ABSTRACT
Quantum simulators enable the exploration of complex quantum phenomena by reproducing their dynamics on controllable quantum devices. However, experimental constraints often restrict the Hamiltonians that can be realized natively, while limited coherence times demand efficient implementations of the desired dynamics. Hamiltonian engineering is the task of finding suitable control pulses to synthesize the dynamics under the target Hamiltonians from the native system Hamiltonian, using local control pulses that implement fast local unitaries on the system.
We start by observing that this task can be solved with an optimally short quantum runtime via an exponentially large linear program (LP), based on specific commutation relations between the control pulses and the interaction terms of the system Hamiltonian.
Then we prove a sequence of results:
- Finding the control pulses for the shortest quantum runtime is NP-hard.
- By subsampling the control pulses, we obtain a small LP, and can hence efficiently find control pulses that simulate the target dynamics at an increased quantum runtime.
- For 2-local Hamiltonians, we can use techniques based on the geometry of complex cut polytopes to reach a guaranteed quantum runtime, which is close to the optimal one for all considered example systems.
- We can correct for various types of errors using average Hamiltonian theory and robust pulses.
To be more concrete, we discuss numerical examples including Ising-type, chiral clock model, and Hubbard model Hamiltonians, and demonstrate the scalability of our approach with the Harper-Hofstadter model on a 32x24 lattice. We hope our unified approach, with close-to-optimal quantum runtime and provable guarantees, paves the way for automatically programmable analog quantum simulators.
BIOGRAPHY
Professor Martin Kliesch is a Full Professor and Head of the Institute for Quantum Inspired and Quantum Optimization at Hamburg University of Technology (TUHH). His research seeks to enable practical quantum advantage through mathematically rigorous approaches to quantum computing and quantum-inspired classical computation. His expertise includes quantum hardware characterization, Pauli-noise and Hamiltonian learning, quantum error correction, quantum algorithms, efficient quantum-computer readout, gate design, analogue quantum simulation, and QUBO optimization.
He studied physics and mathematics at the Technical University of Berlin and earned his doctorate in physics from Freie Universität Berlin under Professor Jens Eisert. His dissertation received the highest distinction and the German Physical Society’s Carl Ramsauer Prize. Following postdoctoral appointments in Berlin and Cologne, he became a POLONEZ Marie Curie Cofund Fellow at the University of Gdańsk and later led the Quantum Technology group at Heinrich Heine University Düsseldorf. He received an Emmy Noether Fellowship from the German Research Foundation in 2021.
Professor Kliesch is also an editor of Quantum, a member of Canada’s NSERC Alliance Quantum Evaluation Committee, and a scientific adviser to the quantum-computing startup eleQtron.
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