Expression of type Lambda

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, Lambda, Variable, VertExprArray, l
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z, ket_plus
from proveit.physics.quantum.QPE import ModAdd, QPE, _U, _b_floor, _ket_u, _s, _s_wire, _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 = Lambda(l, 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, Measure(basis = Z), one, _t), _s_wire], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(ModAdd(_b_floor, l), _t), part = sub_expr1), targets = Interval(one, _t)), one, _t), 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())

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