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 QPE, QPE1, _Psi_circuit, _Psi_ket, _U, _ket_u, _s, _t
from proveit.physics.quantum.circuits import Gate, Input, MultiQubitElem, Output, 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, _t)
sub_expr5 = Interval(one, sub_expr2)
sub_expr6 = Interval(sub_expr3, sub_expr2)
sub_expr7 = MultiQubitElem(element = Gate(operation = QPE1(_U, _t), part = sub_expr1), targets = sub_expr5)
sub_expr8 = MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = sub_expr5)
sub_expr9 = [ExprRange(sub_expr1, sub_expr7, one, _t), ExprRange(sub_expr1, sub_expr7, sub_expr3, sub_expr2)]
sub_expr10 = [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)]
expr = ExprTuple(QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray(sub_expr9, sub_expr10)), Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr8, one, _t), ExprRange(sub_expr1, sub_expr8, sub_expr3, sub_expr2)]))), QcircuitEquiv(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_expr6), one, _s)], sub_expr9, sub_expr10, [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_expr6), one, _s)])), _Psi_circuit).with_wrapping_at(1))

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(\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) \cong \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), \begin{array}{c} \begin{array}{l} \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}\right) \\  \cong \left(\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) \end{array} \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	6, 7
4	Literal
5	ExprTuple	8, 9
6	Operation	operator: 13 operands: 10
7	Operation	operator: 13 operand: 18
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	15, 16
11	ExprTuple	18
12	ExprTuple	17, 15, 16, 19
13	Literal
14	ExprTuple	17, 18, 19
15	ExprTuple	20, 21
16	ExprTuple	22, 23
17	ExprTuple	24, 25
18	ExprTuple	26, 27
19	ExprTuple	28, 29
20	ExprRange	lambda_map: 30 start_index: 99 end_index: 100
21	ExprRange	lambda_map: 30 start_index: 88 end_index: 89
22	ExprRange	lambda_map: 31 start_index: 99 end_index: 100
23	ExprRange	lambda_map: 32 start_index: 99 end_index: 101
24	ExprRange	lambda_map: 33 start_index: 99 end_index: 100
25	ExprRange	lambda_map: 34 start_index: 99 end_index: 101
26	ExprRange	lambda_map: 35 start_index: 99 end_index: 100
27	ExprRange	lambda_map: 35 start_index: 88 end_index: 89
28	ExprRange	lambda_map: 36 start_index: 99 end_index: 100
29	ExprRange	lambda_map: 37 start_index: 99 end_index: 101
30	Lambda	parameter: 87 body: 38
31	Lambda	parameter: 87 body: 39
32	Lambda	parameter: 87 body: 40
33	Lambda	parameter: 87 body: 41
34	Lambda	parameter: 87 body: 42
35	Lambda	parameter: 87 body: 43
36	Lambda	parameter: 87 body: 44
37	Lambda	parameter: 87 body: 46
38	Operation	operator: 54 operands: 47
39	Operation	operator: 54 operands: 48
40	Operation	operator: 72 operands: 49
41	Operation	operator: 71 operands: 50
42	Operation	operator: 54 operands: 51
43	Operation	operator: 54 operands: 52
44	Operation	operator: 54 operands: 53
45	ExprTuple	87
46	Operation	operator: 54 operands: 55
47	NamedExprs	element: 56 targets: 62
48	NamedExprs	element: 57 targets: 64
49	NamedExprs	operation: 58
50	NamedExprs	state: 59
51	NamedExprs	element: 60 targets: 66
52	NamedExprs	element: 61 targets: 62
53	NamedExprs	element: 63 targets: 64
54	Literal
55	NamedExprs	element: 65 targets: 66
56	Operation	operator: 72 operands: 67
57	Operation	operator: 72 operands: 68
58	Literal
59	Operation	operator: 69 operand: 83
60	Operation	operator: 71 operands: 78
61	Operation	operator: 72 operands: 73
62	Operation	operator: 79 operands: 74
63	Operation	operator: 77 operands: 75
64	Operation	operator: 79 operands: 76
65	Operation	operator: 77 operands: 78
66	Operation	operator: 79 operands: 80
67	NamedExprs	operation: 81 part: 87
68	NamedExprs	operation: 82 part: 87
69	Literal
70	ExprTuple	83
71	Literal
72	Literal
73	NamedExprs	operation: 84 part: 87
74	ExprTuple	99, 89
75	NamedExprs	state: 85 part: 87
76	ExprTuple	99, 100
77	Literal
78	NamedExprs	state: 86 part: 87
79	Literal
80	ExprTuple	88, 89
81	Operation	operator: 90 operands: 94
82	Operation	operator: 91 operand: 100
83	Literal
84	Operation	operator: 93 operands: 94
85	Literal
86	Literal
87	Variable
88	Operation	operator: 96 operands: 95
89	Operation	operator: 96 operands: 97
90	Literal
91	Literal
92	ExprTuple	100
93	Literal
94	ExprTuple	98, 100
95	ExprTuple	100, 99
96	Literal
97	ExprTuple	100, 101
98	Literal
99	Literal
100	Literal
101	Literal