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
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _psi__t_ket, _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 = Interval(one, _t)
sub_expr3 = Interval(Add(_t, one), Add(_t, _s))
expr = Prob(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _psi__t_ket, part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr3), one, _s)], [ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr2), 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_expr2), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr3), 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 \psi_{t} \rangle} & \gate{{\mathrm {FT}}^{\dag}_{t}} & \qout{\lvert \Psi \rangle} \\
\qin{\lvert u \rangle} & { /^{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
6	ExprTuple	9, 10
7	ExprTuple	11, 12
8	ExprTuple	13, 14
9	ExprRange	lambda_map: 15 start_index: 66 end_index: 67
10	ExprRange	lambda_map: 16 start_index: 66 end_index: 68
11	ExprRange	lambda_map: 17 start_index: 66 end_index: 67
12	ExprRange	lambda_map: 18 start_index: 66 end_index: 68
13	ExprRange	lambda_map: 19 start_index: 66 end_index: 67
14	ExprRange	lambda_map: 20 start_index: 66 end_index: 68
15	Lambda	parameter: 57 body: 21
16	Lambda	parameter: 57 body: 22
17	Lambda	parameter: 57 body: 23
18	Lambda	parameter: 57 body: 24
19	Lambda	parameter: 57 body: 25
20	Lambda	parameter: 57 body: 27
21	Operation	operator: 33 operands: 28
22	Operation	operator: 33 operands: 29
23	Operation	operator: 33 operands: 30
24	Operation	operator: 45 operands: 31
25	Operation	operator: 33 operands: 32
26	ExprTuple	57
27	Operation	operator: 33 operands: 34
28	NamedExprs	element: 35 targets: 40
29	NamedExprs	element: 36 targets: 42
30	NamedExprs	element: 37 targets: 40
31	NamedExprs	operation: 38
32	NamedExprs	element: 39 targets: 40
33	Literal
34	NamedExprs	element: 41 targets: 42
35	Operation	operator: 44 operands: 43
36	Operation	operator: 44 operands: 50
37	Operation	operator: 45 operands: 46
38	Literal
39	Operation	operator: 49 operands: 47
40	Operation	operator: 51 operands: 48
41	Operation	operator: 49 operands: 50
42	Operation	operator: 51 operands: 52
43	NamedExprs	state: 53 part: 57
44	Literal
45	Literal
46	NamedExprs	operation: 54 part: 57
47	NamedExprs	state: 55 part: 57
48	ExprTuple	66, 67
49	Literal
50	NamedExprs	state: 56 part: 57
51	Literal
52	ExprTuple	58, 59
53	Operation	operator: 60 operand: 67
54	Operation	operator: 61 operand: 67
55	Literal
56	Literal
57	Variable
58	Operation	operator: 64 operands: 63
59	Operation	operator: 64 operands: 65
60	Literal
61	Literal
62	ExprTuple	67
63	ExprTuple	67, 66
64	Literal
65	ExprTuple	67, 68
66	Literal
67	Literal
68	Literal