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, U, Variable, VertExprArray, s, t
from proveit.linear_algebra import Unitary
from proveit.logic import And, Forall, InSet
from proveit.numbers import Add, Exp, Interval, NaturalPos, one, two
from proveit.physics.quantum.QPE import QPE1, QPE1_U_t_circuit
from proveit.physics.quantum.circuits import Gate, MultiQubitElem, Qcircuit, QcircuitEquiv

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(t, s)
sub_expr3 = MultiQubitElem(element = Gate(operation = QPE1(U, t), part = sub_expr1), targets = Interval(one, sub_expr2))
expr = Conditional(Forall(instance_param_or_params = [U], instance_expr = QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr3, one, t), ExprRange(sub_expr1, sub_expr3, Add(t, one), sub_expr2)])), QPE1_U_t_circuit), domain = Unitary(Exp(two, s))), And(InSet(s, NaturalPos), InSet(t, NaturalPos)))

# 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\{\forall_{U \in \textrm{U}\left(2^{s}\right)}~\left(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \multigate{1}{\textrm{QPE}_1\left(U, t\right)} & { /^{t} } \qw \\
& \ghost{\textrm{QPE}_1\left(U, t\right)} & { /^{s} } \qw
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \control{} \qw \qwx[1] & \qw & \gate{\cdots} \qwx[1] & \qw & \qw \\
& \qw \qwx[1] & \control{} \qw \qwx[1] & \gate{\cdots} \qwx[1] & \qw & \qw \\
& \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} & \qw \\
& \qw \qwx[1] & \qw \qwx[1] & \gate{\cdots} \qwx[1] & \control{} \qw \qwx[1] & \qw \\
& \gate{U^{2^{t - 1}}} & \gate{U^{2^{t - 2}}} & \gate{\cdots} & \gate{U^{2^{0}}} & { /^{s} } \qw
} \end{array}\right)\right) \textrm{ if } s \in \mathbb{N}^+ ,  t \in \mathbb{N}^+\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 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 93 body: 11
8	Operation	operator: 19 operands: 12
9	Operation	operator: 19 operands: 13
10	ExprTuple	93
11	Conditional	value: 14 condition: 15
12	ExprTuple	95, 16
13	ExprTuple	103, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Literal
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	93, 23
21	Operation	operator: 25 operand: 29
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operand: 31
24	ExprTuple	29
25	Literal
26	ExprTuple	30
27	Literal
28	ExprTuple	31
29	ExprTuple	32, 33
30	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
31	Operation	operator: 97 operands: 37
32	ExprRange	lambda_map: 38 start_index: 104 end_index: 103
33	ExprRange	lambda_map: 38 start_index: 96 end_index: 81
34	Lambda	parameter: 107 body: 39
35	Operation	operator: 99 operands: 40
36	Literal
37	ExprTuple	101, 95
38	Lambda	parameter: 86 body: 41
39	ExprTuple	42, 43
40	ExprTuple	44, 104
41	Operation	operator: 73 operands: 45
42	ExprRange	lambda_map: 46 start_index: 104 end_index: 103
43	ExprRange	lambda_map: 47 start_index: 104 end_index: 95
44	Operation	operator: 105 operand: 103
45	NamedExprs	element: 49 targets: 50
46	Lambda	parameter: 86 body: 51
47	Lambda	parameter: 86 body: 53
48	ExprTuple	103
49	Operation	operator: 76 operands: 54
50	Operation	operator: 71 operands: 55
51	Operation	operator: 56 operands: 57
52	ExprTuple	86
53	Operation	operator: 73 operands: 58
54	NamedExprs	operation: 59 part: 86
55	ExprTuple	104, 81
56	Literal
57	ExprTuple	60, 61
58	NamedExprs	element: 62 targets: 63
59	Operation	operator: 64 operands: 65
60	Conditional	value: 66 condition: 67
61	Conditional	value: 68 condition: 69
62	Operation	operator: 76 operands: 70
63	Operation	operator: 71 operands: 72
64	Literal
65	ExprTuple	93, 103
66	Operation	operator: 73 operands: 74
67	Operation	operator: 75 operands: 79
68	Operation	operator: 76 operands: 77
69	Operation	operator: 78 operands: 79
70	NamedExprs	operation: 80 part: 86
71	Literal
72	ExprTuple	96, 81
73	Literal
74	NamedExprs	element: 82 targets: 83
75	Literal
76	Literal
77	NamedExprs	operation: 84
78	Literal
79	ExprTuple	85, 86
80	Operation	operator: 87 operands: 88
81	Operation	operator: 99 operands: 89
82	Literal
83	Operation	operator: 90 operand: 96
84	Literal
85	Operation	operator: 99 operands: 92
86	Variable
87	Literal
88	ExprTuple	93, 94
89	ExprTuple	103, 95
90	Literal
91	ExprTuple	96
92	ExprTuple	107, 103
93	Variable
94	Operation	operator: 97 operands: 98
95	Variable
96	Operation	operator: 99 operands: 100
97	Literal
98	ExprTuple	101, 102
99	Literal
100	ExprTuple	103, 104
101	Literal
102	Operation	operator: 105 operand: 107
103	Variable
104	Literal
105	Literal
106	ExprTuple	107
107	Variable

Expression of type Conditional¶

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

Expression of type Conditional ¶

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