Expression of type ScalarMult

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 Variable
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Exp, Mult, Neg, 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
expr = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Variable("_a", latex_format = r"{_{-}a}"))), _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())

\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi} \cdot \lvert 1 \rangle\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',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 12 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 18 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	25, 7
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 32 operands: 10
8	Operation	operator: 21 operand: 15
9	Operation	operator: 12 operands: 13
10	ExprTuple	34, 14
11	ExprTuple	15
12	Literal
13	ExprTuple	16, 17
14	Operation	operator: 18 operands: 19
15	Literal
16	Operation	operator: 32 operands: 20
17	Operation	operator: 21 operand: 25
18	Literal
19	ExprTuple	25, 34
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25
23	Literal
24	Operation	operator: 26 operands: 27
25	Literal
26	Literal
27	ExprTuple	34, 28, 29, 30, 31
28	Literal
29	Literal
30	Operation	operator: 32 operands: 33
31	Literal
32	Literal
33	ExprTuple	34, 35
34	Literal
35	Operation	operator: 36 operand: 38
36	Literal
37	ExprTuple	38
38	Variable