Abstract
The use of quantum processing units (QPUs) promises speed-ups for solving computational problems, but the quantum devices currently available possess only a very limited number of qubits and suffer from considerable imperfections. One possibility to progress towards practical utility is to use a co-design approach: Problem formulation and algorithm, but also the physical QPU properties are tailored to the specific application. Since QPUs will likely be used as accelerators for classical computers, details of systemic integration into existing architectures are another lever to influence and improve the practical utility of QPUs.
In this work, we investigate the influence of different parameters on the runtime of quantum programs on tailored hybrid CPU-QPU-systems. We study the influence of communication times between CPU and QPU, how adapting QPU designs influences quantum and overall execution performance, and how these factors interact. Using a simple model that allows for estimating which design choices should be subjected to optimisation for a given task, we provide an intuition to the HPC community on potentials and limitations of co-design approaches. We also discuss physical limitations for implementing the proposed changes on real quantum hardware devices.
All authors acknowledge funding from the German Federal Ministry of Education and Research within the funding program quantum technologies—from basic research to market, contract number 13N16093.
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Notes
- 1.
The given communication times are rough estimates supposed to illustrate optimisation potentials and relative parameter influence. We obtained the numbers by measuring typical ping durations in cloud and local network scenarios, and estimate QPU-CPU communication time by the round-trip time of an inter-processor-interrupt in a RiscV-system, given the assumptions that a QPU-CPU SoC design will likely be based on modifiable classical architectures, and that communication times between QPU and CPU are similar to inter-core communication times.
Owing to the restricted space, we do not provide more fine-grained and realistic estimates of and models for these quantities, but remark that they would very likely not substantially change our findings and conclusions.
- 2.
Moving from locally connected components to on-chip integration might be beneficial for latency-critical embedded systems with quantum acceleration, but is likely not overly relevant for many HPC use-cases.
- 3.
SoC denotes a system-on-chip solution, where CPU and QPU are integrated on the chip level.
- 4.
The placement of new connection favours augmenting regions with existing high connectivity density, following the assumption that adding extra connections is easier for regions that are already well connected. Given the lack of space, we refer readers to the replication package for the exact details.
- 5.
Technically, we employ a robust quantile regression approach [32] because the stochastic circuit generation process produces pronounced outliers.
References
Preskill, J.: Quantum computing in the NISQ era and beyond, Quantum, 2, 79 (2018). https://doi.org/10.48550/arXiv.1801.00862
Quantum technology and application consortium-QUTAC: industry quantum computing applications. EPJ Quant. Technol. 8(1), 25 (2021)
Krüger, T., Mauerer, W.: Quantum annealing-based software components: an experimental case study with SAT solving, pp. 445–450 (2020). https://doi.org/10.1145/3387940.3391472
Mauerer, W., Scherzinger, S.: 1-2-3 reproducibility for quantum software experiments. In: Q-SANER@IEEE International Conference on Software Analysis, Evolution and Reengineering (2022)
Deutsch, D.E.: Quantum computational networks. Proc. R. Soc. A 425, 73–90 (1989). https://doi.org/10.1098/rspa.1989.0099
Barenco, A., et al.: Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 (1995). https://doi.org/10.1103/PhysRevA.52.3457
Raussendorf, R., Browne, D.E., Briegel, H.J.: Measurement-based quantum computation on cluster states. Nat. Phys. 68, 022312 (2003). https://doi.org/10.1103/PhysRevA.68.022312
Farhi, E., Goldstone, J., Gutmann, S., Lapan, J., Lundgren, A., Preda, D.: A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292, 472–475 (2001). https://doi.org/10.1126%2Fscience.1057726
Farhi, E., Goldstone, J., Gutmann, S.: A quantum approximate optimization algorithm. arXiv:1411.4028 (2014). https://doi.org/10.48550/arXiv.1411.4028
Huang, H.-L., Wu, D., Fan, D., Zhu, X.: Superconducting quantum computing: a review," arXiv:2006.10433 (2020). https://doi.org/10.48550/arxiv.2006.10433
