1 research outputs found
Space-efficient quantum multiplication of polynomials for binary finite fields with sub-quadratic Toffoli gate count
Multiplication is an essential step in a lot of calculations. In this paper
we look at multiplication of 2 binary polynomials of degree at most ,
modulo an irreducible polynomial of degree with input and output
qubits, without ancillary qubits, assuming no errors. With straightforward
schoolbook methods this would result in a quadratic number of Toffoli gates and
a linear number of CNOT gates. This paper introduces a new algorithm that uses
the same space, but by utilizing space-efficient variants of Karatsuba
multiplication methods it requires only Toffoli gates at the
cost of a higher CNOT gate count: theoretically up to but in examples
the CNOT gate count looks a lot better.Comment: 15 pages, 5 figure