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, U, Variable, VertExprArray, s, t
from proveit.numbers import Add, Interval, Mult, one
from proveit.physics.quantum import I, NumKet, Z, ket_plus, var_ket_u
from proveit.physics.quantum.QPE import QPE, phase, two_pow_t
from proveit.physics.quantum.circuits import Gate, Input, Measure, 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 = QPE(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 = var_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, Measure(basis = Z), one, t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, s)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(Mult(two_pow_t, phase), t), part = sub_expr1), targets = Interval(one, t)), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = var_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}\left(U, t\right)} & \meter & \multiqout{3}{\lvert 2^{t} \cdot \varphi \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert 2^{t} \cdot \varphi \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert 2^{t} \cdot \varphi \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert 2^{t} \cdot \varphi \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{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, 7
4	ExprTuple	8, 9
5	ExprTuple	10, 11
6	ExprTuple	12, 13
7	ExprTuple	14, 15
8	ExprRange	lambda_map: 16 start_index: 78 end_index: 87
9	ExprRange	lambda_map: 17 start_index: 78 end_index: 79
10	ExprRange	lambda_map: 18 start_index: 78 end_index: 87
11	ExprRange	lambda_map: 18 start_index: 67 end_index: 68
12	ExprRange	lambda_map: 19 start_index: 78 end_index: 87
13	ExprRange	lambda_map: 20 start_index: 78 end_index: 79
14	ExprRange	lambda_map: 21 start_index: 78 end_index: 87
15	ExprRange	lambda_map: 22 start_index: 78 end_index: 79
16	Lambda	parameter: 66 body: 23
17	Lambda	parameter: 66 body: 24
18	Lambda	parameter: 66 body: 25
19	Lambda	parameter: 66 body: 26
20	Lambda	parameter: 66 body: 27
21	Lambda	parameter: 66 body: 28
22	Lambda	parameter: 66 body: 30
23	Operation	operator: 52 operands: 31
24	Operation	operator: 38 operands: 32
25	Operation	operator: 38 operands: 33
26	Operation	operator: 34 operands: 35
27	Operation	operator: 53 operands: 36
28	Operation	operator: 38 operands: 37
29	ExprTuple	66
30	Operation	operator: 38 operands: 39
31	NamedExprs	state: 40
32	NamedExprs	element: 41 targets: 49
33	NamedExprs	element: 42 targets: 43
34	Literal
35	NamedExprs	basis: 44
36	NamedExprs	operation: 45
37	NamedExprs	element: 46 targets: 47
38	Literal
39	NamedExprs	element: 48 targets: 49
40	Operation	operator: 50 operand: 62
41	Operation	operator: 52 operands: 59
42	Operation	operator: 53 operands: 54
43	Operation	operator: 60 operands: 55
44	Literal
45	Literal
46	Operation	operator: 58 operands: 56
47	Operation	operator: 60 operands: 57
48	Operation	operator: 58 operands: 59
49	Operation	operator: 60 operands: 61
50	Literal
51	ExprTuple	62
52	Literal
53	Literal
54	NamedExprs	operation: 63 part: 66
55	ExprTuple	78, 68
56	NamedExprs	state: 64 part: 66
57	ExprTuple	78, 87
58	Literal
59	NamedExprs	state: 65 part: 66
60	Literal
61	ExprTuple	67, 68
62	Literal
63	Operation	operator: 69 operands: 70
64	Operation	operator: 71 operands: 72
65	Variable
66	Variable
67	Operation	operator: 74 operands: 73
68	Operation	operator: 74 operands: 75
69	Literal
70	ExprTuple	76, 87
71	Literal
72	ExprTuple	77, 87
73	ExprTuple	87, 78
74	Literal
75	ExprTuple	87, 79
76	Variable
77	Operation	operator: 80 operands: 81
78	Literal
79	Variable
80	Literal
81	ExprTuple	82, 83
82	Operation	operator: 84 operands: 85
83	Variable
84	Literal
85	ExprTuple	86, 87
86	Literal
87	Variable