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 k
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.numbers import Exp, Interval, Mult, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import Ket
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
expr = ScalarMult(frac(one, sqrt(two)), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), Ket(k)), domain = Interval(zero, one)))

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(\sum_{k=0}^{1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \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: 16 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 14 operands: 4
3	Operation	operator: 5 operand: 8
4	ExprTuple	32, 7
5	Literal
6	ExprTuple	8
7	Operation	operator: 23 operands: 9
8	Lambda	parameter: 39 body: 10
9	ExprTuple	35, 11
10	Conditional	value: 12 condition: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 18 operands: 19
14	Literal
15	ExprTuple	32, 35
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	39, 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operand: 39
22	Operation	operator: 27 operands: 28
23	Literal
24	ExprTuple	29, 30
25	Literal
26	ExprTuple	39
27	Literal
28	ExprTuple	31, 32
29	Literal
30	Operation	operator: 33 operands: 34
31	Literal
32	Literal
33	Literal
34	ExprTuple	35, 36, 37, 38, 39
35	Literal
36	Literal
37	Literal
38	Literal
39	Variable