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 import Qmult
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _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)
sub_expr3 = InverseFourierTransform(_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 = sub_expr3, part = sub_expr1), targets = sub_expr2), one, _t)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = Qmult(sub_expr3, _psi__t_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{{\mathrm {FT}}^{\dag}_{t} \thinspace \lvert \psi_{t} \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, 40
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: 40 end_index: 48
13	ExprRange	lambda_map: 16 start_index: 40 end_index: 48
14	ExprRange	lambda_map: 17 start_index: 40 end_index: 48
15	Lambda	parameter: 39 body: 18
16	Lambda	parameter: 39 body: 19
17	Lambda	parameter: 39 body: 21
18	Operation	operator: 24 operands: 22
19	Operation	operator: 24 operands: 23
20	ExprTuple	39
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: 44 part: 39
32	Literal
33	NamedExprs	operation: 43 part: 39
34	Literal
35	NamedExprs	state: 38 part: 39
36	Literal
37	ExprTuple	40, 48
38	Operation	operator: 41 operands: 42
39	Variable
40	Literal
41	Literal
42	ExprTuple	43, 44
43	Operation	operator: 45 operand: 48
44	Operation	operator: 46 operand: 48
45	Literal
46	Literal
47	ExprTuple	48
48	Literal