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 Interval, one
from proveit.physics.quantum import NumKet, Z
from proveit.physics.quantum.QPE import _Psi_ket, _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)
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, Measure(basis = Z), one, _t)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = sub_expr2), one, _t)])))

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}}
} \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
7	ExprTuple	10
8	ExprTuple	11
9	ExprRange	lambda_map: 12 start_index: 37 end_index: 41
10	ExprRange	lambda_map: 13 start_index: 37 end_index: 41
11	ExprRange	lambda_map: 14 start_index: 37 end_index: 41
12	Lambda	parameter: 36 body: 15
13	Lambda	parameter: 36 body: 16
14	Lambda	parameter: 36 body: 18
15	Operation	operator: 22 operands: 19
16	Operation	operator: 20 operands: 21
17	ExprTuple	36
18	Operation	operator: 22 operands: 23
19	NamedExprs	element: 24 targets: 27
20	Literal
21	NamedExprs	basis: 25
22	Literal
23	NamedExprs	element: 26 targets: 27
24	Operation	operator: 28 operands: 29
25	Literal
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operands: 33
28	Literal
29	NamedExprs	state: 34 part: 36
30	Literal
31	NamedExprs	state: 35 part: 36
32	Literal
33	ExprTuple	37, 41
34	Literal
35	Operation	operator: 38 operands: 39
36	Variable
37	Literal
38	Literal
39	ExprTuple	40, 41
40	Variable
41	Literal