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, U, Variable, VertExprArray, s, t
from proveit.linear_algebra import Unitary
from proveit.logic import And, Forall, InSet
from proveit.numbers import Add, Exp, Interval, NaturalPos, one, two
from proveit.physics.quantum import I
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import QPE, QPE1
from proveit.physics.quantum.circuits import Gate, MultiQubitElem, Qcircuit, QcircuitEquiv

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(t, s)
sub_expr3 = Add(t, one)
sub_expr4 = Interval(one, sub_expr2)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE(U, t), part = sub_expr1), targets = sub_expr4)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE1(U, t), part = sub_expr1), targets = sub_expr4)
expr = ExprTuple(Lambda([s, t], Conditional(Forall(instance_param_or_params = [U], instance_expr = QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr5, one, t), ExprRange(sub_expr1, sub_expr5, sub_expr3, sub_expr2)])), Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr6, one, t), ExprRange(sub_expr1, sub_expr6, sub_expr3, sub_expr2)], [ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(t), part = sub_expr1), targets = Interval(one, t)), one, t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, s)]))), domain = Unitary(Exp(two, s))), And(InSet(s, NaturalPos), 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(\left(s, t\right) \mapsto \left\{\forall_{U \in \textrm{U}\left(2^{s}\right)}~\left(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \multigate{1}{\textrm{QPE}\left(U, t\right)} & { /^{t} } \qw \\
& \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \multigate{1}{\textrm{QPE}_1\left(U, t\right)} & \gate{{\mathrm {FT}}^{\dag}_{t}} & { /^{t} } \qw \\
& \ghost{\textrm{QPE}_1\left(U, t\right)} & { /^{s} } \qw & { /^{s} } \qw
} \end{array}\right)\right) \textrm{ if } s \in \mathbb{N}^+ ,  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	parameters: 2 body: 3
2	ExprTuple	88, 89
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11, 12
10	Lambda	parameter: 87 body: 14
11	Operation	operator: 22 operands: 15
12	Operation	operator: 22 operands: 16
13	ExprTuple	87
14	Conditional	value: 17 condition: 18
15	ExprTuple	88, 19
16	ExprTuple	89, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	87, 26
24	Operation	operator: 28 operand: 32
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operand: 35
27	ExprTuple	32
28	Literal
29	ExprTuple	33, 34
30	Literal
31	ExprTuple	35
32	ExprTuple	36, 37
33	ExprTuple	38, 39
34	ExprTuple	40, 41
35	Operation	operator: 42 operands: 43
36	ExprRange	lambda_map: 44 start_index: 79 end_index: 89
37	ExprRange	lambda_map: 44 start_index: 46 end_index: 76
38	ExprRange	lambda_map: 45 start_index: 79 end_index: 89
39	ExprRange	lambda_map: 45 start_index: 46 end_index: 76
40	ExprRange	lambda_map: 47 start_index: 79 end_index: 89
41	ExprRange	lambda_map: 48 start_index: 79 end_index: 88
42	Literal
43	ExprTuple	49, 88
44	Lambda	parameter: 78 body: 50
45	Lambda	parameter: 78 body: 51
46	Operation	operator: 83 operands: 52
47	Lambda	parameter: 78 body: 53
48	Lambda	parameter: 78 body: 55
49	Literal
50	Operation	operator: 58 operands: 56
51	Operation	operator: 58 operands: 57
52	ExprTuple	89, 79
53	Operation	operator: 58 operands: 59
54	ExprTuple	78
55	Operation	operator: 70 operands: 60
56	NamedExprs	element: 61 targets: 63
57	NamedExprs	element: 62 targets: 63
58	Literal
59	NamedExprs	element: 64 targets: 65
60	NamedExprs	operation: 66
61	Operation	operator: 70 operands: 67
62	Operation	operator: 70 operands: 68
63	Operation	operator: 72 operands: 69
64	Operation	operator: 70 operands: 71
65	Operation	operator: 72 operands: 73
66	Literal
67	NamedExprs	operation: 74 part: 78
68	NamedExprs	operation: 75 part: 78
69	ExprTuple	79, 76
70	Literal
71	NamedExprs	operation: 77 part: 78
72	Literal
73	ExprTuple	79, 89
74	Operation	operator: 80 operands: 82
75	Operation	operator: 81 operands: 82
76	Operation	operator: 83 operands: 84
77	Operation	operator: 85 operand: 89
78	Variable
79	Literal
80	Literal
81	Literal
82	ExprTuple	87, 89
83	Literal
84	ExprTuple	89, 88
85	Literal
86	ExprTuple	89
87	Variable
88	Variable
89	Variable