Expression of type MultiQubitElem

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 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 MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(sub_expr1, t)
expr = MultiQubitElem(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(sub_expr2, sub_expr2))

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())

\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~\mbox{on}~\{{_{-}a} + t~\ldotp \ldotp~{_{-}a} + t\}} 
} \end{array}

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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