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, U, Variable, VertExprArray, s, t
from proveit.numbers import Add, Interval, Mult, one
from proveit.physics.quantum import I, NumKet, Z, ket_plus, var_ket_u
from proveit.physics.quantum.QPE import QPE, phase, two_pow_t
from proveit.physics.quantum.circuits import Gate, 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 = Add(t, one)
sub_expr3 = Add(t, s)
sub_expr4 = Interval(sub_expr2, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE(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 = var_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, Measure(basis = Z), one, t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, s)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(Mult(two_pow_t, phase), t), part = sub_expr1), targets = Interval(one, t)), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = var_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}\left(U, t\right)} & \meter & \multiqout{3}{\lvert 2^{t} \cdot \varphi \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert 2^{t} \cdot \varphi \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert 2^{t} \cdot \varphi \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert 2^{t} \cdot \varphi \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\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: 90
12	ExprRange	lambda_map: 20 start_index: 81 end_index: 82
13	ExprRange	lambda_map: 21 start_index: 81 end_index: 90
14	ExprRange	lambda_map: 21 start_index: 70 end_index: 71
15	ExprRange	lambda_map: 22 start_index: 81 end_index: 90
16	ExprRange	lambda_map: 23 start_index: 81 end_index: 82
17	ExprRange	lambda_map: 24 start_index: 81 end_index: 90
18	ExprRange	lambda_map: 25 start_index: 81 end_index: 82
19	Lambda	parameter: 69 body: 26
20	Lambda	parameter: 69 body: 27
21	Lambda	parameter: 69 body: 28
22	Lambda	parameter: 69 body: 29
23	Lambda	parameter: 69 body: 30
24	Lambda	parameter: 69 body: 31
25	Lambda	parameter: 69 body: 33
26	Operation	operator: 55 operands: 34
27	Operation	operator: 41 operands: 35
28	Operation	operator: 41 operands: 36
29	Operation	operator: 37 operands: 38
30	Operation	operator: 56 operands: 39
31	Operation	operator: 41 operands: 40
32	ExprTuple	69
33	Operation	operator: 41 operands: 42
34	NamedExprs	state: 43
35	NamedExprs	element: 44 targets: 52
36	NamedExprs	element: 45 targets: 46
37	Literal
38	NamedExprs	basis: 47
39	NamedExprs	operation: 48
40	NamedExprs	element: 49 targets: 50
41	Literal
42	NamedExprs	element: 51 targets: 52
43	Operation	operator: 53 operand: 65
44	Operation	operator: 55 operands: 62
45	Operation	operator: 56 operands: 57
46	Operation	operator: 63 operands: 58
47	Literal
48	Literal
49	Operation	operator: 61 operands: 59
50	Operation	operator: 63 operands: 60
51	Operation	operator: 61 operands: 62
52	Operation	operator: 63 operands: 64
53	Literal
54	ExprTuple	65
55	Literal
56	Literal
57	NamedExprs	operation: 66 part: 69
58	ExprTuple	81, 71
59	NamedExprs	state: 67 part: 69
60	ExprTuple	81, 90
61	Literal
62	NamedExprs	state: 68 part: 69
63	Literal
64	ExprTuple	70, 71
65	Literal
66	Operation	operator: 72 operands: 73
67	Operation	operator: 74 operands: 75
68	Variable
69	Variable
70	Operation	operator: 77 operands: 76
71	Operation	operator: 77 operands: 78
72	Literal
73	ExprTuple	79, 90
74	Literal
75	ExprTuple	80, 90
76	ExprTuple	90, 81
77	Literal
78	ExprTuple	90, 82
79	Variable
80	Operation	operator: 83 operands: 84
81	Literal
82	Variable
83	Literal
84	ExprTuple	85, 86
85	Operation	operator: 87 operands: 88
86	Variable
87	Literal
88	ExprTuple	89, 90
89	Literal
90	Variable