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 Equals, Forall, InSet
from proveit.numbers import Abs, Exp, two
from proveit.physics.quantum import NumBra, Qmult, 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 Prob

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [var_ket_psi], instance_expr = Equals(Prob(register_meas), Exp(Abs(Qmult(NumBra(n, m), var_ket_psi)), two)), domain = m_ket_domain, condition = normalized_var_ket_psi), InSet(n, m_bit_interval))

# 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_{\lvert \psi \rangle \in \mathbb{C}^{2^{m}}~|~\left \|\lvert \psi \rangle\right \| = 1}~\left(\textrm{Pr}\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) = \left|{_{m}}\langle n \rvert \thinspace \lvert \psi \rangle\right|^{2}\right) \textrm{ if } n \in \{0~\ldotp \ldotp~2^{m} - 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 operand: 6
2	Operation	operator: 27 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	89, 7
6	Lambda	parameter: 83 body: 8
7	Operation	operator: 81 operands: 9
8	Conditional	value: 10 condition: 11
9	ExprTuple	12, 13
10	Operation	operator: 29 operands: 14
11	Operation	operator: 15 operands: 16
12	Literal
13	Operation	operator: 17 operands: 18
14	ExprTuple	19, 20
15	Literal
16	ExprTuple	21, 22
17	Literal
18	ExprTuple	50, 23
19	Operation	operator: 24 operand: 33
20	Operation	operator: 56 operands: 26
21	Operation	operator: 27 operands: 28
22	Operation	operator: 29 operands: 30
23	Operation	operator: 31 operand: 86
24	Literal
25	ExprTuple	33
26	ExprTuple	34, 62
27	Literal
28	ExprTuple	83, 35
29	Literal
30	ExprTuple	36, 86
31	Literal
32	ExprTuple	86
33	Operation	operator: 37 operands: 38
34	Operation	operator: 39 operand: 48
35	Operation	operator: 41 operands: 42
36	Operation	operator: 43 operand: 83
37	Literal
38	ExprTuple	45, 46, 47
39	Literal
40	ExprTuple	48
41	Literal
42	ExprTuple	49, 50
43	Literal
44	ExprTuple	83
45	ExprTuple	51
46	ExprTuple	52
47	ExprTuple	53
48	Operation	operator: 54 operands: 55
49	Literal
50	Operation	operator: 56 operands: 57
51	ExprRange	lambda_map: 58 start_index: 86 end_index: 90
52	ExprRange	lambda_map: 59 start_index: 86 end_index: 90
53	ExprRange	lambda_map: 60 start_index: 86 end_index: 90
54	Literal
55	ExprTuple	61, 83
56	Literal
57	ExprTuple	62, 90
58	Lambda	parameter: 85 body: 63
59	Lambda	parameter: 85 body: 64
60	Lambda	parameter: 85 body: 66
61	Operation	operator: 67 operands: 88
62	Literal
63	Operation	operator: 71 operands: 68
64	Operation	operator: 69 operands: 70
65	ExprTuple	85
66	Operation	operator: 71 operands: 72
67	Literal
68	NamedExprs	element: 73 targets: 76
69	Literal
70	NamedExprs	basis: 74
71	Literal
72	NamedExprs	element: 75 targets: 76
73	Operation	operator: 77 operands: 78
74	Literal
75	Operation	operator: 79 operands: 80
76	Operation	operator: 81 operands: 82
77	Literal
78	NamedExprs	state: 83 part: 85
79	Literal
80	NamedExprs	state: 84 part: 85
81	Literal
82	ExprTuple	86, 90
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 Conditional¶

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

Expression of type Conditional ¶

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