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, l
from proveit.logic import InSet
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))
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)])), InSet(l, _neg_domain))

# 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~-\left(e + 1\right)\}\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	104, 11
7	ExprTuple	12, 13
8	ExprTuple	14, 15
9	ExprTuple	16, 17
10	ExprTuple	18, 19
11	Operation	operator: 73 operands: 20
12	ExprRange	lambda_map: 21 start_index: 107 end_index: 101
13	ExprRange	lambda_map: 22 start_index: 107 end_index: 96
14	ExprRange	lambda_map: 23 start_index: 107 end_index: 101
15	ExprRange	lambda_map: 23 start_index: 82 end_index: 83
16	ExprRange	lambda_map: 24 start_index: 107 end_index: 101
17	ExprRange	lambda_map: 25 start_index: 107 end_index: 96
18	ExprRange	lambda_map: 26 start_index: 107 end_index: 101
19	ExprRange	lambda_map: 27 start_index: 107 end_index: 96
20	ExprTuple	28, 29
21	Lambda	parameter: 81 body: 30
22	Lambda	parameter: 81 body: 31
23	Lambda	parameter: 81 body: 32
24	Lambda	parameter: 81 body: 33
25	Lambda	parameter: 81 body: 34
26	Lambda	parameter: 81 body: 35
27	Lambda	parameter: 81 body: 37
28	Operation	operator: 97 operands: 38
29	Operation	operator: 105 operand: 50
30	Operation	operator: 65 operands: 40
31	Operation	operator: 47 operands: 41
32	Operation	operator: 47 operands: 42
33	Operation	operator: 43 operands: 44
34	Operation	operator: 66 operands: 45
35	Operation	operator: 47 operands: 46
36	ExprTuple	81
37	Operation	operator: 47 operands: 48
38	ExprTuple	49, 107
39	ExprTuple	50
40	NamedExprs	state: 51
41	NamedExprs	element: 52 targets: 60
42	NamedExprs	element: 53 targets: 54
43	Literal
44	NamedExprs	basis: 55
45	NamedExprs	operation: 56
46	NamedExprs	element: 57 targets: 58
47	Literal
48	NamedExprs	element: 59 targets: 60
49	Operation	operator: 105 operand: 75
50	Operation	operator: 97 operands: 62
51	Operation	operator: 63 operand: 77
52	Operation	operator: 65 operands: 72
53	Operation	operator: 66 operands: 67
54	Operation	operator: 73 operands: 68
55	Literal
56	Literal
57	Operation	operator: 71 operands: 69
58	Operation	operator: 73 operands: 70
59	Operation	operator: 71 operands: 72
60	Operation	operator: 73 operands: 74
61	ExprTuple	75
62	ExprTuple	76, 107
63	Literal
64	ExprTuple	77
65	Literal
66	Literal
67	NamedExprs	operation: 78 part: 81
68	ExprTuple	107, 83
69	NamedExprs	state: 79 part: 81
70	ExprTuple	107, 101
71	Literal
72	NamedExprs	state: 80 part: 81
73	Literal
74	ExprTuple	82, 83
75	Operation	operator: 84 operands: 85
76	Variable
77	Literal
78	Operation	operator: 86 operands: 87
79	Operation	operator: 88 operands: 89
80	Literal
81	Variable
82	Operation	operator: 97 operands: 90
83	Operation	operator: 97 operands: 91
84	Literal
85	ExprTuple	92, 93
86	Literal
87	ExprTuple	94, 101
88	Literal
89	ExprTuple	95, 101
90	ExprTuple	101, 107
91	ExprTuple	101, 96
92	Literal
93	Operation	operator: 97 operands: 98
94	Literal
95	Operation	operator: 99 operands: 100
96	Literal
97	Literal
98	ExprTuple	101, 102
99	Literal
100	ExprTuple	103, 104
101	Literal
102	Operation	operator: 105 operand: 107
103	Literal
104	Variable
105	Literal
106	ExprTuple	107
107	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 ¶