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Benchmarking Quantum Advantage

   School of Informatics

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  Dr OT Brown, Dr R Garcia Patron-Sanchez  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

About the Project

Quantum computing is coming, and HPC should be ready to integrate it. The most crucial challenge ahead to scale-up the capability of next generation quantum processing units (QPU), together with proposing a scalable architecture, is the improvement of quantum gates’ quality to reach fault-tolerance. The development of tools to benchmark quantum advantage that are rigorous, transparent, and accessible to all stakeholders, will be crucial for its success. The aim of this project is to develop a framework to locate and characterize the boundary between classical and quantum computational advantage, and to investigate if, when, and how quantum computing may provide a practical advantage over classical computing. HPC has been used to implement classical emulators of quantum computation that directly provide lower bounds to the required size of a QPU needs to have to provide a quantum advantage. In this project we will implement a new paradigm of classical emulators of QPU that exploit the existence of error in the QPU to run more efficiently. This will allow us to provide upper-bound on the size of a near-term QPU, which lack the use of quantum error-correction techniques, before it loses its quantum advantage due to the accumulation of error. This approach allows us to construct a rigorous technique to certify future claims of practical advantage, but also to predict the technological improvements required for specific end-user applications.

The emulator will be developed in C++, and is expected to be parallelised using both MPI and OpenMP, in order to take full advantage of modern HPC architectures. It may be that existing tensor network libraries such as iTensor1 or ExaTN2 could be leveraged to support this. Given that simulations of quantum computing are typically bound by the total available memory, we expect the code to at least scale to hundreds of nodes of ARCHER2 (tens of thousands of cores). The project will build on recent result on the classical simulation of large-size quantum circuits using tensor networks3,4,5 to build novel classical emulations that exploit the presence of imperfections in the QPU it aims to emulate, to accelerate the running time of the classical emulation.  

This work will also build on the work of MSc students at EPCC to build a cost model for hybrid quantum algorithms in the style of the LogGP model for parallel programming, which has previously been extended to heterogeneous systems6,7,8. Prior work in these areas focuses on the capabilities of future fault-tolerant quantum computers9, but near-term quantum hardware inherently has errors, and the intention of this project is to exploit the existence of those errors to provide a more accurate picture of current quantum capabilities. This will allow us to more tightly bound the boundary between quantum and classical advantage, and to explore how this will change with improved quality of quantum hardware.

Oliver Brown is an Applications Consultant in HPC at EPCC. He leads EPCC's quantum computing research area, and is course organiser and a lecturer on its Design and Analysis of Parallel Algorithms course. Since joining EPCC in 2018 he has worked on programming models for heterogeneous systems, but his background is in simulating many-body quantum systems using matrix product states10,11.

Raul Garcia-Patron Sanchez is Senior Lecturer at the School of Informatics and instructor of its Introduction to Quantum Computing course. He has years of experience on analyzing the effect of imperfection on quantum computing devices12, where he has successfully implemented a similar research program for quantum photonic devices13,14,15, and has some experience with tensor network simulation of quantum system16.

Overview of research area:

Quantum computing presents a unique challenge in the field of novel computing, as it replaces the classical bit with a quantum bit, or qubit. The qubit has the same information capacity as the bit, but otherwise has quite different properties – it can exist in a superposition of states, can not be copied, and can be entangled with other qubits. Decades of computing research go out the window when such a fundamental change is made. The potential of quantum computing is nevertheless alluring, with algorithms being developed which offer from exponential to quadratic speedup. There's no debate that practical quantum computing is still some years away, but it is crucial to understand where it can be most effectively applied and at the same time develop new programming models.

These are the most pressing questions in this field at the moment. We don't have the large fault-tolerant quantum computers we'd like, but we have enough to start coming up with answers. 

Potential research question(s)

  • Exploit the existence of error on quantum gates of near-term quantum hardware to develop classical emulators for HPC that run more efficiently the more errors are present on the QPU.
  • Challenge recent quantum supremacy claims17 by developing classical algorithms that can pass the cross-entropy benchmark (XEB) used in those experiments to certify quantum supremacy.
  • Characterize the boundary between quantum advantage and classical simulation using our newly developed techniques.
  • Can quantum hardware fidelity be incorporated in to a LogGP style cost model for quantum algorithm performance?
  • Can the cost model be used to compare/predict quantum algorithm performance? Can it be used to compare quantum/classical performance?

