Mapping Quantum Circuits to 2-Dimensional Quantum Architectures

Abstract

We have been witnessing a rapid growth in quantum computing research over the years, with the emergence of demonstrable quantum computers of moderate size. The major issues that are faced to run a quantum algorithm reliably on these systems are: (i) lower qubit coherence period, (ii) noisy primitive gate operations, (iii) limited number of available physical qubits, and (iv) support of restricted set of 2-qubit operations. Overcoming these issues mandates physical resources that exceeds the capabilities of these noisy intermediate scale quantum (NISQ) systems. On the other hand, computation using bare qubits get further disturbed due to the inclusion of additional gates to mitigate the nearest neighbor constraints. In the present work, the 2-dimensional square, heavy-hex and fully hexagonal qubit coupling lattices are considered for mapping quantum circuits. The benefits are assessed in terms of minimal additional gates needed to satisfy the nearest neighbor (NN) constraint and the compilation complexity of mapping circuits on these architectures. From the experiments by mapping benchmark circuits on 16-qubit square and 65-qubit heavy-hex architectures from IBM as well as on a 64-qubit fully hexagonal architecture, it is observed that none of the square or heavy-hex lattice architecture provides uniform compilation advantage compared to the fully hexagonal architecture. It is expected that beyond the NISQ era, strongly connected lattices like hexagonal will become practically feasible.