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 I
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _psi__t_ket, _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 = Interval(one, _t)
sub_expr3 = Add(_t, one)
sub_expr4 = Add(_t, _s)
sub_expr5 = Interval(sub_expr3, sub_expr4)
sub_expr6 = MultiQubitElem(element = Input(state = TensorProd(_psi__t_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr4))
sub_expr7 = [ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, _s)]
sub_expr8 = [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _Psi_ket, part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr5), one, _s)]
expr = Equals(Prob(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _psi__t_ket, part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr5), one, _s)], sub_expr7, sub_expr8))), Prob(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr6, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr6, sub_expr3, sub_expr4).with_wrapping_at(2,6)], sub_expr7, sub_expr8))))

# 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 \psi_{t} \rangle} & \gate{{\mathrm {FT}}^{\dag}_{t}} & \qout{\lvert \Psi \rangle} \\
\qin{\lvert u \rangle} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right) = \textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{1}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} & \gate{{\mathrm {FT}}^{\dag}_{t}} & \qout{\lvert \Psi \rangle} \\
\ghostqin{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} & { /^{s} } \qw & \qout{\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	13, 15, 16
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: 84 end_index: 88
18	ExprRange	lambda_map: 26 start_index: 84 end_index: 85
19	ExprRange	lambda_map: 27 start_index: 84 end_index: 88
20	ExprRange	lambda_map: 27 start_index: 74 end_index: 75
21	ExprRange	lambda_map: 28 start_index: 84 end_index: 88
22	ExprRange	lambda_map: 29 start_index: 84 end_index: 85
23	ExprRange	lambda_map: 30 start_index: 84 end_index: 88
24	ExprRange	lambda_map: 31 start_index: 84 end_index: 85
25	Lambda	parameter: 73 body: 32
26	Lambda	parameter: 73 body: 33
27	Lambda	parameter: 73 body: 34
28	Lambda	parameter: 73 body: 35
29	Lambda	parameter: 73 body: 36
30	Lambda	parameter: 73 body: 37
31	Lambda	parameter: 73 body: 39
32	Operation	operator: 46 operands: 40
33	Operation	operator: 46 operands: 41
34	Operation	operator: 46 operands: 42
35	Operation	operator: 46 operands: 43
36	Operation	operator: 62 operands: 44
37	Operation	operator: 46 operands: 45
38	ExprTuple	73
39	Operation	operator: 46 operands: 47
40	NamedExprs	element: 48 targets: 55
41	NamedExprs	element: 49 targets: 57
42	NamedExprs	element: 50 targets: 51
43	NamedExprs	element: 52 targets: 55
44	NamedExprs	operation: 53
45	NamedExprs	element: 54 targets: 55
46	Literal
47	NamedExprs	element: 56 targets: 57
48	Operation	operator: 59 operands: 58
49	Operation	operator: 59 operands: 67
50	Operation	operator: 59 operands: 60
51	Operation	operator: 68 operands: 61
52	Operation	operator: 62 operands: 63
53	Literal
54	Operation	operator: 66 operands: 64
55	Operation	operator: 68 operands: 65
56	Operation	operator: 66 operands: 67
57	Operation	operator: 68 operands: 69
58	NamedExprs	state: 82 part: 73
59	Literal
60	NamedExprs	state: 70 part: 73
61	ExprTuple	84, 75
62	Literal
63	NamedExprs	operation: 71 part: 73
64	NamedExprs	state: 72 part: 73
65	ExprTuple	84, 88
66	Literal
67	NamedExprs	state: 83 part: 73
68	Literal
69	ExprTuple	74, 75
70	Operation	operator: 76 operands: 77
71	Operation	operator: 78 operand: 88
72	Literal
73	Variable
74	Operation	operator: 80 operands: 79
75	Operation	operator: 80 operands: 81
76	Literal
77	ExprTuple	82, 83
78	Literal
79	ExprTuple	88, 84
80	Literal
81	ExprTuple	88, 85
82	Operation	operator: 86 operand: 88
83	Literal
84	Literal
85	Literal
86	Literal
87	ExprTuple	88
88	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 ¶