Expression of type NamedExprs

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 NamedExprs, 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
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase
from proveit.physics.quantum.circuits import Output

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

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}{l}
{\rm element}: \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^{-{_{-}a}} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)~\mbox{part}~1} 
} \end{array}\\
{\rm targets}: \{\left({_{-}a} - 1 + t\right) + 1~\ldotp \ldotp~{_{-}a} + t\}\\
\end{array} \right\}

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	NamedExprs	element: 1 targets: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	NamedExprs	state: 7 part: 41
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 28 operands: 10
8	Operation	operator: 19 operands: 11
9	Operation	operator: 19 operands: 12
10	ExprTuple	13, 14
11	ExprTuple	15, 41
12	ExprTuple	54, 25
13	Operation	operator: 34 operands: 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	ExprTuple	41, 21
17	Literal
18	ExprTuple	22, 23
19	Literal
20	ExprTuple	54, 24, 25
21	Operation	operator: 48 operands: 26
22	Operation	operator: 37 operand: 31
23	Operation	operator: 28 operands: 29
24	Operation	operator: 52 operand: 41
25	Variable
26	ExprTuple	50, 30
27	ExprTuple	31
28	Literal
29	ExprTuple	32, 33
30	Operation	operator: 34 operands: 35
31	Literal
32	Operation	operator: 48 operands: 36
33	Operation	operator: 37 operand: 41
34	Literal
35	ExprTuple	41, 50
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	41
39	Literal
40	Operation	operator: 42 operands: 43
41	Literal
42	Literal
43	ExprTuple	50, 44, 45, 46, 47
44	Literal
45	Literal
46	Operation	operator: 48 operands: 49
47	Literal
48	Literal
49	ExprTuple	50, 51
50	Literal
51	Operation	operator: 52 operand: 54
52	Literal
53	ExprTuple	54
54	Variable