Expression of type Lambda ¶

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 = Lambda([m, var_ket_psi], 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)))

# 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(m, \lvert \psi \rangle\right) \mapsto \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()

# display the expression information
stored_expr.expr_info()

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

Expression of type Lambda¶

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

Expression of type Lambda ¶

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