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, m, n
from proveit.logic import And, InClass, InSet, SetOfAll
from proveit.numbers import NaturalPos
from proveit.physics.quantum import m_bit_interval, m_ket_domain, normalized_var_ket_psi, var_ket_psi
from proveit.physics.quantum.circuits import register_meas
from proveit.statistics import SampleSpaces

# build up the expression from sub-expressions
expr = Conditional(InClass(SetOfAll(instance_param_or_params = [n], instance_element = register_meas, domain = m_bit_interval), SampleSpaces), And(InSet(m, NaturalPos), InSet(var_ket_psi, m_ket_domain), normalized_var_ket_psi))

# 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\{\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert \psi \rangle} & \meter & \multiqout{3}{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \measure{\begin{array}{c}:\\ \left(m - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}}
} \end{array}\right\}_{n \in \{0~\ldotp \ldotp~2^{m} - 1\}} \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces} \textrm{ if } m \in \mathbb{N}^+ ,  \lvert \psi \rangle \in \mathbb{C}^{2^{m}} ,  \left \|\lvert \psi \rangle\right \| = 1\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: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11
7	Operation	operator: 12 operand: 18
8	Literal
9	Operation	operator: 33 operands: 14
10	Operation	operator: 33 operands: 15
11	Operation	operator: 16 operands: 17
12	Literal
13	ExprTuple	18
14	ExprTuple	83, 19
15	ExprTuple	76, 20
16	Literal
17	ExprTuple	21, 79
18	Lambda	parameter: 82 body: 23
19	Literal
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operand: 76
22	ExprTuple	82
23	Conditional	value: 28 condition: 29
24	Literal
25	ExprTuple	30, 59
26	Literal
27	ExprTuple	76
28	Operation	operator: 31 operands: 32
29	Operation	operator: 33 operands: 34
30	Literal
31	Literal
32	ExprTuple	35, 36, 37
33	Literal
34	ExprTuple	82, 38
35	ExprTuple	39
36	ExprTuple	40
37	ExprTuple	41
38	Operation	operator: 73 operands: 42
39	ExprRange	lambda_map: 43 start_index: 79 end_index: 83
40	ExprRange	lambda_map: 44 start_index: 79 end_index: 83
41	ExprRange	lambda_map: 45 start_index: 79 end_index: 83
42	ExprTuple	46, 47
43	Lambda	parameter: 78 body: 48
44	Lambda	parameter: 78 body: 49
45	Lambda	parameter: 78 body: 51
46	Literal
47	Operation	operator: 52 operands: 53
48	Operation	operator: 57 operands: 54
49	Operation	operator: 55 operands: 56
50	ExprTuple	78
51	Operation	operator: 57 operands: 58
52	Literal
53	ExprTuple	59, 60
54	NamedExprs	element: 61 targets: 64
55	Literal
56	NamedExprs	basis: 62
57	Literal
58	NamedExprs	element: 63 targets: 64
59	Operation	operator: 65 operands: 66
60	Operation	operator: 67 operand: 79
61	Operation	operator: 69 operands: 70
62	Literal
63	Operation	operator: 71 operands: 72
64	Operation	operator: 73 operands: 74
65	Literal
66	ExprTuple	75, 83
67	Literal
68	ExprTuple	79
69	Literal
70	NamedExprs	state: 76 part: 78
71	Literal
72	NamedExprs	state: 77 part: 78
73	Literal
74	ExprTuple	79, 83
75	Literal
76	Variable
77	Operation	operator: 80 operands: 81
78	Variable
79	Literal
80	Literal
81	ExprTuple	82, 83
82	Variable
83	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 ¶