Expression of type Forall ¶

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 Lambda, m, n
from proveit.logic import Bijections, Forall, 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 = Forall(instance_param_or_params = [m, var_ket_psi], instance_expr = 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), domains = [NaturalPos, m_ket_domain], condition = 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())

\forall_{m \in \mathbb{N}^+, \lvert \psi \rangle \in \mathbb{C}^{2^{m}}~|~\left \|\lvert \psi \rangle\right \| = 1}~\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}\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

	core type	sub-expressions
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	90, 83
5	Conditional	value: 6 condition: 7
6	Operation	operator: 40 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14, 15
11	Lambda	parameter: 89 body: 36
12	Operation	operator: 16 operands: 17
13	Operation	operator: 40 operands: 18
14	Operation	operator: 40 operands: 19
15	Operation	operator: 20 operands: 21
16	Literal
17	ExprTuple	45, 22
18	ExprTuple	90, 23
19	ExprTuple	83, 24
20	Literal
21	ExprTuple	25, 86
22	Operation	operator: 26 operand: 32
23	Literal
24	Operation	operator: 28 operands: 29
25	Operation	operator: 30 operand: 83
26	Literal
27	ExprTuple	32
28	Literal
29	ExprTuple	33, 66
30	Literal
31	ExprTuple	83
32	Lambda	parameter: 89 body: 35
33	Literal
34	ExprTuple	89
35	Conditional	value: 36 condition: 37
36	Operation	operator: 38 operands: 39
37	Operation	operator: 40 operands: 41
38	Literal
39	ExprTuple	42, 43, 44
40	Literal
41	ExprTuple	89, 45
42	ExprTuple	46
43	ExprTuple	47
44	ExprTuple	48
45	Operation	operator: 80 operands: 49
46	ExprRange	lambda_map: 50 start_index: 86 end_index: 90
47	ExprRange	lambda_map: 51 start_index: 86 end_index: 90
48	ExprRange	lambda_map: 52 start_index: 86 end_index: 90
49	ExprTuple	53, 54
50	Lambda	parameter: 85 body: 55
51	Lambda	parameter: 85 body: 56
52	Lambda	parameter: 85 body: 58
53	Literal
54	Operation	operator: 59 operands: 60
55	Operation	operator: 64 operands: 61
56	Operation	operator: 62 operands: 63
57	ExprTuple	85
58	Operation	operator: 64 operands: 65
59	Literal
60	ExprTuple	66, 67
61	NamedExprs	element: 68 targets: 71
62	Literal
63	NamedExprs	basis: 69
64	Literal
65	NamedExprs	element: 70 targets: 71
66	Operation	operator: 72 operands: 73
67	Operation	operator: 74 operand: 86
68	Operation	operator: 76 operands: 77
69	Literal
70	Operation	operator: 78 operands: 79
71	Operation	operator: 80 operands: 81
72	Literal
73	ExprTuple	82, 90
74	Literal
75	ExprTuple	86
76	Literal
77	NamedExprs	state: 83 part: 85
78	Literal
79	NamedExprs	state: 84 part: 85
80	Literal
81	ExprTuple	86, 90
82	Literal
83	Variable
84	Operation	operator: 87 operands: 88
85	Variable
86	Literal
87	Literal
88	ExprTuple	89, 90
89	Variable
90	Variable

Expression of type Forall¶

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

Expression of type Forall ¶

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