Expression of type Conditional ¶

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 Conditional, k, t
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import Equals, InSet
from proveit.numbers import Exp, Interval, Mult, NaturalPos, e, frac, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import _phase, _psi_t_ket, two_pow_t

# build up the expression from sub-expressions
expr = Conditional(Equals(_psi_t_ket, ScalarMult(frac(one, Exp(two, frac(t, two))), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, t)), domain = Interval(zero, subtract(two_pow_t, one))))), InSet(t, NaturalPos))

# 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\{\lvert \psi_{t} \rangle = \left(\frac{1}{2^{\frac{t}{2}}} \cdot \left(\sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)\right)\right) \textrm{ if } t \in \mathbb{N}^+\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 29 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	58, 8
6	Operation	operator: 9 operand: 58
7	Operation	operator: 27 operands: 11
8	Literal
9	Literal
10	ExprTuple	58
11	ExprTuple	12, 13
12	Operation	operator: 25 operands: 14
13	Operation	operator: 15 operand: 18
14	ExprTuple	59, 17
15	Literal
16	ExprTuple	18
17	Operation	operator: 53 operands: 19
18	Lambda	parameter: 50 body: 21
19	ExprTuple	57, 22
20	ExprTuple	50
21	Conditional	value: 23 condition: 24
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 29 operands: 30
25	Literal
26	ExprTuple	58, 57
27	Literal
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	50, 33
31	Operation	operator: 53 operands: 34
32	Operation	operator: 35 operands: 36
33	Operation	operator: 37 operands: 38
34	ExprTuple	39, 40
35	Literal
36	ExprTuple	50, 58
37	Literal
38	ExprTuple	41, 42
39	Literal
40	Operation	operator: 43 operands: 44
41	Literal
42	Operation	operator: 45 operands: 46
43	Literal
44	ExprTuple	57, 47, 48, 49, 50
45	Literal
46	ExprTuple	51, 52
47	Literal
48	Literal
49	Literal
50	Variable
51	Operation	operator: 53 operands: 54
52	Operation	operator: 55 operand: 59
53	Literal
54	ExprTuple	57, 58
55	Literal
56	ExprTuple	59
57	Literal
58	Variable
59	Literal

Expression of type Conditional¶

from the theory of proveit.physics.quantum.QPE¶

Expression of type Conditional ¶

from the theory of proveit.physics.quantum.QPE ¶