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.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 = frac(one, sqrt(two))
expr = Equals([ScalarMult(sub_expr1, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(zero)), _phase)), ket1)))], [ScalarMult(sub_expr1, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase)), ket1)))])

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(\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) = \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\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	ExprTuple	5
4	ExprTuple	6
5	Operation	operator: 22 operands: 7
6	Operation	operator: 22 operands: 8
7	ExprTuple	10, 9
8	ExprTuple	10, 11
9	Operation	operator: 14 operands: 12
10	Operation	operator: 29 operands: 13
11	Operation	operator: 14 operands: 15
12	ExprTuple	18, 16
13	ExprTuple	37, 17
14	Literal
15	ExprTuple	18, 19
16	Operation	operator: 22 operands: 20
17	Operation	operator: 45 operands: 21
18	Operation	operator: 32 operand: 51
19	Operation	operator: 22 operands: 23
20	ExprTuple	24, 27
21	ExprTuple	47, 25
22	Literal
23	ExprTuple	26, 27
24	Operation	operator: 45 operands: 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 45 operands: 31
27	Operation	operator: 32 operand: 37
28	ExprTuple	35, 34
29	Literal
30	ExprTuple	37, 47
31	ExprTuple	35, 36
32	Literal
33	ExprTuple	37
34	Operation	operator: 39 operands: 38
35	Literal
36	Operation	operator: 39 operands: 40
37	Literal
38	ExprTuple	47, 42, 43, 41, 44
39	Literal
40	ExprTuple	47, 42, 43, 44
41	Operation	operator: 45 operands: 46
42	Literal
43	Literal
44	Literal
45	Literal
46	ExprTuple	47, 48
47	Literal
48	Operation	operator: 49 operand: 51
49	Literal
50	ExprTuple	51
51	Literal