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
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, _full_domain, _ket_u, _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, _full_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 \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\} ,  \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: 114 end_index: 110
14	ExprRange	lambda_map: 26 start_index: 114 end_index: 99
15	ExprRange	lambda_map: 27 start_index: 114 end_index: 110
16	ExprRange	lambda_map: 27 start_index: 87 end_index: 88
17	ExprRange	lambda_map: 28 start_index: 114 end_index: 110
18	ExprRange	lambda_map: 29 start_index: 114 end_index: 99
19	ExprRange	lambda_map: 30 start_index: 114 end_index: 110
20	ExprRange	lambda_map: 31 start_index: 114 end_index: 99
21	Literal
22	ExprTuple	107, 32
23	Literal
24	ExprTuple	33, 34
25	Lambda	parameter: 86 body: 35
26	Lambda	parameter: 86 body: 36
27	Lambda	parameter: 86 body: 37
28	Lambda	parameter: 86 body: 38
29	Lambda	parameter: 86 body: 39
30	Lambda	parameter: 86 body: 40
31	Lambda	parameter: 86 body: 42
32	Operation	operator: 79 operands: 43
33	Variable
34	Operation	operator: 44 operands: 45
35	Operation	operator: 71 operands: 46
36	Operation	operator: 53 operands: 47
37	Operation	operator: 53 operands: 48
38	Operation	operator: 49 operands: 50
39	Operation	operator: 72 operands: 51
40	Operation	operator: 53 operands: 52
41	ExprTuple	86
42	Operation	operator: 53 operands: 54
43	ExprTuple	55, 96
44	Literal
45	ExprTuple	107, 56
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	Operation	operator: 108 operands: 67
56	Operation	operator: 100 operands: 68
57	Operation	operator: 69 operand: 82
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	ExprTuple	81, 114
68	ExprTuple	104, 110
69	Literal
70	ExprTuple	82
71	Literal
72	Literal
73	NamedExprs	operation: 83 part: 86
74	ExprTuple	114, 88
75	NamedExprs	state: 84 part: 86
76	ExprTuple	114, 110
77	Literal
78	NamedExprs	state: 85 part: 86
79	Literal
80	ExprTuple	87, 88
81	Operation	operator: 112 operand: 96
82	Literal
83	Operation	operator: 90 operands: 91
84	Operation	operator: 92 operands: 93
85	Literal
86	Variable
87	Operation	operator: 108 operands: 94
88	Operation	operator: 108 operands: 95
89	ExprTuple	96
90	Literal
91	ExprTuple	97, 110
92	Literal
93	ExprTuple	98, 110
94	ExprTuple	110, 114
95	ExprTuple	110, 99
96	Operation	operator: 100 operands: 101
97	Literal
98	Operation	operator: 102 operands: 103
99	Literal
100	Literal
101	ExprTuple	104, 105
102	Literal
103	ExprTuple	106, 107
104	Literal
105	Operation	operator: 108 operands: 109
106	Literal
107	Variable
108	Literal
109	ExprTuple	110, 111
110	Literal
111	Operation	operator: 112 operand: 114
112	Literal
113	ExprTuple	114
114	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 ¶