Kjaergaard, M., et al.: Superconducting qubits: current state of play. Ann. Rev. Condens. Matter Phys. 11, 369–395 (2020). https://doi.org/10.1146%2Fannurev-conmatphys-031119-050605
Lucas, A.: Ising formulations of many NP problems, vol. 2 (2014). https://doi.org/10.48550/arXiv.1302.5843
Bharti, K., et al.: Noisy intermediate-scale quantum algorithms. Rev. Mod. Phys. 94, 015004 (2022). https://doi.org/10.1103/RevModPhys.94.015004
Farhi, E., Harrow, A.W.: Quantum supremacy through the quantum approximate optimization algorithm. arXiv:1602.07674 (2016)
C.W. Commander, Maximum cut problem, MAX-CUT Maximum Cut Problem, MAX-CUT. In: Floudas, C., Pardalos, P. (eds.) Encyclopedia of Optimization. Springer, Boston, pp. 1991–1999 (2009). https://doi.org/10.1007/978-0-387-74759-0_358
Goemans, M.X., Williamson, D.P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42(6), 1115–1145 (1995). https://doi.org/10.1145/227683.227684
Fuchs, F.G., Kolden, H.Ø., Aase, N.H., Sartor, G.: Efficient encoding of the weighted MAX \(k\)-CUT on a quantum computer using QAOA. SN Comput. Sci. 2(2), 1–14 (2021). https://doi.org/10.1007/s42979-020-00437-z
Wurtz, J., Lykov, D.: Fixed-angle conjectures for the quantum approximate optimization algorithm on regular maxcut graphs. Phys. Rev. A, 104, 052419 (2021). https://doi.org/10.1103/PhysRevA.104.052419
Marwaha, K.: Local classical MAX-CUT algorithm outperforms \(p=2\) QAOA on high-girth regular graphs. Quantum, 5, 437 (2021). https://doi.org/10.22331/q-2021-04-20-437
Wurtz, J., Love, P.: Maxcut quantum approximate optimization algorithm performance guarantees for \(p>1\). Phys. Rev. A, 103, 042612 (2021). https://doi.org/10.1103/PhysRevA.103.042612
Harrison, S., Sigurdsson, H., Alyatkin, S., Töpfer, J., Lagoudakis, P.: Solving the max-3-cut problem with coherent networks. Phys. Rev. Appl. 17, 024063 (2022). https://doi.org/10.1103/PhysRevApplied.17.024063
Willsch, M., Willsch, D., Jin, F., De Raedt, H., Michielsen, K.: Benchmarking the quantum approximate optimization algorithm. Quantum Inf. Process. 19(7), 1–24 (2020). https://doi.org/10.1007/s11128-020-02692-8
Xue, C., Chen, Z.-Y., Wu, Y.-C., Guo, G.-P.: Effects of quantum noise on quantum approximate optimization algorithm. Chinese Phys. Lett. 38(3) (2021). https://doi.org/10.1088/0256-307x/38/3/030302
Pan, Y., Tong, Y., Yang, Y.: Automatic depth optimization for a quantum approximate ptimization algorithm. Phys. Rev. A, 105, 032433 (2022). https://doi.org/10.1103/PhysRevA.105.032433
Akshay, V., Rabinovich, D., Campos, E., Biamonte, J.: Parameter concentrations in quantum approximate optimization. Phys. Rev. A, 104, L010401 (2021). https://doi.org/10.1103/PhysRevA.104.L010401
Zhou, L., Wang, S.-T., Choi, S., Pichler, H., Lukin, M.D.: Quantum approximate optimization algorithm: performance, mechanism, and implementation on near-term devices. Phys. Rev. X, 10, 021067 (2020). https://link.aps.org/doi/10.1103/PhysRevX.10.021067
Hadfield, S., Wang, Z., O’Gorman, B., Rieffel, E., Venturelli, D., Biswas, R.: From the quantum approximate optimization algorithm to a quantum alternating operator ansatz. Algorithms, 12(2), 34 (2019). https://doi.org/10.3390%2Fa12020034
LaRose, R. Rieffel, E., Venturelli, D.: Mixer-phaser ansätze for quantum optimization with hard constraints. Quantum Mach. Intell. 4(2), 17 (2022). https://doi.org/10.1007/s42484-022-00069-x
Schönberger, M., Franz, M., Scherzinger, S., Mauerer, W.: Peel \(\mid \) Pile? Cross-framework portability of quantum software. In: 2022 IEEE 19th International Conference on Software Architecture Companion (ICSA-C), pp. 164–169 (2022)
Franz, M., et al.: Uncovering instabilities in variational-quantum deep q-networks. J. Franklin Inst. (2022). https://doi.org/10.1016/j.jfranklin.2022.08.021
Bruzewicz, C.D., Chiaverini, J., McConnell, R., Sage, J.M.: Trapped-ion quantum computing: progress and challenges. Appl. Phys. Rev. 6, 021314 (2019). https://doi.org/10.1063%2F1.5088164
Koenker, R.: quantreg: quantile regression, 2022, r package version 5.88 (2022). https://doi.org/10.1201/9781315120256
Acknowledgement
We thank Manuel Schönberger for providing his topology adaptation simulation code as starting point for our efforts.
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Wintersperger, K., Safi, H., Mauerer, W. (2022). QPU-System Co-design for Quantum HPC Accelerators. In: Schulz, M., Trinitis, C., Papadopoulou, N., Pionteck, T. (eds) Architecture of Computing Systems. ARCS 2022. Lecture Notes in Computer Science, vol 13642. Springer, Cham. https://doi.org/10.1007/978-3-031-21867-5_7
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