On the Influence of Initial Qubit Placement During NISQ Circuit
  Compilation
Noisy Intermediate-Scale Quantum (NISQ) machines are not fault-tolerant,
operate few qubits (currently, less than hundred), but are capable of executing
interesting computations. Above the quantum supremacy threshold (approx. 60
qubits), NISQ machines are expected to be more powerful than existing classical
computers. One of the most stringent problems is that computations (expressed
as quantum circuits) have to be adapted (compiled) to the NISQ hardware,
because the hardware does not support arbitrary interactions between the
qubits. This procedure introduces additional gates (e.g. SWAP gates) into the
circuits while leaving the implemented computations unchanged. Each additional
gate increases the failure rate of the adapted (compiled) circuits, because the
hardware and the circuits are not fault-tolerant. It is reasonable to expect
that the placement influences the number of additionally introduced gates.
Therefore, a combinatorial problem arises: how are circuit qubits allocated
(placed) initially to the hardware qubits? The novelty of this work relies on
the methodology used to investigate the influence of the initial placement. To
this end, we introduce a novel heuristic and cost model to estimate the number
of gates necessary to adapt a circuit to a given NISQ architecture. We
implement the heuristic (source code available on github) and benchmark it
using a standard compiler (e.g. from IBM Qiskit) treated as a black box.
Preliminary results indicate that cost reductions of up to 10\% can be achieved
for practical circuit instances on realistic NISQ architectures only by placing
qubits differently than default (trivial placement).
Alexandru Paler