Implementation of Shor's
algorithm
on a linear nearest neighbour qubit array (pp237-251)
Austin G.
Fowler,
Simon J.
Devitt, and Lloyd
C.L.
Hollenberg
doi:
https://doi.org/10.26421/QIC4.4-1
Abstracts:
Shor's algorithm, which given appropriate hardware can
factorise an integer N in
a time polynomial in its binary length L,
has arguably spurred the race to build a practical quantum computer.
Several different quantum circuits implementing Shor's algorithm have
been designed, but each tacitly assumes that arbitrary pairs of qubits
within the computer can be interacted. While some quantum computer
architectures possess this property, many promising proposals are best
suited to realising a single line of qubits with nearest neighbour
interactions only. In light of this, we present a circuit implementing
Shor's factorisation algorithm designed for such a linear nearest
neighbour architecture. Despite the interaction restrictions, the
circuit requires just 2L+4 qubits
and to leading order requires 8L^4 2-qubit
gates arranged in a circuit of depth 32L^3 ---
identical to leading order to that possible using an architecture that
can interact arbitrary pairs of qubits.
Key words:
Shor's algorithm, quantum circuit, linear nearest neighbour |