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.linear_algebra import TensorProd
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 = Add(_t, _s)
sub_expr3 = Add(_t, one)
sub_expr4 = MultiQubitElem(element = Input(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr2))
expr = Prob(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr4, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr4, sub_expr3, sub_expr2).with_wrapping_at(2,6)], [ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = Interval(one, _t)), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(sub_expr3, sub_expr2)), 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{4}{\lvert \Psi \rangle {\otimes} \lvert u \rangle} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle {\otimes} \lvert u \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle {\otimes} \lvert u \rangle} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle {\otimes} \lvert u \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle {\otimes} \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: 15 start_index: 54 end_index: 55
11	ExprRange	lambda_map: 16 start_index: 66 end_index: 67
12	ExprRange	lambda_map: 17 start_index: 66 end_index: 68
13	ExprRange	lambda_map: 18 start_index: 66 end_index: 67
14	ExprRange	lambda_map: 19 start_index: 66 end_index: 68
15	Lambda	parameter: 53 body: 20
16	Lambda	parameter: 53 body: 21
17	Lambda	parameter: 53 body: 22
18	Lambda	parameter: 53 body: 23
19	Lambda	parameter: 53 body: 25
20	Operation	operator: 32 operands: 26
21	Operation	operator: 27 operands: 28
22	Operation	operator: 29 operands: 30
23	Operation	operator: 32 operands: 31
24	ExprTuple	53
25	Operation	operator: 32 operands: 33
26	NamedExprs	element: 34 targets: 35
27	Literal
28	NamedExprs	basis: 36
29	Literal
30	NamedExprs	operation: 37
31	NamedExprs	element: 38 targets: 39
32	Literal
33	NamedExprs	element: 40 targets: 41
34	Operation	operator: 42 operands: 43
35	Operation	operator: 49 operands: 44
36	Literal
37	Literal
38	Operation	operator: 47 operands: 45
39	Operation	operator: 49 operands: 46
40	Operation	operator: 47 operands: 48
41	Operation	operator: 49 operands: 50
42	Literal
43	NamedExprs	state: 51 part: 53
44	ExprTuple	66, 55
45	NamedExprs	state: 52 part: 53
46	ExprTuple	66, 67
47	Literal
48	NamedExprs	state: 64 part: 53
49	Literal
50	ExprTuple	54, 55
51	Operation	operator: 56 operands: 57
52	Operation	operator: 58 operands: 59
53	Variable
54	Operation	operator: 61 operands: 60
55	Operation	operator: 61 operands: 62
56	Literal
57	ExprTuple	63, 64
58	Literal
59	ExprTuple	65, 67
60	ExprTuple	67, 66
61	Literal
62	ExprTuple	67, 68
63	Literal
64	Literal
65	Variable
66	Literal
67	Literal
68	Literal