Expression of type Equals ¶

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

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, ExprRange, Variable, VertExprArray, l
from proveit.logic import And, Equals, InSet, TRUE
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z, ket_plus
from proveit.physics.quantum.QPE import ModAdd, QPE, _U, _b_floor, _ket_u, _neg_domain, _s, _s_wire, _t
from proveit.physics.quantum.circuits import Gate, Input, Measure, MultiQubitElem, Output, Qcircuit

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(_t, one)
sub_expr3 = Add(_t, _s)
sub_expr4 = Interval(sub_expr2, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = Interval(one, sub_expr3))
sub_expr6 = Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Input(state = ket_plus), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)], [ExprRange(sub_expr1, sub_expr5, one, _t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(ModAdd(_b_floor, l), _t), part = sub_expr1), targets = Interval(one, _t)), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)]))
sub_expr7 = InSet(l, _neg_domain)
expr = Equals(Conditional(sub_expr6, And(sub_expr7, TRUE)), Conditional(sub_expr6, sub_expr7)).with_wrapping_at(1)

# 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())

\begin{array}{c} \begin{array}{l} \left\{\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert b_{\textit{f}} \oplus l \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 b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\} ,  \top\right.. \\  = \left\{\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert b_{\textit{f}} \oplus l \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 b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\right.. \end{array} \end{array}

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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.	()	(1)	('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',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

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

Expression of type Equals¶

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

Expression of type Equals ¶

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