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, t
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Interval, NaturalPos, one
from proveit.physics.quantum import ket_plus
from proveit.physics.quantum.QPE import QPE1, _U, _ket_u, _psi_t_ket, _s
from proveit.physics.quantum.circuits import Gate, Input, MultiQubitElem, Output, Qcircuit
from proveit.statistics import Prob

# 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 = QPE1(_U, t), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = Conditional(Equals(Prob(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, MultiQubitElem(element = Output(state = _psi_t_ket, 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)]))), one), 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\{\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}_1\left(U, t\right)} & \multiqout{3}{\lvert \psi_{t} \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \qout{\lvert u \rangle}
} \end{array}\right) = 1 \textrm{ if } 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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 75
5	Literal
6	ExprTuple	76, 8
7	Operation	operator: 9 operand: 11
8	Literal
9	Literal
10	ExprTuple	11
11	Operation	operator: 12 operands: 13
12	Literal
13	ExprTuple	14, 15, 16
14	ExprTuple	17, 18
15	ExprTuple	19, 20
16	ExprTuple	21, 22
17	ExprRange	lambda_map: 23 start_index: 75 end_index: 76
18	ExprRange	lambda_map: 24 start_index: 75 end_index: 77
19	ExprRange	lambda_map: 25 start_index: 75 end_index: 76
20	ExprRange	lambda_map: 25 start_index: 65 end_index: 66
21	ExprRange	lambda_map: 26 start_index: 75 end_index: 76
22	ExprRange	lambda_map: 27 start_index: 75 end_index: 77
23	Lambda	parameter: 64 body: 28
24	Lambda	parameter: 64 body: 29
25	Lambda	parameter: 64 body: 30
26	Lambda	parameter: 64 body: 31
27	Lambda	parameter: 64 body: 33
28	Operation	operator: 50 operands: 34
29	Operation	operator: 38 operands: 35
30	Operation	operator: 38 operands: 36
31	Operation	operator: 38 operands: 37
32	ExprTuple	64
33	Operation	operator: 38 operands: 39
34	NamedExprs	state: 40
35	NamedExprs	element: 41 targets: 47
36	NamedExprs	element: 42 targets: 43
37	NamedExprs	element: 44 targets: 45
38	Literal
39	NamedExprs	element: 46 targets: 47
40	Operation	operator: 48 operand: 60
41	Operation	operator: 50 operands: 57
42	Operation	operator: 51 operands: 52
43	Operation	operator: 58 operands: 53
44	Operation	operator: 56 operands: 54
45	Operation	operator: 58 operands: 55
46	Operation	operator: 56 operands: 57
47	Operation	operator: 58 operands: 59
48	Literal
49	ExprTuple	60
50	Literal
51	Literal
52	NamedExprs	operation: 61 part: 64
53	ExprTuple	75, 66
54	NamedExprs	state: 62 part: 64
55	ExprTuple	75, 76
56	Literal
57	NamedExprs	state: 63 part: 64
58	Literal
59	ExprTuple	65, 66
60	Literal
61	Operation	operator: 67 operands: 68
62	Operation	operator: 69 operand: 76
63	Literal
64	Variable
65	Operation	operator: 72 operands: 71
66	Operation	operator: 72 operands: 73
67	Literal
68	ExprTuple	74, 76
69	Literal
70	ExprTuple	76
71	ExprTuple	76, 75
72	Literal
73	ExprTuple	76, 77
74	Literal
75	Literal
76	Variable
77	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 ¶