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, TensorProd, VecAdd
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, e, frac, i, one, pi, sqrt, two
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase)), ket1)))
expr = Equals(TensorProd(sub_expr1), sub_expr1)

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[{\otimes}\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) = \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, 6
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Operation	operator: 18 operands: 7
7	ExprTuple	8, 9
8	Operation	operator: 24 operands: 10
9	Operation	operator: 11 operands: 12
10	ExprTuple	32, 13
11	Literal
12	ExprTuple	14, 15
13	Operation	operator: 26 operands: 16
14	Operation	operator: 28 operand: 21
15	Operation	operator: 18 operands: 19
16	ExprTuple	35, 20
17	ExprTuple	21
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 24 operands: 25
21	Literal
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operand: 32
24	Literal
25	ExprTuple	32, 35
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32
30	Literal
31	Operation	operator: 33 operands: 34
32	Literal
33	Literal
34	ExprTuple	35, 36, 37, 38
35	Literal
36	Literal
37	Literal
38	Literal