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}")
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(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())

\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}~\{\left({_{-}a} - 1 + t\right) + 1~\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: 43
7	Literal
8	ExprTuple	10, 11
9	Operation	operator: 30 operands: 12
10	Operation	operator: 21 operands: 13
11	Operation	operator: 21 operands: 14
12	ExprTuple	15, 16
13	ExprTuple	17, 43
14	ExprTuple	56, 27
15	Operation	operator: 36 operands: 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	ExprTuple	43, 23
19	Literal
20	ExprTuple	24, 25
21	Literal
22	ExprTuple	56, 26, 27
23	Operation	operator: 50 operands: 28
24	Operation	operator: 39 operand: 33
25	Operation	operator: 30 operands: 31
26	Operation	operator: 54 operand: 43
27	Variable
28	ExprTuple	52, 32
29	ExprTuple	33
30	Literal
31	ExprTuple	34, 35
32	Operation	operator: 36 operands: 37
33	Literal
34	Operation	operator: 50 operands: 38
35	Operation	operator: 39 operand: 43
36	Literal
37	ExprTuple	43, 52
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	43
41	Literal
42	Operation	operator: 44 operands: 45
43	Literal
44	Literal
45	ExprTuple	52, 46, 47, 48, 49
46	Literal
47	Literal
48	Operation	operator: 50 operands: 51
49	Literal
50	Literal
51	ExprTuple	52, 53
52	Literal
53	Operation	operator: 54 operand: 56
54	Literal
55	ExprTuple	56
56	Variable