What the study found
The study found that catalyst towers, a technique for implementing continuous rotation gates in a surface code, can reduce runtime and total spacetime volume at small and medium code distances. The authors also report that conventional Clifford+T synthesis may be more efficient at large code distances.
Why the authors say this matters
The authors suggest this matters because continuous rotation gates are a significant bottleneck in fault-tolerant quantum computing, and the best cost measure may be total runtime or total space rather than only T-count or T-depth. They conclude catalyst towers may be especially useful for early fault-tolerant quantum applications where reducing the runtime of individual circuit runs is important.
What the researchers tested
The researchers explicitly constructed surface code layouts for catalyst towers in two option-pricing application examples: a phase oracle circuit and state preparation using a variational quantum circuit. They compared these layouts against conventional Clifford+T synthesis and considered runtime, space, and spacetime volume.
What worked and what didn't
At small and medium code distances, catalyst towers reduced runtime and could also decrease total spacetime volume of rotations. At large code distances, conventional Clifford+T synthesis may be more efficient. The authors also note that the conclusions depend on the application scenario and parameter choices.
What to keep in mind
The results are based on two specific option-pricing examples, so the conclusions may not apply equally to other applications. The abstract says the findings are sensitive to the scenario and parameter settings, but it does not provide additional limitations beyond that.
Key points
- Catalyst towers can reduce runtime for continuous rotations in a surface code at small and medium code distances.
- The study found that catalyst towers may also lower total spacetime volume in those regimes.
- Conventional Clifford+T synthesis may be more efficient at large code distances.
- The researchers tested two option-pricing examples: a phase oracle circuit and variational quantum state preparation.
- The authors say the choice of cost measure should include total runtime or total space, not only T-count or T-depth.
Disclosure
- Research title:
- Catalyst towers can lower rotation cost at small and medium code distances
- Authors:
- Zhu Sun, Bálint Koczor
- Institutions:
- Quantum Motion Technologies (United Kingdom), Quantum Motion Technologies (United Kingdom), University of Oxford, University of Oxford
- Publication date:
- 2026-04-22
- OpenAlex record:
- View
Get the weekly research newsletter
Stay current with scholarly research without reading academic papers — one filtered digest, every Friday.