arXiv subjects

Özgün Kum

Publications and source records attributed to Özgün Kum.

2 recordsLinked to original sources

arXiv2026

Fermionic Hamiltonian engineering with local control

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.

quant-ph↗

arXiv2026

Fast Hamiltonian engineering from cut polytope geometry

Hamiltonian engineering (HE) simulates quantum dynamics under a target Hamiltonian using a native entangling system Hamiltonian and restricted control, with applications from quantum gate design to analog quantum simulation. Observing that, for many systems, formulating HE as a linear program only requires specific commutation relations between the control pulses and the system Hamiltonian, we provide a unified framework for broad classes of $2$-local qubit, qudit, and fermionic systems. We reformulate time-optimal HE as a complex $k$-cut polytope problem, with $k$ the number of distinct phases in these commutation relations, and prove it NP-complete for every finite $k$. We therefore relax the polytope to the elliptope and apply a Krivine-type rounding, yielding pulses informed by the system and target Hamiltonians, which we then use in a linear program. We derive how many informed pulses are necessary and sufficient for the linear program to be reliably feasible. Additionally mixing in uniformly sampled pulses guarantees a solution close to the relaxation value from $\mathrm{O}(m)$ pulses, with $m$ the number of interaction terms. Together with upper and lower bounds on the optimal quantum run time, this yields an $\mathrm{O}(\sqrt{m})$ approximation ratio. In benchmarks on a fully connected Ising model, a chiral clock model for qudits, and the fermionic Harper-Hofstadter model, our approach attains near-optimal quantum run times wherever the optimum is computable, reaches run times that saturate with the lattice size in the fermionic case, and outperforms state-of-the-art methods with $\mathrm{O}(m)$ pulses. This establishes a unified approach with provable guarantees to the automatic programming of analog quantum simulators.

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