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, m
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, NumKet, Z
from proveit.physics.quantum.QPE import _Psi_ket, _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 = Lambda(sub_expr1, MultiQubitElem(element = Input(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr2)))
expr = Equals(Len(operands = [sub_expr3, sub_expr3, Lambda(sub_expr1, Measure(basis = Z)), Lambda(sub_expr1, Gate(operation = I).with_implicit_representation()), Lambda(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = Interval(one, _t))), 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 \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 \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{
& & \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 m \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, 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: 49 body: 14
9	Lambda	parameter: 49 body: 15
10	Lambda	parameter: 49 body: 16
11	Lambda	parameter: 49 body: 17
12	Lambda	parameter: 49 body: 18
13	ExprRange	lambda_map: 19 start_index: 62 end_index: 20
14	Operation	operator: 27 operands: 21
15	Operation	operator: 22 operands: 23
16	Operation	operator: 24 operands: 25
17	Operation	operator: 27 operands: 26
18	Operation	operator: 27 operands: 28
19	Lambda	parameter: 49 body: 49
20	Literal
21	NamedExprs	element: 30 targets: 31
22	Literal
23	NamedExprs	basis: 32
24	Literal
25	NamedExprs	operation: 33
26	NamedExprs	element: 34 targets: 35
27	Literal
28	NamedExprs	element: 36 targets: 37
29	ExprTuple	49
30	Operation	operator: 38 operands: 39
31	Operation	operator: 45 operands: 40
32	Literal
33	Literal
34	Operation	operator: 43 operands: 41
35	Operation	operator: 45 operands: 42
36	Operation	operator: 43 operands: 44
37	Operation	operator: 45 operands: 46
38	Literal
39	NamedExprs	state: 47 part: 49
40	ExprTuple	62, 51
41	NamedExprs	state: 48 part: 49
42	ExprTuple	62, 63
43	Literal
44	NamedExprs	state: 60 part: 49
45	Literal
46	ExprTuple	50, 51
47	Operation	operator: 52 operands: 53
48	Operation	operator: 54 operands: 55
49	Variable
50	Operation	operator: 57 operands: 56
51	Operation	operator: 57 operands: 58
52	Literal
53	ExprTuple	59, 60
54	Literal
55	ExprTuple	61, 63
56	ExprTuple	63, 62
57	Literal
58	ExprTuple	63, 64
59	Literal
60	Literal
61	Variable
62	Literal
63	Literal
64	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 ¶