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, m
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _s, _s_wire, _t
from proveit.physics.quantum.circuits import Input, Measure, 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 = Interval(one, _t)
sub_expr3 = ExprRange(sub_expr1, Measure(basis = Z), one, _t)
sub_expr4 = Interval(Add(_t, one), Add(_t, _s))
sub_expr5 = ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _Psi_ket, part = sub_expr1), targets = sub_expr2), one, _t)
sub_expr6 = ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = sub_expr2), one, _t)
expr = ExprTuple(Prob(Qcircuit(vert_expr_array = VertExprArray([sub_expr5], [sub_expr3], [sub_expr6]))), Prob(Qcircuit(vert_expr_array = VertExprArray([sub_expr5, ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)], [sub_expr3, _s_wire], [sub_expr6, 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(\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert \Psi \rangle} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}}
} \end{array}\right), \textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert \Psi \rangle} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert u \rangle} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right)\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, 2
1	Operation	operator: 4 operand: 6
2	Operation	operator: 4 operand: 7
3	ExprTuple	6
4	Literal
5	ExprTuple	7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12, 13
9	Literal
10	ExprTuple	14, 15, 16
11	ExprTuple	17
12	ExprTuple	19
13	ExprTuple	21
14	ExprTuple	17, 18
15	ExprTuple	19, 20
16	ExprTuple	21, 22
17	ExprRange	lambda_map: 23 start_index: 73 end_index: 74
18	ExprRange	lambda_map: 24 start_index: 73 end_index: 75
19	ExprRange	lambda_map: 25 start_index: 73 end_index: 74
20	ExprRange	lambda_map: 26 start_index: 73 end_index: 75
21	ExprRange	lambda_map: 27 start_index: 73 end_index: 74
22	ExprRange	lambda_map: 28 start_index: 73 end_index: 75
23	Lambda	parameter: 64 body: 29
24	Lambda	parameter: 64 body: 30
25	Lambda	parameter: 64 body: 31
26	Lambda	parameter: 64 body: 32
27	Lambda	parameter: 64 body: 33
28	Lambda	parameter: 64 body: 35
29	Operation	operator: 43 operands: 36
30	Operation	operator: 43 operands: 37
31	Operation	operator: 38 operands: 39
32	Operation	operator: 40 operands: 41
33	Operation	operator: 43 operands: 42
34	ExprTuple	64
35	Operation	operator: 43 operands: 44
36	NamedExprs	element: 45 targets: 50
37	NamedExprs	element: 46 targets: 52
38	Literal
39	NamedExprs	basis: 47
40	Literal
41	NamedExprs	operation: 48
42	NamedExprs	element: 49 targets: 50
43	Literal
44	NamedExprs	element: 51 targets: 52
45	Operation	operator: 54 operands: 53
46	Operation	operator: 54 operands: 58
47	Literal
48	Literal
49	Operation	operator: 57 operands: 55
50	Operation	operator: 59 operands: 56
51	Operation	operator: 57 operands: 58
52	Operation	operator: 59 operands: 60
53	NamedExprs	state: 61 part: 64
54	Literal
55	NamedExprs	state: 62 part: 64
56	ExprTuple	73, 74
57	Literal
58	NamedExprs	state: 63 part: 64
59	Literal
60	ExprTuple	65, 66
61	Literal
62	Operation	operator: 67 operands: 68
63	Literal
64	Variable
65	Operation	operator: 70 operands: 69
66	Operation	operator: 70 operands: 71
67	Literal
68	ExprTuple	72, 74
69	ExprTuple	74, 73
70	Literal
71	ExprTuple	74, 75
72	Variable
73	Literal
74	Literal
75	Literal