operation	operator: 65 operands: 66
60	Literal
61	ExprTuple	67, 69
62	Literal
63	ExprTuple	69
64	ExprTuple	69, 68
65	Literal
66	ExprTuple	69, 70
67	Literal
68	Literal
69	Variable
70	Literal