Expression of type Equals ¶

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 ExprRange, Variable, VertExprArray
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import ket_plus
from proveit.physics.quantum.QPE import QPE, _Psi_circuit, _Psi_ket, _U, _ket_u, _s, _t
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(one, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = sub_expr4)
sub_expr6 = MultiQubitElem(element = Output(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = sub_expr4)
expr = Equals(Prob(_Psi_circuit), 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 = Interval(sub_expr2, sub_expr3)), one, _s)], [ExprRange(sub_expr1, sub_expr5, one, _t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, sub_expr6, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr6, sub_expr2, sub_expr3).with_wrapping_at(2,6)]))))

# 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())

\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \multiqout{3}{\lvert \Psi \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \qout{\lvert u \rangle}
} \end{array}\right) = \textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \multiqout{4}{\lvert \Psi \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle {\otimes} \lvert u \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle {\otimes} \lvert u \rangle}
} \end{array}\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

	core type	sub-expressions
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operand: 8
4	Operation	operator: 6 operand: 9
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	Operation	operator: 11 operands: 10
9	Operation	operator: 11 operands: 12
10	ExprTuple	14, 15, 13
11	Literal
12	ExprTuple	14, 15, 16
13	ExprTuple	17, 18
14	ExprTuple	19, 20
15	ExprTuple	21, 22
16	ExprTuple	23, 24
17	ExprRange	lambda_map: 25 start_index: 80 end_index: 84
18	ExprRange	lambda_map: 26 start_index: 80 end_index: 85
19	ExprRange	lambda_map: 27 start_index: 80 end_index: 84
20	ExprRange	lambda_map: 28 start_index: 80 end_index: 85
21	ExprRange	lambda_map: 29 start_index: 80 end_index: 84
22	ExprRange	lambda_map: 29 start_index: 68 end_index: 72
23	ExprRange	lambda_map: 30 start_index: 80 end_index: 84
24	ExprRange	lambda_map: 30 start_index: 68 end_index: 72
25	Lambda	parameter: 71 body: 31
26	Lambda	parameter: 71 body: 32
27	Lambda	parameter: 71 body: 33
28	Lambda	parameter: 71 body: 34
29	Lambda	parameter: 71 body: 35
30	Lambda	parameter: 71 body: 37
31	Operation	operator: 43 operands: 38
32	Operation	operator: 43 operands: 39
33	Operation	operator: 58 operands: 40
34	Operation	operator: 43 operands: 41
35	Operation	operator: 43 operands: 42
36	ExprTuple	71
37	Operation	operator: 43 operands: 44
38	NamedExprs	element: 45 targets: 46
39	NamedExprs	element: 47 targets: 50
40	NamedExprs	state: 48
41	NamedExprs	element: 49 targets: 50
42	NamedExprs	element: 51 targets: 53
43	Literal
44	NamedExprs	element: 52 targets: 53
45	Operation	operator: 63 operands: 54
46	Operation	operator: 65 operands: 55
47	Operation	operator: 63 operands: 59
48	Operation	operator: 56 operand: 67
49	Operation	operator: 58 operands: 59
50	Operation	operator: 65 operands: 60
51	Operation	operator: 61 operands: 62
52	Operation	operator: 63 operands: 64
53	Operation	operator: 65 operands: 66
54	NamedExprs	state: 82 part: 71
55	ExprTuple	80, 84
56	Literal
57	ExprTuple	67
58	Literal
59	NamedExprs	state: 83 part: 71
60	ExprTuple	68, 72
61	Literal
62	NamedExprs	operation: 69 part: 71
63	Literal
64	NamedExprs	state: 70 part: 71
65	Literal
66	ExprTuple	80, 72
67	Literal
68	Operation	operator: 78 operands: 73
69	Operation	operator: 74 operands: 75
70	Operation	operator: 76 operands: 77
71	Variable
72	Operation	operator: 78 operands: 79
73	ExprTuple	84, 80
74	Literal
75	ExprTuple	81, 84
76	Literal
77	ExprTuple	82, 83
78	Literal
79	ExprTuple	84, 85
80	Literal
81	Literal
82	Literal
83	Literal
84	Literal
85	Literal

Expression of type Equals¶

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

Expression of type Equals ¶

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