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, 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, one)
sub_expr3 = Add(_t, _s)
sub_expr4 = Interval(one, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = sub_expr4)
expr = ExprTuple(ExprRange(sub_expr1, Input(state = ket_plus), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = Interval(sub_expr2, sub_expr3)), one, _s), ExprRange(sub_expr1, sub_expr5, one, _t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = sub_expr4), one, 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(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert + \rangle} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert + \rangle} & \qw 
} \end{array}, ..\left(t - 3\right) \times.., \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert + \rangle} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~t + 1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~t + 2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~t + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + s~\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, 4, 5
1	ExprRange	lambda_map: 6 start_index: 50 end_index: 54
2	ExprRange	lambda_map: 7 start_index: 50 end_index: 55
3	ExprRange	lambda_map: 8 start_index: 50 end_index: 54
4	ExprRange	lambda_map: 8 start_index: 38 end_index: 42
5	ExprRange	lambda_map: 9 start_index: 50 end_index: 42
6	Lambda	parameter: 41 body: 10
7	Lambda	parameter: 41 body: 11
8	Lambda	parameter: 41 body: 12
9	Lambda	parameter: 41 body: 14
10	Operation	operator: 28 operands: 15
11	Operation	operator: 18 operands: 16
12	Operation	operator: 18 operands: 17
13	ExprTuple	41
14	Operation	operator: 18 operands: 19
15	NamedExprs	state: 20
16	NamedExprs	element: 21 targets: 22
17	NamedExprs	element: 23 targets: 25
18	Literal
19	NamedExprs	element: 24 targets: 25
20	Operation	operator: 26 operand: 37
21	Operation	operator: 28 operands: 29
22	Operation	operator: 35 operands: 30
23	Operation	operator: 31 operands: 32
24	Operation	operator: 33 operands: 34
25	Operation	operator: 35 operands: 36
26	Literal
27	ExprTuple	37
28	Literal
29	NamedExprs	state: 53 part: 41
30	ExprTuple	38, 42
31	Literal
32	NamedExprs	operation: 39 part: 41
33	Literal
34	NamedExprs	state: 40 part: 41
35	Literal
36	ExprTuple	50, 42
37	Literal
38	Operation	operator: 48 operands: 43
39	Operation	operator: 44 operands: 45
40	Operation	operator: 46 operands: 47
41	Variable
42	Operation	operator: 48 operands: 49
43	ExprTuple	54, 50
44	Literal
45	ExprTuple	51, 54
46	Literal
47	ExprTuple	52, 53
48	Literal
49	ExprTuple	54, 55
50	Literal
51	Literal
52	Literal
53	Literal
54	Literal
55	Literal