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.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import ket_plus
from proveit.physics.quantum.QPE import QPE, _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, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = sub_expr4)
sub_expr6 = MultiQubitElem(element = Output(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = sub_expr4)
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 = Interval(sub_expr2, sub_expr3)), one, _s)], [ExprRange(sub_expr1, sub_expr5, one, _t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, sub_expr6, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr6, sub_expr2, sub_expr3).with_wrapping_at(2,6)])))

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}\left(U, t\right)} & \multiqout{4}{\lvert \Psi \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle {\otimes} \lvert u \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle {\otimes} \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
6	ExprTuple	9, 10
7	ExprTuple	11, 12
8	ExprTuple	13, 14
9	ExprRange	lambda_map: 15 start_index: 59 end_index: 63
10	ExprRange	lambda_map: 16 start_index: 59 end_index: 64
11	ExprRange	lambda_map: 17 start_index: 59 end_index: 63
12	ExprRange	lambda_map: 17 start_index: 47 end_index: 51
13	ExprRange	lambda_map: 18 start_index: 59 end_index: 63
14	ExprRange	lambda_map: 18 start_index: 47 end_index: 51
15	Lambda	parameter: 50 body: 19
16	Lambda	parameter: 50 body: 20
17	Lambda	parameter: 50 body: 21
18	Lambda	parameter: 50 body: 23
19	Operation	operator: 37 operands: 24
20	Operation	operator: 27 operands: 25
21	Operation	operator: 27 operands: 26
22	ExprTuple	50
23	Operation	operator: 27 operands: 28
24	NamedExprs	state: 29
25	NamedExprs	element: 30 targets: 31
26	NamedExprs	element: 32 targets: 34
27	Literal
28	NamedExprs	element: 33 targets: 34
29	Operation	operator: 35 operand: 46
30	Operation	operator: 37 operands: 38
31	Operation	operator: 44 operands: 39
32	Operation	operator: 40 operands: 41
33	Operation	operator: 42 operands: 43
34	Operation	operator: 44 operands: 45
35	Literal
36	ExprTuple	46
37	Literal
38	NamedExprs	state: 62 part: 50
39	ExprTuple	47, 51
40	Literal
41	NamedExprs	operation: 48 part: 50
42	Literal
43	NamedExprs	state: 49 part: 50
44	Literal
45	ExprTuple	59, 51
46	Literal
47	Operation	operator: 57 operands: 52
48	Operation	operator: 53 operands: 54
49	Operation	operator: 55 operands: 56
50	Variable
51	Operation	operator: 57 operands: 58
52	ExprTuple	63, 59
53	Literal
54	ExprTuple	60, 63
55	Literal
56	ExprTuple	61, 62
57	Literal
58	ExprTuple	63, 64
59	Literal
60	Literal
61	Literal
62	Literal
63	Literal
64	Literal