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.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 = Interval(Add(_t, one), Add(_t, _s))
sub_expr4 = ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _Psi_ket, part = sub_expr1), targets = sub_expr2), one, _t)
sub_expr5 = ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _psi__t_ket, part = sub_expr1), targets = sub_expr2), one, _t)
sub_expr6 = ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr2), one, _t)
expr = Equals(Prob(Qcircuit(vert_expr_array = VertExprArray([sub_expr5], [sub_expr6], [sub_expr4]))), Prob(Qcircuit(vert_expr_array = VertExprArray([sub_expr5, ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr3), one, _s)], [sub_expr6, ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, _s)], [sub_expr4, ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr3), one, _s)])))).with_wrapping_at(2)

# 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())

\begin{array}{c} \begin{array}{l} \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}
} \end{array}\right) =  \\ \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) \end{array} \end{array}

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.	()	(2)	('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, 14, 15
11	Literal
12	ExprTuple	16, 17, 18
13	ExprTuple	19
14	ExprTuple	21
15	ExprTuple	23
16	ExprTuple	19, 20
17	ExprTuple	21, 22
18	ExprTuple	23, 24
19	ExprRange	lambda_map: 25 start_index: 76 end_index: 77
20	ExprRange	lambda_map: 26 start_index: 76 end_index: 78
21	ExprRange	lambda_map: 27 start_index: 76 end_index: 77
22	ExprRange	lambda_map: 28 start_index: 76 end_index: 78
23	ExprRange	lambda_map: 29 start_index: 76 end_index: 77
24	ExprRange	lambda_map: 30 start_index: 76 end_index: 78
25	Lambda	parameter: 67 body: 31
26	Lambda	parameter: 67 body: 32
27	Lambda	parameter: 67 body: 33
28	Lambda	parameter: 67 body: 34
29	Lambda	parameter: 67 body: 35
30	Lambda	parameter: 67 body: 37
31	Operation	operator: 43 operands: 38
32	Operation	operator: 43 operands: 39
33	Operation	operator: 43 operands: 40
34	Operation	operator: 55 operands: 41
35	Operation	operator: 43 operands: 42
36	ExprTuple	67
37	Operation	operator: 43 operands: 44
38	NamedExprs	element: 45 targets: 50
39	NamedExprs	element: 46 targets: 52
40	NamedExprs	element: 47 targets: 50
41	NamedExprs	operation: 48
42	NamedExprs	element: 49 targets: 50
43	Literal
44	NamedExprs	element: 51 targets: 52
45	Operation	operator: 54 operands: 53
46	Operation	operator: 54 operands: 60
47	Operation	operator: 55 operands: 56
48	Literal
49	Operation	operator: 59 operands: 57
50	Operation	operator: 61 operands: 58
51	Operation	operator: 59 operands: 60
52	Operation	operator: 61 operands: 62
53	NamedExprs	state: 63 part: 67
54	Literal
55	Literal
56	NamedExprs	operation: 64 part: 67
57	NamedExprs	state: 65 part: 67
58	ExprTuple	76, 77
59	Literal
60	NamedExprs	state: 66 part: 67
61	Literal
62	ExprTuple	68, 69
63	Operation	operator: 70 operand: 77
64	Operation	operator: 71 operand: 77
65	Literal
66	Literal
67	Variable
68	Operation	operator: 74 operands: 73
69	Operation	operator: 74 operands: 75
70	Literal
71	Literal
72	ExprTuple	77
73	ExprTuple	77, 76
74	Literal
75	ExprTuple	77, 78
76	Literal
77	Literal
78	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 ¶