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.numbers import Add, Interval, one
from proveit.physics.quantum import I, ket_plus
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import QPE1, _Psi_circuit, _Psi_ket, _U, _ket_u, _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, one)
sub_expr3 = Add(_t, _s)
sub_expr4 = Interval(one, _t)
sub_expr5 = Interval(sub_expr2, sub_expr3)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE1(_U, _t), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = ExprTuple(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Input(state = ket_plus), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr5), one, _s)], [ExprRange(sub_expr1, sub_expr6, one, _t), ExprRange(sub_expr1, sub_expr6, sub_expr2, sub_expr3)], [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 = sub_expr5), one, _s)])), _Psi_circuit)

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{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}_1\left(U, t\right)} & \multigate{3}{{\mathrm {FT}}^{\dag}_{t}} & \multiqout{3}{\lvert \Psi \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghost{{\mathrm {FT}}^{\dag}_{t}} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghost{{\mathrm {FT}}^{\dag}_{t}} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghost{{\mathrm {FT}}^{\dag}_{t}} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \multiqout{3}{\lvert \Psi \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \qout{\lvert u \rangle}
} \end{array}\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, 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	8, 6, 7, 10
4	Literal
5	ExprTuple	8, 9, 10
6	ExprTuple	11, 12
7	ExprTuple	13, 14
8	ExprTuple	15, 16
9	ExprTuple	17, 18
10	ExprTuple	19, 20
11	ExprRange	lambda_map: 21 start_index: 90 end_index: 91
12	ExprRange	lambda_map: 21 start_index: 79 end_index: 80
13	ExprRange	lambda_map: 22 start_index: 90 end_index: 91
14	ExprRange	lambda_map: 23 start_index: 90 end_index: 92
15	ExprRange	lambda_map: 24 start_index: 90 end_index: 91
16	ExprRange	lambda_map: 25 start_index: 90 end_index: 92
17	ExprRange	lambda_map: 26 start_index: 90 end_index: 91
18	ExprRange	lambda_map: 26 start_index: 79 end_index: 80
19	ExprRange	lambda_map: 27 start_index: 90 end_index: 91
20	ExprRange	lambda_map: 28 start_index: 90 end_index: 92
21	Lambda	parameter: 78 body: 29
22	Lambda	parameter: 78 body: 30
23	Lambda	parameter: 78 body: 31
24	Lambda	parameter: 78 body: 32
25	Lambda	parameter: 78 body: 33
26	Lambda	parameter: 78 body: 34
27	Lambda	parameter: 78 body: 35
28	Lambda	parameter: 78 body: 37
29	Operation	operator: 45 operands: 38
30	Operation	operator: 45 operands: 39
31	Operation	operator: 63 operands: 40
32	Operation	operator: 62 operands: 41
33	Operation	operator: 45 operands: 42
34	Operation	operator: 45 operands: 43
35	Operation	operator: 45 operands: 44
36	ExprTuple	78
37	Operation	operator: 45 operands: 46
38	NamedExprs	element: 47 targets: 53
39	NamedExprs	element: 48 targets: 55
40	NamedExprs	operation: 49
41	NamedExprs	state: 50
42	NamedExprs	element: 51 targets: 57
43	NamedExprs	element: 52 targets: 53
44	NamedExprs	element: 54 targets: 55
45	Literal
46	NamedExprs	element: 56 targets: 57
47	Operation	operator: 63 operands: 58
48	Operation	operator: 63 operands: 59
49	Literal
50	Operation	operator: 60 operand: 74
51	Operation	operator: 62 operands: 69
52	Operation	operator: 63 operands: 64
53	Operation	operator: 70 operands: 65
54	Operation	operator: 68 operands: 66
55	Operation	operator: 70 operands: 67
56	Operation	operator: 68 operands: 69
57	Operation	operator: 70 operands: 71
58	NamedExprs	operation: 72 part: 78
59	NamedExprs	operation: 73 part: 78
60	Literal
61	ExprTuple	74
62	Literal
63	Literal
64	NamedExprs	operation: 75 part: 78
65	ExprTuple	90, 80
66	NamedExprs	state: 76 part: 78
67	ExprTuple	90, 91
68	Literal
69	NamedExprs	state: 77 part: 78
70	Literal
71	ExprTuple	79, 80
72	Operation	operator: 81 operands: 85
73	Operation	operator: 82 operand: 91
74	Literal
75	Operation	operator: 84 operands: 85
76	Literal
77	Literal
78	Variable
79	Operation	operator: 87 operands: 86
80	Operation	operator: 87 operands: 88
81	Literal
82	Literal
83	ExprTuple	91
84	Literal
85	ExprTuple	89, 91
86	ExprTuple	91, 90
87	Literal
88	ExprTuple	91, 92
89	Literal
90	Literal
91	Literal
92	Literal