Expression of type Equals

from the theory of proveit.physics.quantum.circuits

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 m, n
from proveit.logic import Equals
from proveit.numbers import Abs, Exp, two
from proveit.physics.quantum import NumBra, Qmult, var_ket_psi
from proveit.physics.quantum.circuits import register_meas
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Equals(Prob(register_meas), Exp(Abs(Qmult(NumBra(n, m), var_ket_psi)), two))

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 n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \measure{\begin{array}{c}:\\ \left(m - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}}
} \end{array}\right) = \left|{_{m}}\langle n \rvert \thinspace \lvert \psi \rangle\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 operands: 24
20	ExprRange	lambda_map: 25 start_index: 52 end_index: 56
21	ExprRange	lambda_map: 26 start_index: 52 end_index: 56
22	ExprRange	lambda_map: 27 start_index: 52 end_index: 56
23	Literal
24	ExprTuple	28, 49
25	Lambda	parameter: 51 body: 29
26	Lambda	parameter: 51 body: 30
27	Lambda	parameter: 51 body: 32
28	Operation	operator: 33 operands: 54
29	Operation	operator: 37 operands: 34
30	Operation	operator: 35 operands: 36
31	ExprTuple	51
32	Operation	operator: 37 operands: 38
33	Literal
34	NamedExprs	element: 39 targets: 42
35	Literal
36	NamedExprs	basis: 40
37	Literal
38	NamedExprs	element: 41 targets: 42
39	Operation	operator: 43 operands: 44
40	Literal
41	Operation	operator: 45 operands: 46
42	Operation	operator: 47 operands: 48
43	Literal
44	NamedExprs	state: 49 part: 51
45	Literal
46	NamedExprs	state: 50 part: 51
47	Literal
48	ExprTuple	52, 56
49	Variable
50	Operation	operator: 53 operands: 54
51	Variable
52	Literal
53	Literal
54	ExprTuple	55, 56
55	Variable
56	Variable