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, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Interval, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1, ket_plus
from proveit.physics.quantum.QPE import QPE1, _U, _ket_u, _phase, _s
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(sub_expr2, sub_expr3)
sub_expr5 = 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_expr4), one, _s)], [ExprRange(sub_expr1, sub_expr5, one, t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, Output(state = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))), Add(Neg(t), one), zero).with_decreasing_order(), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr4), 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{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}_1\left(U, t\right)} & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 1} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 2} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \qout{\vdots} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \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: 86 end_index: 69
8	ExprRange	lambda_map: 14 start_index: 86 end_index: 70
9	ExprRange	lambda_map: 15 start_index: 86 end_index: 69
10	ExprRange	lambda_map: 15 start_index: 55 end_index: 56
11	ExprRange	lambda_map: 16 start_index: 17 end_index: 76
12	ExprRange	lambda_map: 18 start_index: 86 end_index: 70
13	Lambda	parameter: 99 body: 19
14	Lambda	parameter: 99 body: 20
15	Lambda	parameter: 99 body: 21
16	Lambda	parameter: 99 body: 22
17	Operation	operator: 63 operands: 23
18	Lambda	parameter: 99 body: 24
19	Operation	operator: 41 operands: 25
20	Operation	operator: 30 operands: 26
21	Operation	operator: 30 operands: 27
22	Operation	operator: 46 operands: 28
23	ExprTuple	29, 86
24	Operation	operator: 30 operands: 31
25	NamedExprs	state: 32
26	NamedExprs	element: 33 targets: 39
27	NamedExprs	element: 34 targets: 35
28	NamedExprs	state: 36
29	Operation	operator: 97 operand: 69
30	Literal
31	NamedExprs	element: 38 targets: 39
32	Operation	operator: 82 operand: 50
33	Operation	operator: 41 operands: 47
34	Operation	operator: 42 operands: 43
35	Operation	operator: 48 operands: 44
36	Operation	operator: 73 operands: 45
37	ExprTuple	69
38	Operation	operator: 46 operands: 47
39	Operation	operator: 48 operands: 49
40	ExprTuple	50
41	Literal
42	Literal
43	NamedExprs	operation: 51 part: 99
44	ExprTuple	86, 56
45	ExprTuple	52, 53
46	Literal
47	NamedExprs	state: 54 part: 99
48	Literal
49	ExprTuple	55, 56
50	Literal
51	Operation	operator: 57 operands: 58
52	Operation	operator: 79 operands: 59
53	Operation	operator: 60 operands: 61
54	Literal
55	Operation	operator: 63 operands: 62
56	Operation	operator: 63 operands: 64
57	Literal
58	ExprTuple	65, 69
59	ExprTuple	86, 66
60	Literal
61	ExprTuple	67, 68
62	ExprTuple	69, 86
63	Literal
64	ExprTuple	69, 70
65	Literal
66	Operation	operator: 93 operands: 71
67	Operation	operator: 82 operand: 76
68	Operation	operator: 73 operands: 74
69	Variable
70	Literal
71	ExprTuple	95, 75
72	ExprTuple	76
73	Literal
74	ExprTuple	77, 78
75	Operation	operator: 79 operands: 80
76	Literal
77	Operation	operator: 93 operands: 81
78	Operation	operator: 82 operand: 86
79	Literal
80	ExprTuple	86, 95
81	ExprTuple	84, 85
82	Literal
83	ExprTuple	86
84	Literal
85	Operation	operator: 87 operands: 88
86	Literal
87	Literal
88	ExprTuple	95, 89, 90, 91, 92
89	Literal
90	Literal
91	Operation	operator: 93 operands: 94
92	Literal
93	Literal
94	ExprTuple	95, 96
95	Literal
96	Operation	operator: 97 operand: 99
97	Literal
98	ExprTuple	99
99	Variable