Hamiltonian Engineering for Quantum Systems

Yi-Xiang Liu, Ashok Ajoy, Jordan Hines +1 more

Hugo Ribeiro, Alexandre Baksic, Aashish A. Clerk

Ashok Ajoy, Paola Cappellaro

Özgün Kum, Matthias Zipper, Ludwig Mathey +1 more

Quantum simulators enable the exploration of complex quantum phenomena in condensed-matter systems by reproducing their dynamics on controllable quantum devices. However, experimental constraints often restrict the class of Hamiltonians that can be realized natively. Hamiltonian engineering addresses this limitation by expanding the set of accessible Hamiltonians beyond the fixed system Hamiltonian provided by the hardware. We introduce a framework for fermionic Hamiltonian engineering based on interleaving free evolution under the system Hamiltonian with a sequence of experimentally feasible local fermionic unitaries. The required sequences and free-evolution times are obtained efficiently through a linear program, enabling effective time evolution under a broad class of target Hamiltonians. In particular, our method realizes arbitrary complex tunnelling coefficients, constrained only by the connectivity of the underlying system Hamiltonian. We further show that symmetries of the Hamiltonian engineering task can be exploited to drastically reduce the cost of computing the control parameters, and that errors arising from finite pulse times can be compensated within the same framework through a simple modification of the linear program. To our knowledge, this is the first automated method to realize locally tunable artificial gauge fields in interacting fermionic lattice models using only site-resolved energy shifts as control. We demonstrate the method by engineering the dynamics of interacting Fermi-Hubbard chains with complex tunnelling coefficients and of the Harper-Hofstadter model on a 1088-mode lattice. For the latter, we exploit the translation symmetry of the model to determine a provably optimal six-pulse sequence that produces the desired dynamics independent of the lattice size.

Özgün Kum, Matthias Zipper, Ludwig Mathey +1 more

Quantum simulators enable the exploration of complex quantum phenomena in condensed-matter systems by reproducing their dynamics on controllable quantum devices. However, experimental constraints often restrict the class of Hamiltonians that can be realized natively. Hamiltonian engineering addresses this limitation by expanding the set of accessible target Hamiltonians from a fixed system Hamiltonian defined by the hardware. We introduce a new framework for fermionic Hamiltonian engineering based on conjugating free evolution under the system Hamiltonian with sequences of experimentally feasible local fermionic unitaries. The required sequences and free-evolution times are obtained efficiently via a linear program. By interleaving system evolution with these local unitaries, our method realizes effective time evolution under a broad class of target Hamiltonians, with intrinsic robustness to finite-pulse-time errors. In particular, we demonstrate that arbitrary complex tunnelling coefficients can be realized, constrained only by the connectivity of the underlying system Hamiltonian. We illustrate this capability by engineering the dynamics of the non-interacting Harper-Hofstadter model on a 1088-mode lattice and an interacting Fermi-Hubbard chain with complex tunnelling coefficients. By construction, our approach avoids the continuous energy absorption inherent to Floquet engineering.

V. M. Bastidas, Tobias Haug, Claude Gravel +3 more

We propose a scheme to perform stroboscopic Hamiltonian engineering in the low frequency regime using a quantum system with one-dimensional nearest-neighbor coupling that are commonly available in the NISQ era. Computational problems are encoded in the effective Hamiltonian of the quantum systems under the effect of external driving. Our approach is nonperturbative and it does not rely on high-frequency expansions, which are a common tool in Floquet engineering. In our paper, the effective Hamiltonian that we want to engineer is fully tailored through designing the periodic driving. We illustrate how this quantum computation proceeds with two examples, an instance from the 3-SAT problem and the LiH molecule quantum chemistry simulation. In the case of the 3-SAT Hamiltonian, we show that by starting from the ground state of the trivial Hamiltonian, the quantum systems go through an adiabatic process in the stroboscopic picture towards the target Hamiltonian of the problem.