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 t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Exp, Mult, e, frac, i, one, pi, sqrt, subtract, 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, subtract(t, one)), _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^{t - 1} \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	40, 7
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 30 operands: 10
8	Operation	operator: 21 operand: 15
9	Operation	operator: 12 operands: 13
10	ExprTuple	32, 14
11	ExprTuple	15
12	Literal
13	ExprTuple	16, 17
14	Operation	operator: 18 operands: 19
15	Literal
16	Operation	operator: 30 operands: 20
17	Operation	operator: 21 operand: 40
18	Literal
19	ExprTuple	40, 32
20	ExprTuple	22, 23
21	Literal
22	Literal
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	32, 26, 27, 28, 29
26	Literal
27	Literal
28	Operation	operator: 30 operands: 31
29	Literal
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36, 37
36	Variable
37	Operation	operator: 38 operand: 40
38	Literal
39	ExprTuple	40
40	Literal