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 Conditional, ExprRange, ExprTuple, Lambda, Variable, VertExprArray, t
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Interval, NaturalPos, 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(Lambda(t, Conditional(Equals(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), InSet(t, NaturalPos))))

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(t \mapsto \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 \textrm{ if } t \in \mathbb{N}^+\right..\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	Lambda	parameter: 78 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 77
7	Literal
8	ExprTuple	78, 10
9	Operation	operator: 11 operand: 13
10	Literal
11	Literal
12	ExprTuple	13
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17, 18
16	ExprTuple	19, 20
17	ExprTuple	21, 22
18	ExprTuple	23, 24
19	ExprRange	lambda_map: 25 start_index: 77 end_index: 78
20	ExprRange	lambda_map: 26 start_index: 77 end_index: 79
21	ExprRange	lambda_map: 27 start_index: 77 end_index: 78
22	ExprRange	lambda_map: 27 start_index: 67 end_index: 68
23	ExprRange	lambda_map: 28 start_index: 77 end_index: 78
24	ExprRange	lambda_map: 29 start_index: 77 end_index: 79
25	Lambda	parameter: 66 body: 30
26	Lambda	parameter: 66 body: 31
27	Lambda	parameter: 66 body: 32
28	Lambda	parameter: 66 body: 33
29	Lambda	parameter: 66 body: 35
30	Operation	operator: 52 operands: 36
31	Operation	operator: 40 operands: 37
32	Operation	operator: 40 operands: 38
33	Operation	operator: 40 operands: 39
34	ExprTuple	66
35	Operation	operator: 40 operands: 41
36	NamedExprs	state: 42
37	NamedExprs	element: 43 targets: 49
38	NamedExprs	element: 44 targets: 45
39	NamedExprs	element: 46 targets: 47
40	Literal
41	NamedExprs	element: 48 targets: 49
42	Operation	operator: 50 operand: 62
43	Operation	operator: 52 operands: 59
44	Operation	operator: 53 operands: 54
45	Operation	operator: 60 operands: 55
46	Operation	operator: 58 operands: 56
47	Operation	operator: 60 operands: 57
48	Operation	operator: 58 operands: 59
49	Operation	operator: 60 operands: 61
50	Literal
51	ExprTuple	62
52	Literal
53	Literal
54	NamedExprs	operation: 63 part: 66
55	ExprTuple	77, 68
56	NamedExprs	state: 64 part: 66
57	ExprTuple	77, 78
58	Literal
59	NamedExprs	state: 65 part: 66
60	Literal
61	ExprTuple	67, 68
62	Literal
63	Operation	operator: 69 operands: 70
64	Operation	operator: 71 operand: 78
65	Literal
66	Variable
67	Operation	operator: 74 operands: 73
68	Operation	operator: 74 operands: 75
69	Literal
70	ExprTuple	76, 78
71	Literal
72	ExprTuple	78
73	ExprTuple	78, 77
74	Literal
75	ExprTuple	78, 79
76	Literal
77	Literal
78	Variable
79	Literal