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, t
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), TensorProd(ket1, NumKet(k, t))), domain = Interval(zero, subtract(two_pow_t, 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())

\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \left(\sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{t}\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',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 14 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 45 operands: 4
3	Operation	operator: 5 operand: 8
4	ExprTuple	26, 7
5	Literal
6	ExprTuple	8
7	Operation	operator: 32 operands: 9
8	Lambda	parameter: 42 body: 11
9	ExprTuple	49, 39, 40, 41, 43
10	ExprTuple	42
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	42, 20
18	Operation	operator: 45 operands: 21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	ExprTuple	26, 27
22	Literal
23	ExprTuple	28, 29
24	Literal
25	ExprTuple	30, 31
26	Literal
27	Operation	operator: 32 operands: 33
28	Operation	operator: 34 operand: 51
29	Operation	operator: 35 operands: 36
30	Literal
31	Operation	operator: 37 operands: 38
32	Literal
33	ExprTuple	49, 39, 40, 41, 42
34	Literal
35	Literal
36	ExprTuple	42, 50
37	Literal
38	ExprTuple	43, 44
39	Literal
40	Literal
41	Literal
42	Variable
43	Operation	operator: 45 operands: 46
44	Operation	operator: 47 operand: 51
45	Literal
46	ExprTuple	49, 50
47	Literal
48	ExprTuple	51
49	Literal
50	Variable
51	Literal