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, m
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _s, _s_wire, _t
from proveit.physics.quantum.circuits import 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 = Add(_t, one)
sub_expr4 = MultiQubitElem(element = Input(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr2))
expr = ExprTuple(ExprRange(sub_expr1, sub_expr4, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr4, sub_expr3, sub_expr2).with_wrapping_at(2,6), ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire, ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = Interval(one, _t)), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(sub_expr3, sub_expr2)), one, _s))

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 \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array}, ..\left(t - 3\right) \times.., \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, ..\left(s - 3\right) \times.., \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~s~\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, 4, 5, 6
1	ExprRange	lambda_map: 7 start_index: 58 end_index: 59
2	ExprRange	lambda_map: 7 start_index: 46 end_index: 47
3	ExprRange	lambda_map: 8 start_index: 58 end_index: 59
4	ExprRange	lambda_map: 9 start_index: 58 end_index: 60
5	ExprRange	lambda_map: 10 start_index: 58 end_index: 59
6	ExprRange	lambda_map: 11 start_index: 58 end_index: 60
7	Lambda	parameter: 45 body: 12
8	Lambda	parameter: 45 body: 13
9	Lambda	parameter: 45 body: 14
10	Lambda	parameter: 45 body: 15
11	Lambda	parameter: 45 body: 17
12	Operation	operator: 24 operands: 18
13	Operation	operator: 19 operands: 20
14	Operation	operator: 21 operands: 22
15	Operation	operator: 24 operands: 23
16	ExprTuple	45
17	Operation	operator: 24 operands: 25
18	NamedExprs	element: 26 targets: 27
19	Literal
20	NamedExprs	basis: 28
21	Literal
22	NamedExprs	operation: 29
23	NamedExprs	element: 30 targets: 31
24	Literal
25	NamedExprs	element: 32 targets: 33
26	Operation	operator: 34 operands: 35
27	Operation	operator: 41 operands: 36
28	Literal
29	Literal
30	Operation	operator: 39 operands: 37
31	Operation	operator: 41 operands: 38
32	Operation	operator: 39 operands: 40
33	Operation	operator: 41 operands: 42
34	Literal
35	NamedExprs	state: 43 part: 45
36	ExprTuple	58, 47
37	NamedExprs	state: 44 part: 45
38	ExprTuple	58, 59
39	Literal
40	NamedExprs	state: 56 part: 45
41	Literal
42	ExprTuple	46, 47
43	Operation	operator: 48 operands: 49
44	Operation	operator: 50 operands: 51
45	Variable
46	Operation	operator: 53 operands: 52
47	Operation	operator: 53 operands: 54
48	Literal
49	ExprTuple	55, 56
50	Literal
51	ExprTuple	57, 59
52	ExprTuple	59, 58
53	Literal
54	ExprTuple	59, 60
55	Literal
56	Literal
57	Variable
58	Literal
59	Literal
60	Literal