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
from proveit.logic import Equals
from proveit.numbers import Interval, one
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _Psi_ket, _psi__t_ket, _t
from proveit.physics.quantum.circuits import Gate, Input, 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__t_ket, part = sub_expr1), targets = sub_expr2), one, _t)], [ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr2), one, _t)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _Psi_ket, part = sub_expr1), targets = sub_expr2), one, _t)]))), one)

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{
\qin{\lvert \psi_{t} \rangle} & \gate{{\mathrm {FT}}^{\dag}_{t}} & \qout{\lvert \Psi \rangle}
} \end{array}\right) = 1

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, 42
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Operation	operator: 7 operands: 8
7	Literal
8	ExprTuple	9, 10, 11
9	ExprTuple	12
10	ExprTuple	13
11	ExprTuple	14
12	ExprRange	lambda_map: 15 start_index: 42 end_index: 46
13	ExprRange	lambda_map: 16 start_index: 42 end_index: 46
14	ExprRange	lambda_map: 17 start_index: 42 end_index: 46
15	Lambda	parameter: 41 body: 18
16	Lambda	parameter: 41 body: 19
17	Lambda	parameter: 41 body: 21
18	Operation	operator: 24 operands: 22
19	Operation	operator: 24 operands: 23
20	ExprTuple	41
21	Operation	operator: 24 operands: 25
22	NamedExprs	element: 26 targets: 29
23	NamedExprs	element: 27 targets: 29
24	Literal
25	NamedExprs	element: 28 targets: 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operands: 33
28	Operation	operator: 34 operands: 35
29	Operation	operator: 36 operands: 37
30	Literal
31	NamedExprs	state: 38 part: 41
32	Literal
33	NamedExprs	operation: 39 part: 41
34	Literal
35	NamedExprs	state: 40 part: 41
36	Literal
37	ExprTuple	42, 46
38	Operation	operator: 43 operand: 46
39	Operation	operator: 44 operand: 46
40	Literal
41	Variable
42	Literal
43	Literal
44	Literal
45	ExprTuple	46
46	Literal