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
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import I
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _psi__t_ket, _s, _t
from proveit.physics.quantum.circuits import Gate, Input, MultiQubitElem, Output, Qcircuit

# 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, _t)
sub_expr5 = MultiQubitElem(element = Input(state = TensorProd(_psi__t_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr2))
expr = ExprTuple(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr5, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr5, sub_expr3, sub_expr2).with_wrapping_at(2,6)], [ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr4), one, _t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, _s)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _Psi_ket, part = sub_expr1), targets = sub_expr4), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(sub_expr3, sub_expr2)), 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(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{1}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} & \gate{{\mathrm {FT}}^{\dag}_{t}} & \qout{\lvert \Psi \rangle} \\
\ghostqin{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\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	Operation	operator: 2 operands: 3
2	Literal
3	ExprTuple	4, 5, 6
4	ExprTuple	7, 8
5	ExprTuple	9, 10
6	ExprTuple	11, 12
7	ExprRange	lambda_map: 13 start_index: 63 end_index: 67
8	ExprRange	lambda_map: 13 start_index: 53 end_index: 54
9	ExprRange	lambda_map: 14 start_index: 63 end_index: 67
10	ExprRange	lambda_map: 15 start_index: 63 end_index: 64
11	ExprRange	lambda_map: 16 start_index: 63 end_index: 67
12	ExprRange	lambda_map: 17 start_index: 63 end_index: 64
13	Lambda	parameter: 52 body: 18
14	Lambda	parameter: 52 body: 19
15	Lambda	parameter: 52 body: 20
16	Lambda	parameter: 52 body: 21
17	Lambda	parameter: 52 body: 23
18	Operation	operator: 28 operands: 24
19	Operation	operator: 28 operands: 25
20	Operation	operator: 41 operands: 26
21	Operation	operator: 28 operands: 27
22	ExprTuple	52
23	Operation	operator: 28 operands: 29
24	NamedExprs	element: 30 targets: 31
25	NamedExprs	element: 32 targets: 35
26	NamedExprs	operation: 33
27	NamedExprs	element: 34 targets: 35
28	Literal
29	NamedExprs	element: 36 targets: 37
30	Operation	operator: 38 operands: 39
31	Operation	operator: 47 operands: 40
32	Operation	operator: 41 operands: 42
33	Literal
34	Operation	operator: 45 operands: 43
35	Operation	operator: 47 operands: 44
36	Operation	operator: 45 operands: 46
37	Operation	operator: 47 operands: 48
38	Literal
39	NamedExprs	state: 49 part: 52
40	ExprTuple	63, 54
41	Literal
42	NamedExprs	operation: 50 part: 52
43	NamedExprs	state: 51 part: 52
44	ExprTuple	63, 67
45	Literal
46	NamedExprs	state: 62 part: 52
47	Literal
48	ExprTuple	53, 54
49	Operation	operator: 55 operands: 56
50	Operation	operator: 57 operand: 67
51	Literal
52	Variable
53	Operation	operator: 59 operands: 58
54	Operation	operator: 59 operands: 60
55	Literal
56	ExprTuple	61, 62
57	Literal
58	ExprTuple	67, 63
59	Literal
60	ExprTuple	67, 64
61	Operation	operator: 65 operand: 67
62	Literal
63	Literal
64	Literal
65	Literal
66	ExprTuple	67
67	Literal