On the Influence of Initial Qubit Placement During NISQ Circuit Compilation

  • Alexandru PalerEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11413)


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).



The author thanks Ali Javadi Abhari for suggesting some of the circuits, and Lucian Mircea Sasu for very helpful discussions. This work was supported by project CHARON funded by Linz Institute of Technology.


  1. 1.
    Viyuela, O., Rivas, A., Gasparinetti, S., Wallraff, A., Filipp, S., Martin-Delgado, M.A.: Observation of topological Uhlmann phases with superconducting qubits. npj Quantum Inf. 4(1), 10 (2018)CrossRefGoogle Scholar
  2. 2.
    Zulehner, A., Paler, A., Wille, R.: Efficient mapping of quantum circuits to the IBM QX architectures. In: Design, Automation & Test in Europe Conference & Exhibition (DATE), 2018. IEEE (2018)Google Scholar
  3. 3.
    Hattori, W., Yamashita, S.: Quantum circuit optimization by changing the gate order for 2D nearest neighbor architectures. In: Kari, J., Ulidowski, I. (eds.) RC 2018. LNCS, vol. 11106, pp. 228–243. Springer, Cham (2018). Scholar
  4. 4.
    Russell , S., Norvig, P.: Artificial Intelligence: A Modern Approach (2002)Google Scholar
  5. 5.
    Saeedi, M., Markov, I.L.: Synthesis and optimization of reversible circuits-a survey. ACM Comput. Surv. (CSUR) 45(2), 21 (2013)CrossRefGoogle Scholar
  6. 6.
    Venturelli, D., Do, M., Rieffel, E., Frank, J.: Compiling quantum circuits to realistic hardware architectures using temporal planners. Quantum Sci. Technol. 3(2), 025004 (2018)CrossRefGoogle Scholar
  7. 7.
    Paler, A., Zulehner, A., Wille, R.: NISQ circuit compilers: search space structure and heuristics, arXiv preprint arXiv:1806.07241 (2018)
  8. 8.
    Li, G., Ding, Y., Xie, Y.: Tackling the qubit mapping problem for nisq-era quantum devices, arXiv preprint arXiv:1809.02573 (2018)
  9. 9.
    Zulehner, A., Wille, R.: Compiling SU (4) quantum circuits to IBM QX architectures, arXiv preprint arXiv:1808.05661 (2018)

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Linz Institute of TechnologyJohannes Kepler UniversityLinzAustria

Personalised recommendations