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.linear_algebra import TensorProd
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 = ExprTuple(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)]))

expr:

# 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 \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)|\right)

stored_expr.style_options()

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',)

# display the expression information
stored_expr.expr_info()

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