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.QPE import QPE1, QPE1_U_t_circuit
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 = MultiQubitElem(element = Gate(operation = QPE1(U, t), part = sub_expr1), targets = Interval(one, sub_expr2))
expr = ExprTuple(Lambda(U, Conditional(QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr3, one, t), ExprRange(sub_expr1, sub_expr3, Add(t, one), sub_expr2)])), QPE1_U_t_circuit), 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}_1\left(U, t\right)} & { /^{t} } \qw \\
& \ghost{\textrm{QPE}_1\left(U, t\right)} & { /^{s} } \qw
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \control{} \qw \qwx[1] & \qw & \gate{\cdots} \qwx[1] & \qw & \qw \\
& \qw \qwx[1] & \control{} \qw \qwx[1] & \gate{\cdots} \qwx[1] & \qw & \qw \\
& \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} & \qw \\
& \qw \qwx[1] & \qw \qwx[1] & \gate{\cdots} \qwx[1] & \control{} \qw \qwx[1] & \qw \\
& \gate{U^{2^{t - 1}}} & \gate{U^{2^{t - 2}}} & \gate{\cdots} & \gate{U^{2^{0}}} & { /^{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: 82 body: 3
2	ExprTuple	82
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	82, 12
10	Operation	operator: 14 operand: 18
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operand: 20
13	ExprTuple	18
14	Literal
15	ExprTuple	19
16	Literal
17	ExprTuple	20
18	ExprTuple	21, 22
19	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
20	Operation	operator: 86 operands: 26
21	ExprRange	lambda_map: 27 start_index: 93 end_index: 92
22	ExprRange	lambda_map: 27 start_index: 85 end_index: 70
23	Lambda	parameter: 96 body: 28
24	Operation	operator: 88 operands: 29
25	Literal
26	ExprTuple	90, 84
27	Lambda	parameter: 75 body: 30
28	ExprTuple	31, 32
29	ExprTuple	33, 93
30	Operation	operator: 62 operands: 34
31	ExprRange	lambda_map: 35 start_index: 93 end_index: 92
32	ExprRange	lambda_map: 36 start_index: 93 end_index: 84
33	Operation	operator: 94 operand: 92
34	NamedExprs	element: 38 targets: 39
35	Lambda	parameter: 75 body: 40
36	Lambda	parameter: 75 body: 42
37	ExprTuple	92
38	Operation	operator: 65 operands: 43
39	Operation	operator: 60 operands: 44
40	Operation	operator: 45 operands: 46
41	ExprTuple	75
42	Operation	operator: 62 operands: 47
43	NamedExprs	operation: 48 part: 75
44	ExprTuple	93, 70
45	Literal
46	ExprTuple	49, 50
47	NamedExprs	element: 51 targets: 52
48	Operation	operator: 53 operands: 54
49	Conditional	value: 55 condition: 56
50	Conditional	value: 57 condition: 58
51	Operation	operator: 65 operands: 59
52	Operation	operator: 60 operands: 61
53	Literal
54	ExprTuple	82, 92
55	Operation	operator: 62 operands: 63
56	Operation	operator: 64 operands: 68
57	Operation	operator: 65 operands: 66
58	Operation	operator: 67 operands: 68
59	NamedExprs	operation: 69 part: 75
60	Literal
61	ExprTuple	85, 70
62	Literal
63	NamedExprs	element: 71 targets: 72
64	Literal
65	Literal
66	NamedExprs	operation: 73
67	Literal
68	ExprTuple	74, 75
69	Operation	operator: 76 operands: 77
70	Operation	operator: 88 operands: 78
71	Literal
72	Operation	operator: 79 operand: 85
73	Literal
74	Operation	operator: 88 operands: 81
75	Variable
76	Literal
77	ExprTuple	82, 83
78	ExprTuple	92, 84
79	Literal
80	ExprTuple	85
81	ExprTuple	96, 92
82	Variable
83	Operation	operator: 86 operands: 87
84	Variable
85	Operation	operator: 88 operands: 89
86	Literal
87	ExprTuple	90, 91
88	Literal
89	ExprTuple	92, 93
90	Literal
91	Operation	operator: 94 operand: 96
92	Variable
93	Literal
94	Literal
95	ExprTuple	96
96	Variable