Expression of type Conditional ¶

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

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, U, m
from proveit.linear_algebra import Unitary
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Exp, NaturalPos, one, two
from proveit.physics.quantum import m_ket_domain, var_ket_psi
from proveit.physics.quantum.circuits import unitary_gate_op
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [U, var_ket_psi], instance_expr = Equals(Prob(unitary_gate_op), one), domains = [Unitary(Exp(two, m)), m_ket_domain]), InSet(m, 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\{\forall_{U \in \textrm{U}\left(2^{m}\right), \lvert \psi \rangle \in \mathbb{C}^{2^{m}}}~\left(\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi \rangle} & \gate{U} & \qout{U \thinspace \lvert \psi \rangle}
} \end{array}\right) = 1\right) \textrm{ if } m \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 operand: 6
2	Operation	operator: 21 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	69, 7
6	Lambda	parameters: 71 body: 8
7	Literal
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 68
13	Literal
14	ExprTuple	16, 17
15	Operation	operator: 18 operand: 23
16	Operation	operator: 21 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	ExprTuple	23
20	ExprTuple	72, 24
21	Literal
22	ExprTuple	73, 25
23	Operation	operator: 26 operands: 27
24	Operation	operator: 28 operand: 36
25	Operation	operator: 30 operands: 31
26	Literal
27	ExprTuple	32, 33, 34
28	Literal
29	ExprTuple	36
30	Literal
31	ExprTuple	35, 36
32	ExprTuple	37
33	ExprTuple	38
34	ExprTuple	39
35	Literal
36	Operation	operator: 40 operands: 41
37	ExprRange	lambda_map: 42 start_index: 68 end_index: 69
38	ExprRange	lambda_map: 43 start_index: 68 end_index: 69
39	ExprRange	lambda_map: 44 start_index: 68 end_index: 69
40	Literal
41	ExprTuple	45, 69
42	Lambda	parameter: 67 body: 46
43	Lambda	parameter: 67 body: 47
44	Lambda	parameter: 67 body: 49
45	Literal
46	Operation	operator: 52 operands: 50
47	Operation	operator: 52 operands: 51
48	ExprTuple	67
49	Operation	operator: 52 operands: 53
50	NamedExprs	element: 54 targets: 57
51	NamedExprs	element: 55 targets: 57
52	Literal
53	NamedExprs	element: 56 targets: 57
54	Operation	operator: 58 operands: 59
55	Operation	operator: 60 operands: 61
56	Operation	operator: 62 operands: 63
57	Operation	operator: 64 operands: 65
58	Literal
59	NamedExprs	state: 73 part: 67
60	Literal
61	NamedExprs	operation: 72 part: 67
62	Literal
63	NamedExprs	state: 66 part: 67
64	Literal
65	ExprTuple	68, 69
66	Operation	operator: 70 operands: 71
67	Variable
68	Literal
69	Variable
70	Literal
71	ExprTuple	72, 73
72	Variable
73	Variable

Expression of type Conditional¶

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

Expression of type Conditional ¶

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