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