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
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import I
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _s, _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 = [ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = Interval(one, _t)), one, _t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, _s)]), Add(_t, _s)).with_wrapping_at(1)

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())

\begin{array}{c} \begin{array}{l} |\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{{\mathrm {FT}}^{\dag}_{t}~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{{\mathrm {FT}}^{\dag}_{t}~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{{\mathrm {FT}}^{\dag}_{t}~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t\}} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, ..\left(s - 3\right) \times.., \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}\right)| \\  = \left(t + s\right) \end{array} \end{array}

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.	()	(1)	('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 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	32, 13
9	ExprRange	lambda_map: 11 start_index: 29 end_index: 32
10	ExprRange	lambda_map: 12 start_index: 29 end_index: 13
11	Lambda	parameter: 28 body: 14
12	Lambda	parameter: 28 body: 16
13	Literal
14	Operation	operator: 17 operands: 18
15	ExprTuple	28
16	Operation	operator: 23 operands: 19
17	Literal
18	NamedExprs	element: 20 targets: 21
19	NamedExprs	operation: 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	Literal
23	Literal
24	NamedExprs	operation: 27 part: 28
25	Literal
26	ExprTuple	29, 32
27	Operation	operator: 30 operand: 32
28	Variable
29	Literal
30	Literal
31	ExprTuple	32
32	Literal