Luke Schaeffer

Luke Schaeffer is an Assistant Professor at the University of Waterloo, affiliated with the Cheriton School of Computer Science and the Institute for Quantum Computing (IQC). His academic journey includes a BMath and MMath from Waterloo, a PhD from MIT under Scott Aaronson, and postdoctoral positions at Waterloo and UMD.

His research bridges quantum computing and theoretical computer science, with focuses on quantum circuit complexity, classical simulation of quantum systems, and combinatorics on words. Notable projects include studying the Clifford group's structure, low-depth quantum vs. classical circuits, query complexity of regular languages, and fermion-to-qubit encodings. He also explores non-quantum areas like combinatorial game theory and cellular automata.

His work on interactive quantum advantage protocols demonstrated separations between quantum and classical circuit models, including results against AC⁰[p] and NC¹ classes. He co-developed sample-optimal classical shadow algorithms for pure states and classified Clifford gates over qubits into 57 distinct classes.

• Education:
  • BMath and MMath, University of Waterloo
  • PhD in Computer Science, MIT (advisor: Scott Aaronson)
• Key Research Themes:
  • Quantum advantage and circuit complexity
  • Automata and combinatorics on words
  • Classical simulation techniques for quantum systems
  • Algorithmic foundations of quantum computing

He advises students in the Cheriton School of Computer Science, emphasizing quantum computing and theoretical computer science. His contributions include foundational results in quantum-classical separations and decidability of word properties via first-order logic.