Expression of type And ¶

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

In [1]:

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, l, m
from proveit.logic import And, Bijections, InSet
from proveit.numbers import Add, Mod
from proveit.physics.quantum.QPE import _Omega, _b_floor, _full_domain, _m_domain, _phase_est_circuit, _two_pow_t

In [2]:

# build up the expression from sub-expressions
expr = And(InSet(Lambda(l, Mod(Add(_b_floor, l), _two_pow_t)), Bijections(_full_domain, _m_domain)), InSet(Lambda(m, _phase_est_circuit), Bijections(_m_domain, _Omega)))

expr:

In [3]:

# 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

In [4]:

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left[l \mapsto \left(\left(b_{\textit{f}} + l\right) ~\textup{mod}~ 2^{t}\right)\right] \in \left[\{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\} \xrightarrow[\text{onto}]{\text{1-to-1}} \{0~\ldotp \ldotp~2^{t} - 1\}\right]\right) \land \left(\left[m \mapsto \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right)\right] \in \left[\{0~\ldotp \ldotp~2^{t} - 1\} \xrightarrow[\text{onto}]{\text{1-to-1}} \Omega\right]\right)

In [5]:

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

In [6]:

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Lambda	parameter: 46 body: 13
9	Operation	operator: 17 operands: 14
10	Lambda	parameter: 121 body: 16
11	Operation	operator: 17 operands: 18
12	ExprTuple	46
13	Operation	operator: 19 operands: 20
14	ExprTuple	21, 24
15	ExprTuple	121
16	Operation	operator: 22 operands: 23
17	Literal
18	ExprTuple	24, 25
19	Literal
20	ExprTuple	26, 65
21	Operation	operator: 100 operands: 27
22	Literal
23	ExprTuple	28, 29, 30, 31
24	Operation	operator: 100 operands: 32
25	Literal
26	Operation	operator: 117 operands: 33
27	ExprTuple	34, 77
28	ExprTuple	35, 36
29	ExprTuple	37, 38
30	ExprTuple	39, 40
31	ExprTuple	41, 42
32	ExprTuple	43, 44
33	ExprTuple	45, 46
34	Operation	operator: 117 operands: 47
35	ExprRange	lambda_map: 48 start_index: 126 end_index: 122
36	ExprRange	lambda_map: 49 start_index: 126 end_index: 123
37	ExprRange	lambda_map: 50 start_index: 126 end_index: 122
38	ExprRange	lambda_map: 50 start_index: 109 end_index: 110
39	ExprRange	lambda_map: 51 start_index: 126 end_index: 122
40	ExprRange	lambda_map: 52 start_index: 126 end_index: 123
41	ExprRange	lambda_map: 53 start_index: 126 end_index: 122
42	ExprRange	lambda_map: 54 start_index: 126 end_index: 123
43	Literal
44	Operation	operator: 117 operands: 55
45	Literal
46	Variable
47	ExprTuple	56, 126
48	Lambda	parameter: 108 body: 57
49	Lambda	parameter: 108 body: 58
50	Lambda	parameter: 108 body: 59
51	Lambda	parameter: 108 body: 60
52	Lambda	parameter: 108 body: 61
53	Lambda	parameter: 108 body: 62
54	Lambda	parameter: 108 body: 64
55	ExprTuple	65, 119
56	Operation	operator: 124 operand: 77
57	Operation	operator: 92 operands: 67
58	Operation	operator: 74 operands: 68
59	Operation	operator: 74 operands: 69
60	Operation	operator: 70 operands: 71
61	Operation	operator: 93 operands: 72
62	Operation	operator: 74 operands: 73
63	ExprTuple	108
64	Operation	operator: 74 operands: 75
65	Operation	operator: 88 operands: 76
66	ExprTuple	77
67	NamedExprs	state: 78
68	NamedExprs	element: 79 targets: 87
69	NamedExprs	element: 80 targets: 81
70	Literal
71	NamedExprs	basis: 82
72	NamedExprs	operation: 83
73	NamedExprs	element: 84 targets: 85
74	Literal
75	NamedExprs	element: 86 targets: 87
76	ExprTuple	102, 122
77	Operation	operator: 88 operands: 89
78	Operation	operator: 90 operand: 104
79	Operation	operator: 92 operands: 99
80	Operation	operator: 93 operands: 94
81	Operation	operator: 100 operands: 95
82	Literal
83	Literal
84	Operation	operator: 98 operands: 96
85	Operation	operator: 100 operands: 97
86	Operation	operator: 98 operands: 99
87	Operation	operator: 100 operands: 101
88	Literal
89	ExprTuple	102, 103
90	Literal
91	ExprTuple	104
92	Literal
93	Literal
94	NamedExprs	operation: 105 part: 108
95	ExprTuple	126, 110
96	NamedExprs	state: 106 part: 108
97	ExprTuple	126, 122
98	Literal
99	NamedExprs	state: 107 part: 108
100	Literal
101	ExprTuple	109, 110
102	Literal
103	Operation	operator: 117 operands: 111
104	Literal
105	Operation	operator: 112 operands: 113
106	Operation	operator: 114 operands: 115
107	Literal
108	Variable
109	Operation	operator: 117 operands: 116
110	Operation	operator: 117 operands: 118
111	ExprTuple	122, 119
112	Literal
113	ExprTuple	120, 122
114	Literal
115	ExprTuple	121, 122
116	ExprTuple	122, 126
117	Literal
118	ExprTuple	122, 123
119	Operation	operator: 124 operand: 126
120	Literal
121	Variable
122	Literal
123	Literal
124	Literal
125	ExprTuple	126
126	Literal

Expression of type And¶

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

Expression of type And ¶

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