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, n
from proveit.numbers import Add, Interval, 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(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(n, _t), part = sub_expr1), targets = Interval(one, _t))), Lambda(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr3)))

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