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, Lambda, Variable
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Interval, one, two
from proveit.physics.quantum import I
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _t
from proveit.physics.quantum.circuits import Gate, MultiQubitElem

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [Lambda(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = Interval(one, _t))), Lambda(sub_expr1, Gate(operation = I).with_implicit_representation())]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, 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())

|\left({_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{{\mathrm {FT}}^{\dag}_{t}~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t\}} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}\right)| = |\left(1, \ldots, 2\right)|

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: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10
8	Lambda	parameter: 27 body: 11
9	Lambda	parameter: 27 body: 12
10	ExprRange	lambda_map: 13 start_index: 28 end_index: 14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 22 operands: 17
13	Lambda	parameter: 27 body: 27
14	Literal
15	Literal
16	NamedExprs	element: 19 targets: 20
17	NamedExprs	operation: 21
18	ExprTuple	27
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	Literal
22	Literal
23	NamedExprs	operation: 26 part: 27
24	Literal
25	ExprTuple	28, 31
26	Operation	operator: 29 operand: 31
27	Variable
28	Literal
29	Literal
30	ExprTuple	31
31	Literal