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
from proveit.core_expr_types import Len
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals
from proveit.numbers import Add, Interval, one, six
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

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(_t, _s)
sub_expr3 = Interval(one, _t)
sub_expr4 = Lambda(sub_expr1, MultiQubitElem(element = Input(state = TensorProd(_psi__t_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr2)))
expr = Equals(Len(operands = [sub_expr4, sub_expr4, Lambda(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr3)), Lambda(sub_expr1, Gate(operation = I).with_implicit_representation()), Lambda(sub_expr1, MultiQubitElem(element = Output(state = _Psi_ket, part = sub_expr1), targets = sub_expr3)), Lambda(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(Add(_t, one), sub_expr2)))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, six)]))

# 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 \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{{\mathrm {FT}}^{\dag}_{t}~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t\}} & \qw 
} \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 \Psi \rangle~\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, 6\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, 8, 9, 10, 11, 12
6	Literal
7	ExprTuple	13
8	Lambda	parameter: 50 body: 14
9	Lambda	parameter: 50 body: 15
10	Lambda	parameter: 50 body: 16
11	Lambda	parameter: 50 body: 17
12	Lambda	parameter: 50 body: 18
13	ExprRange	lambda_map: 19 start_index: 61 end_index: 20
14	Operation	operator: 25 operands: 21
15	Operation	operator: 25 operands: 22
16	Operation	operator: 39 operands: 23
17	Operation	operator: 25 operands: 24
18	Operation	operator: 25 operands: 26
19	Lambda	parameter: 50 body: 50
20	Literal
21	NamedExprs	element: 28 targets: 29
22	NamedExprs	element: 30 targets: 33
23	NamedExprs	operation: 31
24	NamedExprs	element: 32 targets: 33
25	Literal
26	NamedExprs	element: 34 targets: 35
27	ExprTuple	50
28	Operation	operator: 36 operands: 37
29	Operation	operator: 45 operands: 38
30	Operation	operator: 39 operands: 40
31	Literal
32	Operation	operator: 43 operands: 41
33	Operation	operator: 45 operands: 42
34	Operation	operator: 43 operands: 44
35	Operation	operator: 45 operands: 46
36	Literal
37	NamedExprs	state: 47 part: 50
38	ExprTuple	61, 52
39	Literal
40	NamedExprs	operation: 48 part: 50
41	NamedExprs	state: 49 part: 50
42	ExprTuple	61, 65
43	Literal
44	NamedExprs	state: 60 part: 50
45	Literal
46	ExprTuple	51, 52
47	Operation	operator: 53 operands: 54
48	Operation	operator: 55 operand: 65
49	Literal
50	Variable
51	Operation	operator: 57 operands: 56
52	Operation	operator: 57 operands: 58
53	Literal
54	ExprTuple	59, 60
55	Literal
56	ExprTuple	65, 61
57	Literal
58	ExprTuple	65, 62
59	Operation	operator: 63 operand: 65
60	Literal
61	Literal
62	Literal
63	Literal
64	ExprTuple	65
65	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 ¶