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 InSet
from proveit.numbers import Add, Exp, Interval, one, two
from proveit.physics.quantum import I
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import QPE, QPE1
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 = Add(t, one)
sub_expr4 = Interval(one, sub_expr2)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE(U, t), part = sub_expr1), targets = sub_expr4)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE1(U, t), part = sub_expr1), targets = sub_expr4)
expr = Conditional(QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr5, one, t), ExprRange(sub_expr1, sub_expr5, sub_expr3, sub_expr2)])), Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr6, one, t), ExprRange(sub_expr1, sub_expr6, sub_expr3, sub_expr2)], [ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(t), part = sub_expr1), targets = Interval(one, t)), one, t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, s)]))), InSet(U, Unitary(Exp(two, s))))

# 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\{\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \multigate{1}{\textrm{QPE}\left(U, t\right)} & { /^{t} } \qw \\
& \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \multigate{1}{\textrm{QPE}_1\left(U, t\right)} & \gate{{\mathrm {FT}}^{\dag}_{t}} & { /^{t} } \qw \\
& \ghost{\textrm{QPE}_1\left(U, t\right)} & { /^{s} } \qw & { /^{s} } \qw
} \end{array}\right) \textrm{ if } U \in \textrm{U}\left(2^{s}\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
5	Literal
6	ExprTuple	70, 9
7	Operation	operator: 11 operand: 15
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operand: 18
10	ExprTuple	15
11	Literal
12	ExprTuple	16, 17
13	Literal
14	ExprTuple	18
15	ExprTuple	19, 20
16	ExprTuple	21, 22
17	ExprTuple	23, 24
18	Operation	operator: 25 operands: 26
19	ExprRange	lambda_map: 27 start_index: 62 end_index: 72
20	ExprRange	lambda_map: 27 start_index: 29 end_index: 59
21	ExprRange	lambda_map: 28 start_index: 62 end_index: 72
22	ExprRange	lambda_map: 28 start_index: 29 end_index: 59
23	ExprRange	lambda_map: 30 start_index: 62 end_index: 72
24	ExprRange	lambda_map: 31 start_index: 62 end_index: 71
25	Literal
26	ExprTuple	32, 71
27	Lambda	parameter: 61 body: 33
28	Lambda	parameter: 61 body: 34
29	Operation	operator: 66 operands: 35
30	Lambda	parameter: 61 body: 36
31	Lambda	parameter: 61 body: 38
32	Literal
33	Operation	operator: 41 operands: 39
34	Operation	operator: 41 operands: 40
35	ExprTuple	72, 62
36	Operation	operator: 41 operands: 42
37	ExprTuple	61
38	Operation	operator: 53 operands: 43
39	NamedExprs	element: 44 targets: 46
40	NamedExprs	element: 45 targets: 46
41	Literal
42	NamedExprs	element: 47 targets: 48
43	NamedExprs	operation: 49
44	Operation	operator: 53 operands: 50
45	Operation	operator: 53 operands: 51
46	Operation	operator: 55 operands: 52
47	Operation	operator: 53 operands: 54
48	Operation	operator: 55 operands: 56
49	Literal
50	NamedExprs	operation: 57 part: 61
51	NamedExprs	operation: 58 part: 61
52	ExprTuple	62, 59
53	Literal
54	NamedExprs	operation: 60 part: 61
55	Literal
56	ExprTuple	62, 72
57	Operation	operator: 63 operands: 65
58	Operation	operator: 64 operands: 65
59	Operation	operator: 66 operands: 67
60	Operation	operator: 68 operand: 72
61	Variable
62	Literal
63	Literal
64	Literal
65	ExprTuple	70, 72
66	Literal
67	ExprTuple	72, 71
68	Literal
69	ExprTuple	72
70	Variable
71	Variable
72	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 ¶