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, t
from proveit.core_expr_types import Len
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [ExprRange(sub_expr1, ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1))), Neg(t), zero)]), Variable("_b", latex_format = r"{_{-}b}"))

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(\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-\left(-t\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right), \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-\left(-t + 1\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right), \ldots, \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right)\right)| = {_{-}b}

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 operands: 6
4	Variable
5	Literal
6	ExprTuple	7
7	ExprRange	lambda_map: 8 start_index: 9 end_index: 27
8	Lambda	parameter: 50 body: 10
9	Operation	operator: 48 operand: 13
10	Operation	operator: 24 operands: 12
11	ExprTuple	13
12	ExprTuple	14, 15
13	Variable
14	Operation	operator: 30 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	37, 19
17	Literal
18	ExprTuple	20, 21
19	Operation	operator: 44 operands: 22
20	Operation	operator: 33 operand: 27
21	Operation	operator: 24 operands: 25
22	ExprTuple	46, 26
23	ExprTuple	27
24	Literal
25	ExprTuple	28, 29
26	Operation	operator: 30 operands: 31
27	Literal
28	Operation	operator: 44 operands: 32
29	Operation	operator: 33 operand: 37
30	Literal
31	ExprTuple	37, 46
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	37
35	Literal
36	Operation	operator: 38 operands: 39
37	Literal
38	Literal
39	ExprTuple	46, 40, 41, 42, 43
40	Literal
41	Literal
42	Operation	operator: 44 operands: 45
43	Literal
44	Literal
45	ExprTuple	46, 47
46	Literal
47	Operation	operator: 48 operand: 50
48	Literal
49	ExprTuple	50
50	Variable