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, _pos_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 = InSet(l, _pos_domain)
sub_expr7 = 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)]))
expr = Equals(Conditional(sub_expr7, And(sub_expr6, TRUE)), Conditional(sub_expr7, sub_expr6)).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 \{e + 1~\ldotp \ldotp~2^{t - 1}\} ,  \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 \{e + 1~\ldotp \ldotp~2^{t - 1}\}\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	109, 27
19	ExprRange	lambda_map: 28 start_index: 105 end_index: 103
20	ExprRange	lambda_map: 29 start_index: 105 end_index: 104
21	ExprRange	lambda_map: 30 start_index: 105 end_index: 103
22	ExprRange	lambda_map: 30 start_index: 89 end_index: 90
23	ExprRange	lambda_map: 31 start_index: 105 end_index: 103
24	ExprRange	lambda_map: 32 start_index: 105 end_index: 104
25	ExprRange	lambda_map: 33 start_index: 105 end_index: 103
26	ExprRange	lambda_map: 34 start_index: 105 end_index: 104
27	Operation	operator: 81 operands: 35
28	Lambda	parameter: 88 body: 36
29	Lambda	parameter: 88 body: 37
30	Lambda	parameter: 88 body: 38
31	Lambda	parameter: 88 body: 39
32	Lambda	parameter: 88 body: 40
33	Lambda	parameter: 88 body: 41
34	Lambda	parameter: 88 body: 43
35	ExprTuple	44, 45
36	Operation	operator: 73 operands: 46
37	Operation	operator: 53 operands: 47
38	Operation	operator: 53 operands: 48
39	Operation	operator: 49 operands: 50
40	Operation	operator: 74 operands: 51
41	Operation	operator: 53 operands: 52
42	ExprTuple	88
43	Operation	operator: 53 operands: 54
44	Operation	operator: 97 operands: 55
45	Operation	operator: 56 operands: 57
46	NamedExprs	state: 58
47	NamedExprs	element: 59 targets: 67
48	NamedExprs	element: 60 targets: 61
49	Literal
50	NamedExprs	basis: 62
51	NamedExprs	operation: 63
52	NamedExprs	element: 64 targets: 65
53	Literal
54	NamedExprs	element: 66 targets: 67
55	ExprTuple	68, 105
56	Literal
57	ExprTuple	69, 70
58	Operation	operator: 71 operand: 84
59	Operation	operator: 73 operands: 80
60	Operation	operator: 74 operands: 75
61	Operation	operator: 81 operands: 76
62	Literal
63	Literal
64	Operation	operator: 79 operands: 77
65	Operation	operator: 81 operands: 78
66	Operation	operator: 79 operands: 80
67	Operation	operator: 81 operands: 82
68	Variable
69	Literal
70	Operation	operator: 97 operands: 83
71	Literal
72	ExprTuple	84
73	Literal
74	Literal
75	NamedExprs	operation: 85 part: 88
76	ExprTuple	105, 90
77	NamedExprs	state: 86 part: 88
78	ExprTuple	105, 103
79	Literal
80	NamedExprs	state: 87 part: 88
81	Literal
82	ExprTuple	89, 90
83	ExprTuple	103, 91
84	Literal
85	Operation	operator: 92 operands: 93
86	Operation	operator: 94 operands: 95
87	Literal
88	Variable
89	Operation	operator: 97 operands: 96
90	Operation	operator: 97 operands: 98
91	Operation	operator: 99 operand: 105
92	Literal
93	ExprTuple	101, 103
94	Literal
95	ExprTuple	102, 103
96	ExprTuple	103, 105
97	Literal
98	ExprTuple	103, 104
99	Literal
100	ExprTuple	105
101	Literal
102	Operation	operator: 106 operands: 107
103	Literal
104	Literal
105	Literal
106	Literal
107	ExprTuple	108, 109
108	Literal
109	Variable

Expression of type Equals¶

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

Expression of type Equals ¶

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