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arXiv:2010.07965

Observation of separated dynamics of charge and spin in the Fermi-Hubbard model

Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, R. Barends, Andreas Bengtsson, Sergio Boixo, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Yu Chen, Zijun Chen, Chen, Yu-An, B. Chiaro, Roberto Collins, Stephen J. Cotton, William Courtney, Sean Demura, Alan R. Derk, A. Dunsworth, Daniel Eppens, Thomas Eckl, Catherine Erickson, Edward Farhi, Austin G. Fowler, Brooks Foxen, Craig Gidney, Marissa Giustina, R. Graff, Jonathan A. Gross, Steve Habegger, Matthew P. Harrigan, Alan Ho, Sabrina Hong, Trent Huang, William J. Huggins, L. B. Ioffe, Sergei V. Isakov, Evan R. Jeffrey, Jiang Zhang, Cody Jones, Dvir Kafri, Kostyantyn Kechedzhi, J. Kelly, Seon Kim, Paul V. Klimov, Alexander N. Korotkov, Fedor Kostritsa, David Landhuis, Pavel Laptev, Mike Lindmark, Erik A. Lucero, Michael Marthaler, Orion Martin, John M. Martinis, Anika Marusczyk, Sam McArdle, Jarrod R. McClean, Trevor McCourt, Matt McEwen, A. Megrant, Carlos Mejuto-Zaera, Xiao Mi, Masoud Mohseni, Wojciech Mruczkiewicz, J. Mutus, Ofer Naaman, M. Neeley, Charles Neill, Hartmut Neven, Michael Newman, Murphy Yuezhen Niu, Thomas E. O’Brien, Eric P. Ostby, Bálint Pató, A. G. Petukhov, Harald Putterman, Chris Quintana, Jan-Michael Reiner, P. Roushan, Nicholas C. Rubin, D. Sank, Kevin J. Satzinger, Vadim Smelyanskiy, Doug Strain, Kevin J. Sung, Peter Schmitteckert, Marco Szalay, Norm M. Tubman, A. Vainsencher, T. White, Nicolas Vogt, Z. Jamie Yao, P. Yeh, Adam Zalcman, Sebastian Zanker

Published Oct 15, 2020• 75 citations
arXivHTMLPDF

Abstract

Strongly correlated quantum systems give rise to many exotic physical phenomena, including high-temperature superconductivity. Simulating these systems on quantum computers may avoid the prohibitively high computational cost incurred in classical approaches. However, systematic errors and decoherence effects presented in current quantum devices make it difficult to achieve this. Here, we simulate the dynamics of the one-dimensional Fermi-Hubbard model using 16 qubits on a digital superconducting quantum processor. We observe separations in the spreading velocities of charge and spin densities in the highly excited regime, a regime that is beyond the conventional quasiparticle picture. To minimize systematic errors, we introduce an accurate gate calibration procedure that is fast enough to capture temporal drifts of the gate parameters. We also employ a sequence of error-mitigation techniques to reduce decoherence effects and residual systematic errors. These procedures allow us to simulate the time evolution of the model faithfully despite having over 600 two-qubit gates in our circuits. Our experiment charts a path to practical quantum simulation of strongly correlated phenomena using available quantum devices.

DOI
10.48550/arxiv.2010.07965

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Quantum computers are the ideal platform for quantum simulations. Given enough coherent operations and qubits, such machines can be leveraged to simulate strongly correlated materials, where intricate quantum effects give rise to counterintuitive macroscopic phenomena such as high-temperature superconductivity. In this paper, we provide a gate decomposition and an architecture for a quantum simulator used to simulate the Fermi-Hubbard model in a hybrid variational quantum-classical algorithm. We propose a simple planar implementation-independent layout of qubits that can also be used to simulate more general fermionic systems. By working through a concrete application, we show the gate decomposition used to simulate the Hamiltonian of a cluster of the Fermi-Hubbard model. We briefly analyze the Trotter-Suzuki errors and estimate the scaling properties of the algorithm for more complex applications.
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The Fermi–Hubbard model is a fundamental model in condensed matter physics that describes strongly correlated electrons. On the other hand, quantum computers are emerging as powerful tools for exploring the complex dynamics of these quantum many-body systems. In this work, we demonstrate the quantum simulation of the one-dimensional Fermi–Hubbard model using IBM's superconducting quantum computers, employing over 100 qubits. We introduce a first-order Trotterization scheme and extend it to an optimized second-order Trotterization for the time evolution in the Fermi–Hubbard model, specifically tailored for the limited qubit connectivity of quantum architectures, such as IBM's platforms. Notably, both Trotterization approaches are scalable and maintain a constant circuit depth at each Trotter step, regardless of the qubit count, enabling us to precisely investigate the relaxation dynamics in the Fermi–Hubbard model by measuring the expectation value of the Néel observable (staggered magnetization) for time-evolved quantum states. Finally, our successful measurement of expectation values in such large-scale quantum many-body systems, especially at longer time scales with larger entanglement, highlights the quantum utility of superconducting quantum platforms over conventional classical approximation methods.