Expression of type Prob

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, 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_ket, _U, _ket_u, _s, _t
from proveit.physics.quantum.circuits import Gate, Input, MultiQubitElem, Output, Qcircuit
from proveit.statistics import Prob

# 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 = Prob(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)])))

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())

\textrm{Pr}\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)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7, 8, 9
6	ExprTuple	10, 11
7	ExprTuple	12, 13
8	ExprTuple	14, 15
9	ExprTuple	16, 17
10	ExprRange	lambda_map: 18 start_index: 80 end_index: 81
11	ExprRange	lambda_map: 19 start_index: 80 end_index: 82
12	ExprRange	lambda_map: 20 start_index: 80 end_index: 81
13	ExprRange	lambda_map: 20 start_index: 70 end_index: 71
14	ExprRange	lambda_map: 21 start_index: 80 end_index: 81
15	ExprRange	lambda_map: 22 start_index: 80 end_index: 82
16	ExprRange	lambda_map: 23 start_index: 80 end_index: 81
17	ExprRange	lambda_map: 24 start_index: 80 end_index: 82
18	Lambda	parameter: 69 body: 25
19	Lambda	parameter: 69 body: 26
20	Lambda	parameter: 69 body: 27
21	Lambda	parameter: 69 body: 28
22	Lambda	parameter: 69 body: 29
23	Lambda	parameter: 69 body: 30
24	Lambda	parameter: 69 body: 32
25	Operation	operator: 53 operands: 33
26	Operation	operator: 39 operands: 34
27	Operation	operator: 39 operands: 35
28	Operation	operator: 39 operands: 36
29	Operation	operator: 56 operands: 37
30	Operation	operator: 39 operands: 38
31	ExprTuple	69
32	Operation	operator: 39 operands: 40
33	NamedExprs	state: 41
34	NamedExprs	element: 42 targets: 50
35	NamedExprs	element: 43 targets: 44
36	NamedExprs	element: 45 targets: 48
37	NamedExprs	operation: 46
38	NamedExprs	element: 47 targets: 48
39	Literal
40	NamedExprs	element: 49 targets: 50
41	Operation	operator: 51 operand: 64
42	Operation	operator: 53 operands: 61
43	Operation	operator: 56 operands: 54
44	Operation	operator: 62 operands: 55
45	Operation	operator: 56 operands: 57
46	Literal
47	Operation	operator: 60 operands: 58
48	Operation	operator: 62 operands: 59
49	Operation	operator: 60 operands: 61
50	Operation	operator: 62 operands: 63
51	Literal
52	ExprTuple	64
53	Literal
54	NamedExprs	operation: 65 part: 69
55	ExprTuple	80, 71
56	Literal
57	NamedExprs	operation: 66 part: 69
58	NamedExprs	state: 67 part: 69
59	ExprTuple	80, 81
60	Literal
61	NamedExprs	state: 68 part: 69
62	Literal
63	ExprTuple	70, 71
64	Literal
65	Operation	operator: 72 operands: 73
66	Operation	operator: 74 operand: 81
67	Literal
68	Literal
69	Variable
70	Operation	operator: 77 operands: 76
71	Operation	operator: 77 operands: 78
72	Literal
73	ExprTuple	79, 81
74	Literal
75	ExprTuple	81
76	ExprTuple	81, 80
77	Literal
78	ExprTuple	81, 82
79	Literal
80	Literal
81	Literal
82	Literal