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, m
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _s, _s_wire, _t
from proveit.physics.quantum.circuits import Input, Measure, 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_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, Measure(basis = Z), one, _t), _s_wire], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), 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{
\multiqin{3}{\lvert \Psi \rangle} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\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: 65 end_index: 66
10	ExprRange	lambda_map: 16 start_index: 65 end_index: 67
11	ExprRange	lambda_map: 17 start_index: 65 end_index: 66
12	ExprRange	lambda_map: 18 start_index: 65 end_index: 67
13	ExprRange	lambda_map: 19 start_index: 65 end_index: 66
14	ExprRange	lambda_map: 20 start_index: 65 end_index: 67
15	Lambda	parameter: 56 body: 21
16	Lambda	parameter: 56 body: 22
17	Lambda	parameter: 56 body: 23
18	Lambda	parameter: 56 body: 24
19	Lambda	parameter: 56 body: 25
20	Lambda	parameter: 56 body: 27
21	Operation	operator: 35 operands: 28
22	Operation	operator: 35 operands: 29
23	Operation	operator: 30 operands: 31
24	Operation	operator: 32 operands: 33
25	Operation	operator: 35 operands: 34
26	ExprTuple	56
27	Operation	operator: 35 operands: 36
28	NamedExprs	element: 37 targets: 42
29	NamedExprs	element: 38 targets: 44
30	Literal
31	NamedExprs	basis: 39
32	Literal
33	NamedExprs	operation: 40
34	NamedExprs	element: 41 targets: 42
35	Literal
36	NamedExprs	element: 43 targets: 44
37	Operation	operator: 46 operands: 45
38	Operation	operator: 46 operands: 50
39	Literal
40	Literal
41	Operation	operator: 49 operands: 47
42	Operation	operator: 51 operands: 48
43	Operation	operator: 49 operands: 50
44	Operation	operator: 51 operands: 52
45	NamedExprs	state: 53 part: 56
46	Literal
47	NamedExprs	state: 54 part: 56
48	ExprTuple	65, 66
49	Literal
50	NamedExprs	state: 55 part: 56
51	Literal
52	ExprTuple	57, 58
53	Literal
54	Operation	operator: 59 operands: 60
55	Literal
56	Variable
57	Operation	operator: 62 operands: 61
58	Operation	operator: 62 operands: 63
59	Literal
60	ExprTuple	64, 66
61	ExprTuple	66, 65
62	Literal
63	ExprTuple	66, 67
64	Variable
65	Literal
66	Literal
67	Literal