Funding Notes

EPCC holds the following funding opportunities across its PhD opportunities at present for which this project is one of many eligible (i.e. competitive funding):
For entry during academic year 2021-22:
1 EPSRC studentship with standard EPSRC eligibility:
For entry during academic year 2022-23:
3 EPSRC studentships with standard EPSRC eligibility:, of which one may have open (i.e. international) eligibility
We also welcome applications for these projects from students with their own source(s) of funding.


• Matthew Fishman, Steven R. White and E. Miles Stoudenmire. The ITensor Software Library for Tensor Network Calculations. (2020). arXiv:2007.14822.
• Dmitry I. Lyakh, Alex McCaskey, Joe Osborn, and Thien Nguyen. ExaTN. (2021).
• Mateusz Meller, Benchmarking (simulated) Quantum Computer, MSc Dissertation, (2021).
• Johnnie Gray, Stefanos Kourtis, Hyper-optimized tensor network contraction, Quantum 5, 410 (2021)
• Cupjin Huang, Fang Zhang, Michael Newman, Junjie Cai, Xun Gao, Zhengxiong Tian, Junyin Wu, Haihong Xu, Huanjun Yu, Bo Yuan, Mario Szegedy, Yaoyun Shi, Jianxin Chen, Classical Simulation of Quantum Supremacy Circuits,
• Feng Pan, Pan Zhang, Simulating the Sycamore quantum supremacy circuits,
• Albert Alexandrov, Mihai F. Ionescu, Klaus E. Schauser, Chris Scheiman, LogGP: Incorporating Long Messages into the LogP Model for Parallel Computation, Journal of Parallel and Distributed Computing, Volume 44, Issue 1, 1997,
• J. L. Bosque and L. P. Perez, "HLogGP: a new parallel computational model for heterogeneous clusters," IEEE International Symposium on Cluster Computing and the Grid, 2004. CCGrid 2004., 2004, pp. 403-410, doi: 10.1109/CCGrid.2004.1336594
• Keith A. Britt and Travis S. Humble. 2017. High-Performance Computing with Quantum Processing Units. J. Emerg. Technol. Comput. Syst. 13, 3, Article 39 (May 2017), 13 pages. DOI:
• E. T. Owen, O. T. Brown, and M. J. "Hartmann. Dissipation-induced mobility and coherence in frustrated lattices". Phys. Rev. A. 95, 063851. (2017).
• O. T. Brown, and M. J. Hartmann. "Localization to delocalization crossover in a driven nonlinear cavity array". New Journal of Physics, 20, 055004. (2018).
• Daniel Stilck Franca, Raul Garcia-Patron, Limitations of optimization algorithms on noisy quantum devices, Nat. Phys. (2021)
• Nicolás Quesada, Rachel S. Chadwick, Bryn A. Bell, Juan Miguel Arrazola, Trevor Vincent, Haoyu Qi, Raúl García-Patrón, Quadratic speedup for simulating Gaussian boson sampling,
• Alexandra E. Moylett, Raúl García-Patrón, Jelmer J. Renema, Peter S. Turner, Classically simulating near-term partially-distinguishable and lossy boson sampling, Quantum Science and Technology 5, 015001 (2020)
• Raúl García-Patrón, Jelmer J. Renema, Valery Shchesnovich, Simulating boson sampling in lossy architectures, Quantum 3, 169 (2019)
• Michael Lubasch, Antonio A. Valido, Jelmer J. Renema, W. Steven Kolthammer, Dieter Jaksch, Myungshik S. Kim, Ian Walmsley, Raúl García-Patrón, Tensor network states in time-bin quantum optics, Phys. Rev. A 97, 062304 (2018)
• Arute, F., Arya, K., Babbush, R. et al. Quantum supremacy using a programmable superconducting processor. Nature 574, 505–510 (2019).
Additional References
• Johnnie Gray, Stefanos Kourtis, Hyper-optimized tensor network contraction, Quantum 5, 410 (2021)
• Cupjin Huang, Fang Zhang, Michael Newman, Junjie Cai, Xun Gao, Zhengxiong Tian, Junyin Wu, Haihong Xu, Huanjun Yu, Bo Yuan, Mario Szegedy, Yaoyun Shi, Jianxin Chen, Classical Simulation of Quantum Supremacy Circuits,
• Feng Pan, Pan Zhang, Simulating the Sycamore quantum supremacy circuits,

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