Research

Digital quantum simulation on quantum computers

Making Trotterization adaptive and energy-self-correcting for NISQ devices and beyond

Simulation of continuous-time evolution requires time discretization on both classical and quantum computers. A finer time step improves simulation precision but it inevitably leads to increased computational efforts. Classical adaptive solvers are well developed to save numerical computation times. However, it remains an outstanding challenge to make optimal usage of the available quantum resources by means of adaptive time steps. Here, we introduce a quantum algorithm to solve this problem, providing a controlled solution of the quantum many-body dynamics of local observables. The key conceptual element of our algorithm is a feedback loop that self-corrects the simulation errors by adapting time steps, thereby significantly outperforming conventional Trotter schemes on a fundamental level and reducing the circuit depth.

H. Zhao, M. Bukov, M. Heyl, R. Moessner. PRX Quantum 4, 030319 (2023).
H. Zhao, M. Bukov, M. Heyl, R. Moessner. PRL 133, 010603 (2024).

Non-equilibrium phases of matter in driven many-body systems

Time-dependent driving has been widely used as a crucial tool to drastically modify properties of quantum systems and to engineer non-equilibrium phases of matter, like discrete time crystals. I am interested in seeking a universal classification of different thermalization pathways, e.g. based on symmetry classification, and discovering exotic non-equilibrium phases of matter that do not have any static (and even Floquet) counterpart.

Engineering hierarchical symmetries

We present a general driving protocol for many-body systems to generate a sequence of prethermal regimes, each exhibiting a lower symmetry than the preceding one. We provide an explicit construction of effective Hamiltonians exhibiting these symmetries. This imprints emergent quasiconservation laws hierarchically, enabling us to engineer the respective symmetries and concomitant orders in nonequilibrium matter. We provide explicit examples, including spatiotemporal and topological phenomena, as well as a spin chain realizing the symmetry ladder SU(2)→U(1)→Z2→E.

Z. Fu, R.Moessner, H. Zhao, M. Bukov. PRX 14, 041070 (2024)

Random multipolar driving and prethermalization

We propose n-random multipolar driving protocols as a family of correlated random drives. For n ≥ 1 and large driving frequencies, we find a prethermal regime where heating is significantly suppressed. The prethermal lifetime grows algebraically for larger driving frequencies, with an integer exponent 2n + 1. A simple theory based on Fermi’s golden rule accounts for this behaviour. We furthermore derive rigorous bounds on the heating rate by generalizing Floquet Magnus expansion. The long-lived prethermal phenomenon even survives extra higher-band particle excitation, which commonly occurs in cold atoms experiments.

H. Zhao, F. Mintert, R.Moessner and J. Knolle. Phys. Rev. Lett. 126, 040601 (2021).
T. Mori, H. Zhao, F. Mintert, R.Moessner and J. Knolle. Phys. Rev. Lett. 127, 050602 (2021).
H. Zhao, J. Knolle, R. Moessner and F. Mintert. Phys. Rev. Lett. 129, 120605 (2022).
J. Yan, R. Moessner and H. Zhao, Physical Review B 109 (6), 064305 (2024).

Temporal disorder in spatiotemporal order

We introduce a correlated random driving protocol to realize a spatiotemporal order that cannot be achieved even by periodic driving --- a time rondeau crystal. It extends the discussion of time-translation-symmetry-breaking to randomly driven systems. We find a combination of temporally disordered micro-motion with prethermal stroboscopic spatiotemporal long-range order. This spatiotemporal order remains robust against generic perturbations, with an algebraically long prethermal lifetime where the scaling exponent strongly depends on the symmetry of the perturbation, which we account for analytically. Time rondeau crystals have now been experimentally realized by Ajoy Lab from Berkeley!

H. Zhao, J. Knolle, R. Moessner, Phys. Rev. B 108, L100203 (2023).
L. J. Moon, P. Schindler, Y. Sun, E. Druga, J. Knolle, R. Moessner, H. Zhao, M. Bukov, A. Ajoy, arXiv:2404.05620 (2024).

Quantum many-body scars and weak breaking of ergodicity

Quantum many-body scars in optical lattices

We propose a simple setup to generate quantum many-body scars in a doubly modulated Bose-Hubbard system which can be readily implemented in cold atomic gases. The dynamics are shown to be governed by kinetic constraints which appear via density-assisted tunneling in a high-frequency expansion. The experimental signatures and the transition to fully thermalizing behavior as a function of driving frequency are analyzed.

H. Zhao, J. Vovrosh, F. Mintert and J. Knolle. Phys. Rev. Lett. 124, 160604 (2020).

Orthogonal quantum many-body scars

Here we show that, by adding kinetic constraints to a fractionalized orthogonal metal, we can construct a minimal model with orthogonal quantum many-body scars leading to persistent oscillations with infinite lifetime coexisting with rapid volume-law entanglement generation. Our example provides new insights into the link between quantum ergodicity and many-body entanglement while opening new avenues for exotic non-equilibrium dynamics in strongly correlated multi-component quantum systems.

H. Zhao, A. Smith, F. Mintert, J. Knolle, Phys. Rev. Lett. 127, 150601 (2021).

Disorder-free localization

Stabilizing disorder-free localization

Disorder-free localization is a paradigm of nonergodicity in translation-invariant quantum many-body systems hosting gauge symmetries. An open question concerns the stability of disorder-free localization in the presence of gauge-breaking errors, and whether processes due to the latter can be controllably suppressed. Here, we show that translation-invariant single-body gauge terms induce a quantum Zeno effect that reliably protects disorder-free localization against errors up to times at least polynomial in the protection strength.

J. C. Halimeh, L. Homeier, H. Zhao, A. Bohrdt, F. Grusdt, P. Hauke and J. Knolle. PRX Quantum 3, 020345 (2022).
J. C. Halimeh, H. Zhao, P. Hauke, J. Knolle, arXiv: 2111. 02427 (2021).

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