Expression of type Conditional ¶

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, e, l
from proveit.logic import And, InSet, Union
from proveit.numbers import Add, Interval, ModAbs, greater, 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, _pos_domain, _s, _s_wire, _t, _two_pow_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))
expr = Conditional(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)])), And(InSet(l, Union(_neg_domain, _pos_domain)), greater(ModAbs(l, _two_pow_t), e)))

# 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\{\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 \left(\{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\} \cup \{e + 1~\ldotp \ldotp~2^{t - 1}\}\right) ,  \left|l\right|_{\textup{mod}\thinspace 2^{t}} > e\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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8, 9, 10
5	Literal
6	ExprTuple	11, 12
7	ExprTuple	13, 14
8	ExprTuple	15, 16
9	ExprTuple	17, 18
10	ExprTuple	19, 20
11	Operation	operator: 21 operands: 22
12	Operation	operator: 23 operands: 24
13	ExprRange	lambda_map: 25 start_index: 123 end_index: 119
14	ExprRange	lambda_map: 26 start_index: 123 end_index: 104
15	ExprRange	lambda_map: 27 start_index: 123 end_index: 119
16	ExprRange	lambda_map: 27 start_index: 90 end_index: 91
17	ExprRange	lambda_map: 28 start_index: 123 end_index: 119
18	ExprRange	lambda_map: 29 start_index: 123 end_index: 104
19	ExprRange	lambda_map: 30 start_index: 123 end_index: 119
20	ExprRange	lambda_map: 31 start_index: 123 end_index: 104
21	Literal
22	ExprTuple	112, 32
23	Literal
24	ExprTuple	110, 33
25	Lambda	parameter: 89 body: 34
26	Lambda	parameter: 89 body: 35
27	Lambda	parameter: 89 body: 36
28	Lambda	parameter: 89 body: 37
29	Lambda	parameter: 89 body: 38
30	Lambda	parameter: 89 body: 39
31	Lambda	parameter: 89 body: 41
32	Operation	operator: 42 operands: 43
33	Operation	operator: 44 operands: 45
34	Operation	operator: 73 operands: 46
35	Operation	operator: 53 operands: 47
36	Operation	operator: 53 operands: 48
37	Operation	operator: 49 operands: 50
38	Operation	operator: 74 operands: 51
39	Operation	operator: 53 operands: 52
40	ExprTuple	89
41	Operation	operator: 53 operands: 54
42	Literal
43	ExprTuple	55, 56
44	Literal
45	ExprTuple	112, 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	Operation	operator: 81 operands: 68
56	Operation	operator: 81 operands: 69
57	Operation	operator: 113 operands: 70
58	Operation	operator: 71 operand: 85
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	ExprTuple	83, 84
69	ExprTuple	101, 109
70	ExprTuple	115, 119
71	Literal
72	ExprTuple	85
73	Literal
74	Literal
75	NamedExprs	operation: 86 part: 89
76	ExprTuple	123, 91
77	NamedExprs	state: 87 part: 89
78	ExprTuple	123, 119
79	Literal
80	NamedExprs	state: 88 part: 89
81	Literal
82	ExprTuple	90, 91
83	Operation	operator: 117 operands: 92
84	Operation	operator: 121 operand: 101
85	Literal
86	Operation	operator: 94 operands: 95
87	Operation	operator: 96 operands: 97
88	Literal
89	Variable
90	Operation	operator: 117 operands: 98
91	Operation	operator: 117 operands: 99
92	ExprTuple	100, 123
93	ExprTuple	101
94	Literal
95	ExprTuple	102, 119
96	Literal
97	ExprTuple	103, 119
98	ExprTuple	119, 123
99	ExprTuple	119, 104
100	Operation	operator: 121 operand: 109
101	Operation	operator: 117 operands: 106
102	Literal
103	Operation	operator: 107 operands: 108
104	Literal
105	ExprTuple	109
106	ExprTuple	110, 123
107	Literal
108	ExprTuple	111, 112
109	Operation	operator: 113 operands: 114
110	Variable
111	Literal
112	Variable
113	Literal
114	ExprTuple	115, 116
115	Literal
116	Operation	operator: 117 operands: 118
117	Literal
118	ExprTuple	119, 120
119	Literal
120	Operation	operator: 121 operand: 123
121	Literal
122	ExprTuple	123
123	Literal

Expression of type Conditional¶

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

Expression of type Conditional ¶

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