Expression of type Conditional ¶

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

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, i, n
from proveit.core_expr_types import v_i, w_i
from proveit.linear_algebra import OrthoNormBases, Unitary, VecSum
from proveit.logic import And, CartExp, InSet, Set
from proveit.numbers import Complex, Interval, one
from proveit.physics.quantum import Bra, Ket, Qmult
from proveit.physics.quantum.algebra import v_1_to_n_kets, w_1_to_n_kets

# build up the expression from sub-expressions
sub_expr1 = OrthoNormBases(CartExp(Complex, n))
expr = Conditional(InSet(VecSum(index_or_indices = [i], summand = Qmult(Ket(v_i), Bra(w_i)), domain = Interval(one, n)), Unitary(n)), And(InSet(Set(v_1_to_n_kets), sub_expr1), InSet(Set(w_1_to_n_kets), sub_expr1)))

# 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\{\left(\sum_{i=1}^{n} \left(\lvert v_{i} \rangle \thinspace \langle w_{i} \rvert\right)\right) \in \textrm{U}\left(n\right) \textrm{ if } \left\{\left\{\lvert v_{1} \rangle, \lvert v_{2} \rangle, \ldots, \lvert v_{n} \rangle\right\}\right\} \in \textrm{O.N.Bases}\left(\mathbb{C}^{n}\right) ,  \left\{\left\{\lvert w_{1} \rangle, \lvert w_{2} \rangle, \ldots, \lvert w_{n} \rangle\right\}\right\} \in \textrm{O.N.Bases}\left(\mathbb{C}^{n}\right)\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: 32 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9
6	Operation	operator: 10 operand: 16
7	Operation	operator: 12 operand: 55
8	Operation	operator: 32 operands: 14
9	Operation	operator: 32 operands: 15
10	Literal
11	ExprTuple	16
12	Literal
13	ExprTuple	55
14	ExprTuple	17, 19
15	ExprTuple	18, 19
16	Lambda	parameter: 62 body: 20
17	Operation	operator: 35 operand: 27
18	Operation	operator: 35 operand: 28
19	Operation	operator: 23 operand: 29
20	Conditional	value: 25 condition: 26
21	ExprTuple	27
22	ExprTuple	28
23	Literal
24	ExprTuple	29
25	Operation	operator: 30 operands: 31
26	Operation	operator: 32 operands: 33
27	Operation	operator: 35 operands: 34
28	Operation	operator: 35 operands: 36
29	Operation	operator: 37 operands: 38
30	Literal
31	ExprTuple	39, 40
32	Literal
33	ExprTuple	62, 41
34	ExprTuple	42
35	Literal
36	ExprTuple	43
37	Literal
38	ExprTuple	44, 55
39	Operation	operator: 60 operand: 52
40	Operation	operator: 46 operand: 53
41	Operation	operator: 48 operands: 49
42	ExprRange	lambda_map: 50 start_index: 54 end_index: 55
43	ExprRange	lambda_map: 51 start_index: 54 end_index: 55
44	Literal
45	ExprTuple	52
46	Literal
47	ExprTuple	53
48	Literal
49	ExprTuple	54, 55
50	Lambda	parameter: 68 body: 56
51	Lambda	parameter: 68 body: 57
52	IndexedVar	variable: 65 index: 62
53	IndexedVar	variable: 66 index: 62
54	Literal
55	Variable
56	Operation	operator: 60 operand: 63
57	Operation	operator: 60 operand: 64
58	ExprTuple	62
59	ExprTuple	63
60	Literal
61	ExprTuple	64
62	Variable
63	IndexedVar	variable: 65 index: 68
64	IndexedVar	variable: 66 index: 68
65	Variable
66	Variable
67	ExprTuple	68
68	Variable

Expression of type Conditional¶

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

Expression of type Conditional ¶

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