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arXiv:2210.10799 · Nature Physics

Purification-based quantum error mitigation of pair-correlated electron simulations

Thomas E. O’Brien, Gian-Luca Anselmetti, Fotios Gkritsis, Vincent E. Elfving, Stefano Polla, William J. Huggins, Oumarou Oumarou, Kostyantyn Kechedzhi, Dmitry A. Abanin, Rajeev Acharya, I. L. Aleǐner, R. M. Allen, Trond I. Andersen, Kyle Anderson, M. Ansmann, Frank Arute, Kunal Arya, Abraham T. Asfaw, Juan Atalaya, Dave Bacon, Joseph C. Bardin, Andreas Bengtsson, Sergio Boixo, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, L. Brill, Michael Broughton, Bob Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Juan Campero, Yu Chen, Zijun Chen, B. Chiaro, Desmond Chik, J. G. Cogan, Roberto Collins, Paul Conner, William Courtney, Alexander Crook, Ben Curtin, Dripto M. Debroy, Alexander Del Toro Barba, Sean Demura, Ilya Drozdov, Andrew Dunsworth, Daniel Eppens, Catherine Erickson, Lara Faoro, Edward Farhi, Reza Fatemi, Vinicius Ferreira, Leslie Flores Burgos, Ebrahim Forati, Austin G. Fowler, Brooks Foxen, William Giang, Craig Gidney, Dar Gilboa, Marissa Giustina, Raja Gosula, Alejandro Grajales Dau, Jonathan A. Gross, Steve Habegger, Michael Hamilton, Monica Hansen, Matthew P. Harrigan, Sean David Harrington, Paula Heu, Jeremy Hilton, Markus Hoffmann, Sabrina Hong, Trent Huang, Ashley Huff, L. B. Ioffe, Sergei V. Isakov, Justin Iveland, E. Jeffrey, Jiang Zhang, Cody Jones, Pavol Juhás, Dvir Kafri, J. Kelly, Tanuj Khattar, Mostafa Khezri, Marika Kieferova, Seon Kim, Paul V. Klimov, Andrey Klots, Alexander Korotkov, Fedor Kostritsa, John Mark Kreikebaum, David Landhuis, Pavel Laptev, Kim-Ming Lau, Lily Laws, Joonho Lee

Published Oct 12, 2023• 74 citations
arXivHTMLPDF

Abstract

Abstract An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Before fault-tolerant quantum computing, robust error-mitigation strategies were necessary to continue this growth. Here, we validate recently introduced error-mitigation strategies that exploit the expectation that the ideal output of a quantum algorithm would be a pure state. We consider the task of simulating electron systems in the seniority-zero subspace where all electrons are paired with their opposite spin. This affords a computational stepping stone to a fully correlated model. We compare the performance of error mitigations on the basis of doubling quantum resources in time or in space on up to 20 qubits of a superconducting qubit quantum processor. We observe a reduction of error by one to two orders of magnitude below less sophisticated techniques such as postselection. We study how the gain from error mitigation scales with the system size and observe a polynomial suppression of error with increased resources. Extrapolation of our results indicates that substantial hardware improvements will be required for classically intractable variational chemistry simulations.

DOI
10.1038/s41567-023-02240-y

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Abstract An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Before fault-tolerant quantum computing, robust error-mitigation strategies were necessary to continue this growth. Here, we validate recently introduced error-mitigation strategies that exploit the expectation that the ideal output of a quantum algorithm would be a pure state. We consider the task of simulating electron systems in the seniority-zero subspace where all electrons are paired with their opposite spin. This affords a computational stepping stone to a fully correlated model. We compare the performance of error mitigations on the basis of doubling quantum resources in time or in space on up to 20 qubits of a superconducting qubit quantum processor. We observe a reduction of error by one to two orders of magnitude below less sophisticated techniques such as postselection. We study how the gain from error mitigation scales with the system size and observe a polynomial suppression of error with increased resources. Extrapolation of our results indicates that substantial hardware improvements will be required for classically intractable variational chemistry simulations.
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Quantum computing promises to address problems in simulation, optimization, and chemistry, but current hardware operates in the noisy intermediate-scale (NISQ) regime where coherence limits, gate imperfections, and readout errors restrict performance. Improving calibration and mitigating errors therefore remain essential. This thesis analyzes error reduction on superconducting transmon qubits through calibration, gate analysis, and circuit-level mitigation. It compares single-qubit amplitude calibration methods and analyzes two-qubit gates based on the cross-resonance interaction, identifying differences in precision, convergence, and performance. In addition, it develops Inverted-Circuit Zero-Noise-Extrapolation (IC-ZNE) which measures effective error strength using inverted circuits. Compared to standard ZNE, IC-ZNE achieves results closer to ideal values and reduces observable errors. Overall, the presented methods improve the reliability of near-term quantum processors.