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, Lambda, m, n
from proveit.logic import And, Bijections, 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

# build up the expression from sub-expressions
expr = Conditional(InSet(Lambda(n, register_meas), Bijections(m_bit_interval, SetOfAll(instance_param_or_params = [n], instance_element = register_meas, domain = m_bit_interval))).with_wrapping_at(2), And(InSet(m, NaturalPos), InSet(var_ket_psi, m_ket_domain), normalized_var_ket_psi))

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())

\left\{\begin{array}{c} \begin{array}{l} \left[n \mapsto \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)\right] \in  \\ \left[\{0~\ldotp \ldotp~2^{m} - 1\} \xrightarrow[\text{onto}]{\text{1-to-1}} \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\}}\right] \end{array} \end{array} \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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 35 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9, 10
6	Lambda	parameter: 84 body: 31
7	Operation	operator: 11 operands: 12
8	Operation	operator: 35 operands: 13
9	Operation	operator: 35 operands: 14
10	Operation	operator: 15 operands: 16
11	Literal
12	ExprTuple	40, 17
13	ExprTuple	85, 18
14	ExprTuple	78, 19
15	Literal
16	ExprTuple	20, 81
17	Operation	operator: 21 operand: 27
18	Literal
19	Operation	operator: 23 operands: 24
20	Operation	operator: 25 operand: 78
21	Literal
22	ExprTuple	27
23	Literal
24	ExprTuple	28, 61
25	Literal
26	ExprTuple	78
27	Lambda	parameter: 84 body: 30
28	Literal
29	ExprTuple	84
30	Conditional	value: 31 condition: 32
31	Operation	operator: 33 operands: 34
32	Operation	operator: 35 operands: 36
33	Literal
34	ExprTuple	37, 38, 39
35	Literal
36	ExprTuple	84, 40
37	ExprTuple	41
38	ExprTuple	42
39	ExprTuple	43
40	Operation	operator: 75 operands: 44
41	ExprRange	lambda_map: 45 start_index: 81 end_index: 85
42	ExprRange	lambda_map: 46 start_index: 81 end_index: 85
43	ExprRange	lambda_map: 47 start_index: 81 end_index: 85
44	ExprTuple	48, 49
45	Lambda	parameter: 80 body: 50
46	Lambda	parameter: 80 body: 51
47	Lambda	parameter: 80 body: 53
48	Literal
49	Operation	operator: 54 operands: 55
50	Operation	operator: 59 operands: 56
51	Operation	operator: 57 operands: 58
52	ExprTuple	80
53	Operation	operator: 59 operands: 60
54	Literal
55	ExprTuple	61, 62
56	NamedExprs	element: 63 targets: 66
57	Literal
58	NamedExprs	basis: 64
59	Literal
60	NamedExprs	element: 65 targets: 66
61	Operation	operator: 67 operands: 68
62	Operation	operator: 69 operand: 81
63	Operation	operator: 71 operands: 72
64	Literal
65	Operation	operator: 73 operands: 74
66	Operation	operator: 75 operands: 76
67	Literal
68	ExprTuple	77, 85
69	Literal
70	ExprTuple	81
71	Literal
72	NamedExprs	state: 78 part: 80
73	Literal
74	NamedExprs	state: 79 part: 80
75	Literal
76	ExprTuple	81, 85
77	Literal
78	Variable
79	Operation	operator: 82 operands: 83
80	Variable
81	Literal
82	Literal
83	ExprTuple	84, 85
84	Variable
85	Variable