Topological-Graph Dependencies and Scaling Properties of a Heuristic Qubit-Assignment Algorithm

Topological-Graph Dependencies and Scaling Properties of a Heuristic Qubit-Assignment Algorithm

Steinberg, M.A. (TU Delft QCD/Feld Group; TU Delft QuTech Advanced Research Centre; Quantum Simulations , Karlsruhe)
Feld, S. (TU Delft Quantum Circuit Architectures and Technology; TU Delft QuTech Advanced Research Centre)
Almudever, Carmen G. (TU Delft QCD/Sebastiano Lab; TU Delft QuTech Advanced Research Centre; Universitat Politécnica de Valencia)
Marthaler, Michael (Quantum Simulations , Karlsruhe)
Reiner, Jan Michael (Quantum Simulations , Karlsruhe)

2022

The qubit-mapping problem aims to assign and route qubits of a quantum circuit onto an noisy intermediate-scale quantum (NISQ) device in an optimized fashion, with respect to some cost function. Finding an optimal solution to this problem is known to scale exponentially in computational complexity; as such, it is imperative to investigate scalable qubit-mapping solutions for NISQ computation. In this work, a noise-aware heuristic qubit-assignment algorithm (which assigns initial placements for qubits in a quantum algorithm to qubits on an NISQ device, but does not route qubits during the quantum algorithm's execution) is presented and compared against the optimal brute-force solution, as well as a trivial qubit assignment, with the aim to quantify the performance of our heuristic qubit-assignment algorithm. We find that for small, connected-graph algorithms, our heuristic-assignment algorithm faithfully lies in between the effective upper and lower bounds given by the brute-force and trivial qubit-assignment algorithms. Additionally, we find that the topological-graph properties of quantum algorithms with over six qubits play an important role in our heuristic qubit-assignment algorithm's performance on NISQ devices. Finally, we investigate the scaling properties of our heuristic algorithm for quantum processors with up to 100 qubits; here, the algorithm was found to be scalable for quantum-algorithms that admit path-like graphs. Our findings show that as the size of the quantum processor in our simulation grows, so do the benefits from utilizing the heuristic qubit-assignment algorithm, under particular constraints for our heuristic algorithm. This work, thus, characterizes the performance of a heuristic qubit-assignment algorithm with respect to the topological-graph and scaling properties of a quantum algorithm that one may wish to run on a given NISQ device.

Heuristic algorithms
INDEX TERMS Quantum Computing, Qubit-Mapping Problem
Logic gates
Quantum algorithm
Quantum circuit
Quantum computing
Quantum mechanics
Qubit

http://resolver.tudelft.nl/uuid:6516f412-bb94-4cc3-95ab-04998ad93442

https://doi.org/10.1109/TQE.2022.3160015

2689-1808

IEEE Transactions on Quantum Engineering, 3

Institutional Repository

journal article

© 2022 M.A. Steinberg, S. Feld, Carmen G. Almudever, Michael Marthaler, Jan Michael Reiner