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, U, Variable, VertExprArray, s, t
from proveit.logic import Equals
from proveit.numbers import Add, Interval, Mult, one
from proveit.physics.quantum import I, NumKet, Z, ket_plus, var_ket_u
from proveit.physics.quantum.QPE import QPE, phase, two_pow_t
from proveit.physics.quantum.circuits import Gate, Input, Measure, 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 = QPE(U, t), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = Equals(Prob(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Input(state = ket_plus), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = var_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, Measure(basis = Z), one, t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, s)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(Mult(two_pow_t, phase), t), part = sub_expr1), targets = Interval(one, t)), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = var_ket_u, part = sub_expr1), targets = sub_expr4), one, s)]))), one)

# 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)} & \meter & \multiqout{3}{\lvert 2^{t} \cdot \varphi \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert 2^{t} \cdot \varphi \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert 2^{t} \cdot \varphi \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert 2^{t} \cdot \varphi \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right) = 1

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, 83
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Operation	operator: 7 operands: 8
7	Literal
8	ExprTuple	9, 10, 11, 12
9	ExprTuple	13, 14
10	ExprTuple	15, 16
11	ExprTuple	17, 18
12	ExprTuple	19, 20
13	ExprRange	lambda_map: 21 start_index: 83 end_index: 92
14	ExprRange	lambda_map: 22 start_index: 83 end_index: 84
15	ExprRange	lambda_map: 23 start_index: 83 end_index: 92
16	ExprRange	lambda_map: 23 start_index: 72 end_index: 73
17	ExprRange	lambda_map: 24 start_index: 83 end_index: 92
18	ExprRange	lambda_map: 25 start_index: 83 end_index: 84
19	ExprRange	lambda_map: 26 start_index: 83 end_index: 92
20	ExprRange	lambda_map: 27 start_index: 83 end_index: 84
21	Lambda	parameter: 71 body: 28
22	Lambda	parameter: 71 body: 29
23	Lambda	parameter: 71 body: 30
24	Lambda	parameter: 71 body: 31
25	Lambda	parameter: 71 body: 32
26	Lambda	parameter: 71 body: 33
27	Lambda	parameter: 71 body: 35
28	Operation	operator: 57 operands: 36
29	Operation	operator: 43 operands: 37
30	Operation	operator: 43 operands: 38
31	Operation	operator: 39 operands: 40
32	Operation	operator: 58 operands: 41
33	Operation	operator: 43 operands: 42
34	ExprTuple	71
35	Operation	operator: 43 operands: 44
36	NamedExprs	state: 45
37	NamedExprs	element: 46 targets: 54
38	NamedExprs	element: 47 targets: 48
39	Literal
40	NamedExprs	basis: 49
41	NamedExprs	operation: 50
42	NamedExprs	element: 51 targets: 52
43	Literal
44	NamedExprs	element: 53 targets: 54
45	Operation	operator: 55 operand: 67
46	Operation	operator: 57 operands: 64
47	Operation	operator: 58 operands: 59
48	Operation	operator: 65 operands: 60
49	Literal
50	Literal
51	Operation	operator: 63 operands: 61
52	Operation	operator: 65 operands: 62
53	Operation	operator: 63 operands: 64
54	Operation	operator: 65 operands: 66
55	Literal
56	ExprTuple	67
57	Literal
58	Literal
59	NamedExprs	operation: 68 part: 71
60	ExprTuple	83, 73
61	NamedExprs	state: 69 part: 71
62	ExprTuple	83, 92
63	Literal
64	NamedExprs	state: 70 part: 71
65	Literal
66	ExprTuple	72, 73
67	Literal
68	Operation	operator: 74 operands: 75
69	Operation	operator: 76 operands: 77
70	Variable
71	Variable
72	Operation	operator: 79 operands: 78
73	Operation	operator: 79 operands: 80
74	Literal
75	ExprTuple	81, 92
76	Literal
77	ExprTuple	82, 92
78	ExprTuple	92, 83
79	Literal
80	ExprTuple	92, 84
81	Variable
82	Operation	operator: 85 operands: 86
83	Literal
84	Variable
85	Literal
86	ExprTuple	87, 88
87	Operation	operator: 89 operands: 90
88	Variable
89	Literal
90	ExprTuple	91, 92
91	Literal
92	Variable

Expression of type Equals¶

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

Expression of type Equals ¶

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