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, Lambda, Variable, n
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Add, Interval, eight, one
from proveit.physics.quantum import I, NumKet, Z, ket_plus
from proveit.physics.quantum.QPE import QPE, _U, _ket_u, _s, _t
from proveit.physics.quantum.circuits import Gate, Input, Measure, MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(_t, _s)
sub_expr3 = Interval(Add(_t, one), sub_expr2)
sub_expr4 = Lambda(sub_expr1, MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = Interval(one, sub_expr2)))
expr = Equals(Len(operands = [Lambda(sub_expr1, Input(state = ket_plus)), Lambda(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr3)), sub_expr4, sub_expr4, Lambda(sub_expr1, Measure(basis = Z)), Lambda(sub_expr1, Gate(operation = I).with_implicit_representation()), Lambda(sub_expr1, MultiQubitElem(element = Output(state = NumKet(n, _t), part = sub_expr1), targets = Interval(one, _t))), Lambda(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr3))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, eight)]))

# 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({_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert + \rangle} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert n \rangle_{t}~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}\right)| = |\left(1, 2, \ldots, 8\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 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9, 10, 10, 11, 12, 13, 14
6	Literal
7	ExprTuple	15
8	Lambda	parameter: 61 body: 16
9	Lambda	parameter: 61 body: 17
10	Lambda	parameter: 61 body: 18
11	Lambda	parameter: 61 body: 19
12	Lambda	parameter: 61 body: 20
13	Lambda	parameter: 61 body: 21
14	Lambda	parameter: 61 body: 22
15	ExprRange	lambda_map: 23 start_index: 73 end_index: 24
16	Operation	operator: 47 operands: 25
17	Operation	operator: 32 operands: 26
18	Operation	operator: 32 operands: 27
19	Operation	operator: 28 operands: 29
20	Operation	operator: 48 operands: 30
21	Operation	operator: 32 operands: 31
22	Operation	operator: 32 operands: 33
23	Lambda	parameter: 61 body: 61
24	Literal
25	NamedExprs	state: 35
26	NamedExprs	element: 36 targets: 44
27	NamedExprs	element: 37 targets: 38
28	Literal
29	NamedExprs	basis: 39
30	NamedExprs	operation: 40
31	NamedExprs	element: 41 targets: 42
32	Literal
33	NamedExprs	element: 43 targets: 44
34	ExprTuple	61
35	Operation	operator: 45 operand: 57
36	Operation	operator: 47 operands: 54
37	Operation	operator: 48 operands: 49
38	Operation	operator: 55 operands: 50
39	Literal
40	Literal
41	Operation	operator: 53 operands: 51
42	Operation	operator: 55 operands: 52
43	Operation	operator: 53 operands: 54
44	Operation	operator: 55 operands: 56
45	Literal
46	ExprTuple	57
47	Literal
48	Literal
49	NamedExprs	operation: 58 part: 61
50	ExprTuple	73, 63
51	NamedExprs	state: 59 part: 61
52	ExprTuple	73, 74
53	Literal
54	NamedExprs	state: 60 part: 61
55	Literal
56	ExprTuple	62, 63
57	Literal
58	Operation	operator: 64 operands: 65
59	Operation	operator: 66 operands: 67
60	Literal
61	Variable
62	Operation	operator: 69 operands: 68
63	Operation	operator: 69 operands: 70
64	Literal
65	ExprTuple	71, 74
66	Literal
67	ExprTuple	72, 74
68	ExprTuple	74, 73
69	Literal
70	ExprTuple	74, 75
71	Literal
72	Variable
73	Literal
74	Literal
75	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 ¶