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
from proveit.core_expr_types import Len
from proveit.linear_algebra import TensorProd
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 = ExprTuple(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(|\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)|\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, 6, 7, 8, 9, 10
4	Literal
5	ExprTuple	11
6	Lambda	parameter: 48 body: 12
7	Lambda	parameter: 48 body: 13
8	Lambda	parameter: 48 body: 14
9	Lambda	parameter: 48 body: 15
10	Lambda	parameter: 48 body: 16
11	ExprRange	lambda_map: 17 start_index: 59 end_index: 18
12	Operation	operator: 23 operands: 19
13	Operation	operator: 23 operands: 20
14	Operation	operator: 37 operands: 21
15	Operation	operator: 23 operands: 22
16	Operation	operator: 23 operands: 24
17	Lambda	parameter: 48 body: 48
18	Literal
19	NamedExprs	element: 26 targets: 27
20	NamedExprs	element: 28 targets: 31
21	NamedExprs	operation: 29
22	NamedExprs	element: 30 targets: 31
23	Literal
24	NamedExprs	element: 32 targets: 33
25	ExprTuple	48
26	Operation	operator: 34 operands: 35
27	Operation	operator: 43 operands: 36
28	Operation	operator: 37 operands: 38
29	Literal
30	Operation	operator: 41 operands: 39
31	Operation	operator: 43 operands: 40
32	Operation	operator: 41 operands: 42
33	Operation	operator: 43 operands: 44
34	Literal
35	NamedExprs	state: 45 part: 48
36	ExprTuple	59, 50
37	Literal
38	NamedExprs	operation: 46 part: 48
39	NamedExprs	state: 47 part: 48
40	ExprTuple	59, 63
41	Literal
42	NamedExprs	state: 58 part: 48
43	Literal
44	ExprTuple	49, 50
45	Operation	operator: 51 operands: 52
46	Operation	operator: 53 operand: 63
47	Literal
48	Variable
49	Operation	operator: 55 operands: 54
50	Operation	operator: 55 operands: 56
51	Literal
52	ExprTuple	57, 58
53	Literal
54	ExprTuple	63, 59
55	Literal
56	ExprTuple	63, 60
57	Operation	operator: 61 operand: 63
58	Literal
59	Literal
60	Literal
61	Literal
62	ExprTuple	63
63	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 ¶