From the operation an algorithm asks for to the pulses a device can actually apply.

Quantum devices typically support only a limited set of "native" operations that can be implemented directly and efficiently. Any algorithm executed on the device must therefore be translated into a sequence of these native operations, a process known as quantum compilation. Each additional operation takes time and introduces errors, making it harder to preserve quantum coherence. A key challenge in building practically useful quantum computers is therefore to compile abstract quantum algorithms into the most efficient possible sequences of native operations. Since the available native interactions depend strongly on the underlying hardware architecture, quantum compilation is inherently hardware-dependent and presents challenges beyond those encountered in classical compilation.

We approach quantum compilation from both directions. Starting from the native couplings of a quantum device, we determine which useful instructions can be synthesized and derive fundamental limits on how quickly they can be implemented. These limits provide a benchmark against which compilation methods can be assessed. Conversely, starting from a desired many-body operation, we develop robust control sequences that realize it on the available hardware while remaining resilient to imperfections such as calibration errors.

The robust control techniques we develop are also useful for analog quantum simulation, where engineering desired quantum dynamics is itself a central challenge. In an analog quantum device, the continuous-time dynamics is governed by its Hamiltonian, which describes the interactions within the system. The task is then to use the native system Hamiltonian, together with available controls, to reproduce the dynamics of a desired target Hamiltonian.
 

What we work on

• Time-optimal global multi-qubit entangling gates for registers with fixed, non-local Ising-type couplings, as found in trapped-ion platforms.
• Compilation strategies that build circuits from few multi-qubit gates rather than many two-qubit gates.
• The computational complexity of gate synthesis, and rigorous lower bounds on the time any such gate can take.
• Robust Hamiltonian engineering: efficiently computable pulse sequences that convert a device's native interaction into a wide class of target Hamiltonians.
• Fermionic Hamiltonian engineering with purely local control, aimed at cold-atom simulators of Fermi–Hubbard-type models.
• The mathematics of randomized and stochastic control, which underpins both decoupling sequences and benchmarking.

Selected results

• Fewer, faster entangling gates.
  For platforms whose qubits all couple to each other through a fixed Ising-type interaction, we construct global entangling gates that are time-optimal within this model, and show how to compile circuits with fewer gates executed in less time, minimizing decoherence.
  Baßler, Zipper, Cedzich, Heinrich, Huber, Johanning, Kliesch, Synthesis of and compilation with time-optimal multi-qubit gates, [arXiv:2206.06387], Quantum 7, 984 (2023).
• Complexity of time optimal multi-qubit gates.
  We prove that finding time-optimal global entangling gates is computationally hard in general, and provide both a heuristic that works well in practice and rigorous lower bounds on the achievable gate time. We find that for a device with a given fixed coupling strength, the interaction itself sets a gate time that no amount of compiler optimization can undercut.
  Baßler, Heinrich, Kliesch, Time-optimal multi-qubit gates: Complexity, efficient heuristic and gate-time bounds, [arXiv:2307.11160], Quantum 8, 1279 (2024).
• A general, robust and efficient Hamiltonian engineering scheme for qubits. Our framework takes the interaction a device natively has and turns it into a target many-body Hamiltonian from a broad class of Hamiltonians, and using pulse sequences that can be computed efficiently and that stay accurate under experimental imperfections.
  Baßler, Heinrich, Kliesch, General, efficient, and robust Hamiltonian engineering, [arXiv:2410.19903], PRX Quantum 6, 040346 (2025). Presented as a talk at QCTiP 2025, Berlin.
• Efficient Hamiltonian engineering on fermionic hardware with local control only.
  For fermionic lattice systems such as ultracold atoms in optical lattices, we develop an efficient framework for simulating target Hamiltonians with arbitrary complex-valued tunnelling coefficients in the presence of strong interactions. Our method uses local operations only and is particularly useful for simulating Fermi-Hubbard type Hamiltonians with engineered gauge fields.
  Kum, Zipper, Mathey, Kliesch, Fermionic Hamiltonian engineering with local control, [arXiv:2606.17158].
• Improved and generalized 2-local Hamiltonian engineering with rigorous runtime guarantees.
  Friese, Kum, Harrow, Kliesch, Fast Hamiltonian engineering from cut polytope geometry, [arXiv:2609.36006].
• How quickly random dynamics scrambles.
  We bound how fast continuous-time random Hamiltonian evolution approaches an approximate unitary design, which supplies the mathematical basis both for randomized control and decoupling schemes and for randomized-benchmarking arguments.
  Onorati, Buerschaper, Kliesch, Brown, Werner, Eisert, Mixing properties of stochastic quantum Hamiltonians, [arXiv:1606.01914], Commun. Math. Phys. 355, 905 (2017).

All our publications on this topic

The following search runs live at arXiv, so the list stays current without manual maintenance:
[All our preprints on Hamiltonian engineering, gate synthesis and quantum control (arXiv)].

Funding

Part of this work belongs to TouQan, Towards a useful quantum advantage, a [QuantERA] project whose Hamburg node is funded by the DFG under reference KL 3047/2-1, 2024 to 2027.
Hamiltonian engineering is how a quantum simulator is actually implemented, so the control quality reachable here decides how much of a claimed advantage survives the noise.