Expression of type ExprTuple ¶

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, ExprTuple, Lambda, Variable, m
from proveit.core_expr_types import Len
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 = ExprTuple(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(m, _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(|\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 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, 8\right)|\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

	core type	sub-expressions
0	ExprTuple	1, 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7, 8, 8, 9, 10, 11, 12
4	Literal
5	ExprTuple	13
6	Lambda	parameter: 59 body: 14
7	Lambda	parameter: 59 body: 15
8	Lambda	parameter: 59 body: 16
9	Lambda	parameter: 59 body: 17
10	Lambda	parameter: 59 body: 18
11	Lambda	parameter: 59 body: 19
12	Lambda	parameter: 59 body: 20
13	ExprRange	lambda_map: 21 start_index: 71 end_index: 22
14	Operation	operator: 45 operands: 23
15	Operation	operator: 30 operands: 24
16	Operation	operator: 30 operands: 25
17	Operation	operator: 26 operands: 27
18	Operation	operator: 46 operands: 28
19	Operation	operator: 30 operands: 29
20	Operation	operator: 30 operands: 31
21	Lambda	parameter: 59 body: 59
22	Literal
23	NamedExprs	state: 33
24	NamedExprs	element: 34 targets: 42
25	NamedExprs	element: 35 targets: 36
26	Literal
27	NamedExprs	basis: 37
28	NamedExprs	operation: 38
29	NamedExprs	element: 39 targets: 40
30	Literal
31	NamedExprs	element: 41 targets: 42
32	ExprTuple	59
33	Operation	operator: 43 operand: 55
34	Operation	operator: 45 operands: 52
35	Operation	operator: 46 operands: 47
36	Operation	operator: 53 operands: 48
37	Literal
38	Literal
39	Operation	operator: 51 operands: 49
40	Operation	operator: 53 operands: 50
41	Operation	operator: 51 operands: 52
42	Operation	operator: 53 operands: 54
43	Literal
44	ExprTuple	55
45	Literal
46	Literal
47	NamedExprs	operation: 56 part: 59
48	ExprTuple	71, 61
49	NamedExprs	state: 57 part: 59
50	ExprTuple	71, 72
51	Literal
52	NamedExprs	state: 58 part: 59
53	Literal
54	ExprTuple	60, 61
55	Literal
56	Operation	operator: 62 operands: 63
57	Operation	operator: 64 operands: 65
58	Literal
59	Variable
60	Operation	operator: 67 operands: 66
61	Operation	operator: 67 operands: 68
62	Literal
63	ExprTuple	69, 72
64	Literal
65	ExprTuple	70, 72
66	ExprTuple	72, 71
67	Literal
68	ExprTuple	72, 73
69	Literal
70	Variable
71	Literal
72	Literal
73	Literal

Expression of type ExprTuple¶

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

Expression of type ExprTuple ¶

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