Expression of type ExprTuple

from the theory of proveit.physics.quantum.circuits

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 ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Interval, Mult, e, frac, i, one, pi, sqrt, two
from proveit.physics.quantum import ket0, ket1, var_ket_u, varphi
from proveit.physics.quantum.circuits import MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Output(state = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, varphi)), ket1)))), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = var_ket_u, part = sub_expr1), targets = Interval(two, Add(m, two))), one, Add(m, one)))

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{
& & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{2~\ldotp \ldotp~m + 2\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{2~\ldotp \ldotp~m + 2\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~m + 1~\mbox{on}~\{2~\ldotp \ldotp~m + 2\}} 
} \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
1	Operation	operator: 20 operands: 3
2	ExprRange	lambda_map: 4 start_index: 49 end_index: 5
3	NamedExprs	state: 6
4	Lambda	parameter: 28 body: 8
5	Operation	operator: 34 operands: 9
6	Operation	operator: 32 operands: 10
7	ExprTuple	28
8	Operation	operator: 11 operands: 12
9	ExprTuple	40, 49
10	ExprTuple	13, 14
11	Literal
12	NamedExprs	element: 15 targets: 16
13	Operation	operator: 41 operands: 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operands: 21
16	Operation	operator: 22 operands: 23
17	ExprTuple	49, 24
18	Literal
19	ExprTuple	25, 26
20	Literal
21	NamedExprs	state: 27 part: 28
22	Literal
23	ExprTuple	52, 29
24	Operation	operator: 43 operands: 30
25	Operation	operator: 45 operand: 37
26	Operation	operator: 32 operands: 33
27	Variable
28	Variable
29	Operation	operator: 34 operands: 35
30	ExprTuple	52, 36
31	ExprTuple	37
32	Literal
33	ExprTuple	38, 39
34	Literal
35	ExprTuple	40, 52
36	Operation	operator: 41 operands: 42
37	Literal
38	Operation	operator: 43 operands: 44
39	Operation	operator: 45 operand: 49
40	Variable
41	Literal
42	ExprTuple	49, 52
43	Literal
44	ExprTuple	47, 48
45	Literal
46	ExprTuple	49
47	Literal
48	Operation	operator: 50 operands: 51
49	Literal
50	Literal
51	ExprTuple	52, 53, 54, 55
52	Literal
53	Literal
54	Literal
55	Variable