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, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Interval, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _ket_u, _phase, _s
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([ExprRange(sub_expr1, Output(state = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))), Add(Neg(t), one), zero).with_decreasing_order(), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(Add(t, one), Add(t, _s))), 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(\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 2^{t - 1} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array}, \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 2^{t - 2} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array}, \ldots, \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 2^{0} \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}~\{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)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	ExprTuple	2, 3
2	ExprRange	lambda_map: 4 start_index: 5 end_index: 44
3	ExprRange	lambda_map: 6 start_index: 54 end_index: 38
4	Lambda	parameter: 67 body: 7
5	Operation	operator: 32 operands: 8
6	Lambda	parameter: 67 body: 9
7	Operation	operator: 19 operands: 10
8	ExprTuple	11, 54
9	Operation	operator: 12 operands: 13
10	NamedExprs	state: 14
11	Operation	operator: 65 operand: 37
12	Literal
13	NamedExprs	element: 16 targets: 17
14	Operation	operator: 41 operands: 18
15	ExprTuple	37
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	ExprTuple	23, 24
19	Literal
20	NamedExprs	state: 25 part: 67
21	Literal
22	ExprTuple	26, 27
23	Operation	operator: 47 operands: 28
24	Operation	operator: 29 operands: 30
25	Literal
26	Operation	operator: 32 operands: 31
27	Operation	operator: 32 operands: 33
28	ExprTuple	54, 34
29	Literal
30	ExprTuple	35, 36
31	ExprTuple	37, 54
32	Literal
33	ExprTuple	37, 38
34	Operation	operator: 61 operands: 39
35	Operation	operator: 50 operand: 44
36	Operation	operator: 41 operands: 42
37	Variable
38	Literal
39	ExprTuple	63, 43
40	ExprTuple	44
41	Literal
42	ExprTuple	45, 46
43	Operation	operator: 47 operands: 48
44	Literal
45	Operation	operator: 61 operands: 49
46	Operation	operator: 50 operand: 54
47	Literal
48	ExprTuple	54, 63
49	ExprTuple	52, 53
50	Literal
51	ExprTuple	54
52	Literal
53	Operation	operator: 55 operands: 56
54	Literal
55	Literal
56	ExprTuple	63, 57, 58, 59, 60
57	Literal
58	Literal
59	Operation	operator: 61 operands: 62
60	Literal
61	Literal
62	ExprTuple	63, 64
63	Literal
64	Operation	operator: 65 operand: 67
65	Literal
66	ExprTuple	67
67	Variable