Our research areas

• Quantum system characterization (a.k.a. QCVV):
  How can one find out how well a quantum device really works?
   
• Quantum algorithms and the cost of measurement:
  What computational problems are worth running on a quantum computer, and how many measurements does it take?
   
• Quantum compiling, gate synthesis and Hamiltonian engineering:
  How do we turn an abstract algorithm into the fastest possible sequence of physical operations?
   
• Classical algorithms: quantum-inspired computing:
  How far do classical solvers reach, and what can algorithms borrowed from quantum theory add? We work on state-of-the-art QUBO and Ising solvers, and on tensor-network methods for differential equations.
   
• Quantum error correction:
  How can one learn the errors of a device and protect computations against them?
   
• Classical simulation of quantum many-body systems:
  Where exactly does classical computing become practically infeasible?
   
• Limitations of quantum computing:
  What can quantum computers provably *not* do efficiently?

What are quantum computers good for?

Quantum computing is frequently oversold. Public expectations have run ahead of what has been demonstrated, and sometimes ahead of what is mathematically possible. 
Timelines get compressed, speed-ups are quoted without the classical baseline they should be measured against, and today's noisy devices are described as though the challenge of achieving fault-tolerance was already solved.

We consider honest expectation management to be part of our academic responsibility.
Our mission is to answer the question “What are quantum computers good for?” as precisely as the evidence allows, and happily publish negative answers as well. 
Several of our results are no-go theorems and hardness proofs showing that popular approaches cannot work the way they are often advertised.
On the practical side, we also benchmark strong classical solvers to set a bar for quantum computers.

Quantum computers can solve some computational problems dramatically faster than classical computers. This raises a simple but difficult question: which problems can they actually solve better?
We are a theory group at Hamburg University of Technology working on the mathematics and computer science needed to answer it, from characterizing real devices to designing algorithms and proving what cannot be done.

Our work combines applied mathematics, computational complexity, signal processing, convex and non-convex optimization, representation theory, random matrix theory and tensor networks. We test our methods against real hardware and against the best classical algorithms we can find.

Currently five externally funded projects carry this work, supported by the German Research Foundation (DFG), the Federal Ministry of Research, Technology and Space (BMFTR) and IFB Hamburg, alongside a research collaboration with Fujitsu. 
We teach quantum computing and theoretical computer science at TUHH, supervise Bachelor's and Master's theses, and work with partners in Hamburg, across Germany and internationally.