Expression of type Equals

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.logic import Equals
from proveit.numbers import Interval, one
from proveit.physics.quantum import NumKet, Z
from proveit.physics.quantum.QPE import _Psi_ket, _alpha_m_sqrd, _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 = Equals(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)]))), _alpha_m_sqrd)

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) = \left|\alpha_{m}\right|^{2}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operand: 19
11	Literal
12	Literal
13	ExprTuple	16, 17, 18
14	Literal
15	ExprTuple	19
16	ExprTuple	20
17	ExprTuple	21
18	ExprTuple	22
19	Operation	operator: 23 operand: 53
20	ExprRange	lambda_map: 25 start_index: 50 end_index: 54
21	ExprRange	lambda_map: 26 start_index: 50 end_index: 54
22	ExprRange	lambda_map: 27 start_index: 50 end_index: 54
23	Literal
24	ExprTuple	53
25	Lambda	parameter: 49 body: 28
26	Lambda	parameter: 49 body: 29
27	Lambda	parameter: 49 body: 31
28	Operation	operator: 35 operands: 32
29	Operation	operator: 33 operands: 34
30	ExprTuple	49
31	Operation	operator: 35 operands: 36
32	NamedExprs	element: 37 targets: 40
33	Literal
34	NamedExprs	basis: 38
35	Literal
36	NamedExprs	element: 39 targets: 40
37	Operation	operator: 41 operands: 42
38	Literal
39	Operation	operator: 43 operands: 44
40	Operation	operator: 45 operands: 46
41	Literal
42	NamedExprs	state: 47 part: 49
43	Literal
44	NamedExprs	state: 48 part: 49
45	Literal
46	ExprTuple	50, 54
47	Literal
48	Operation	operator: 51 operands: 52
49	Variable
50	Literal
51	Literal
52	ExprTuple	53, 54
53	Variable
54	Literal