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
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import ket_plus
from proveit.physics.quantum.QPE import QPE, _Psi_ket, _U, _ket_u, _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, sub_expr2)
sub_expr4 = Lambda(sub_expr1, MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = sub_expr3))
expr = ExprTuple(Lambda(sub_expr1, Input(state = ket_plus)), Lambda(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = Interval(Add(_t, one), sub_expr2))), sub_expr4, sub_expr4, Lambda(sub_expr1, MultiQubitElem(element = Output(state = TensorProd(_Psi_ket, _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{
& & \qout{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{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
1	Lambda	parameter: 36 body: 5
2	Lambda	parameter: 36 body: 6
3	Lambda	parameter: 36 body: 7
4	Lambda	parameter: 36 body: 9
5	Operation	operator: 23 operands: 10
6	Operation	operator: 13 operands: 11
7	Operation	operator: 13 operands: 12
8	ExprTuple	36
9	Operation	operator: 13 operands: 14
10	NamedExprs	state: 15
11	NamedExprs	element: 16 targets: 17
12	NamedExprs	element: 18 targets: 20
13	Literal
14	NamedExprs	element: 19 targets: 20
15	Operation	operator: 21 operand: 32
16	Operation	operator: 23 operands: 24
17	Operation	operator: 30 operands: 25
18	Operation	operator: 26 operands: 27
19	Operation	operator: 28 operands: 29
20	Operation	operator: 30 operands: 31
21	Literal
22	ExprTuple	32
23	Literal
24	NamedExprs	state: 48 part: 36
25	ExprTuple	33, 37
26	Literal
27	NamedExprs	operation: 34 part: 36
28	Literal
29	NamedExprs	state: 35 part: 36
30	Literal
31	ExprTuple	45, 37
32	Literal
33	Operation	operator: 43 operands: 38
34	Operation	operator: 39 operands: 40
35	Operation	operator: 41 operands: 42
36	Variable
37	Operation	operator: 43 operands: 44
38	ExprTuple	49, 45
39	Literal
40	ExprTuple	46, 49
41	Literal
42	ExprTuple	47, 48
43	Literal
44	ExprTuple	49, 50
45	Literal
46	Literal
47	Literal
48	Literal
49	Literal
50	Literal