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 ExprTuple, Lambda, Variable, m
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
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(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))))

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({_{-}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)

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, 1, 2, 3, 4, 5
1	Lambda	parameter: 39 body: 6
2	Lambda	parameter: 39 body: 7
3	Lambda	parameter: 39 body: 8
4	Lambda	parameter: 39 body: 9
5	Lambda	parameter: 39 body: 11
6	Operation	operator: 18 operands: 12
7	Operation	operator: 13 operands: 14
8	Operation	operator: 15 operands: 16
9	Operation	operator: 18 operands: 17
10	ExprTuple	39
11	Operation	operator: 18 operands: 19
12	NamedExprs	element: 20 targets: 21
13	Literal
14	NamedExprs	basis: 22
15	Literal
16	NamedExprs	operation: 23
17	NamedExprs	element: 24 targets: 25
18	Literal
19	NamedExprs	element: 26 targets: 27
20	Operation	operator: 28 operands: 29
21	Operation	operator: 35 operands: 30
22	Literal
23	Literal
24	Operation	operator: 33 operands: 31
25	Operation	operator: 35 operands: 32
26	Operation	operator: 33 operands: 34
27	Operation	operator: 35 operands: 36
28	Literal
29	NamedExprs	state: 37 part: 39
30	ExprTuple	52, 41
31	NamedExprs	state: 38 part: 39
32	ExprTuple	52, 53
33	Literal
34	NamedExprs	state: 50 part: 39
35	Literal
36	ExprTuple	40, 41
37	Operation	operator: 42 operands: 43
38	Operation	operator: 44 operands: 45
39	Variable
40	Operation	operator: 47 operands: 46
41	Operation	operator: 47 operands: 48
42	Literal
43	ExprTuple	49, 50
44	Literal
45	ExprTuple	51, 53
46	ExprTuple	53, 52
47	Literal
48	ExprTuple	53, 54
49	Literal
50	Literal
51	Variable
52	Literal
53	Literal
54	Literal