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Paper 1
Characterizing Universal Gate Sets via Dihedral Benchmarking
Arnaud Carignan-Dugas, Joel J. Wallman, Joseph Emerson
- Year
- 2015
- Journal
- arXiv preprint
- DOI
- arXiv:1508.06312
- arXiv
- 1508.06312
We describe a practical experimental protocol for robustly characterizing the error rates of non-Clifford gates associated with dihedral groups, including gates in SU(2) associated with arbitrarily small angle rotations. Our dihedral benchmarking protocol is a generalization of randomized benchmarking that relaxes the usual unitary 2-design condition. Combining this protocol with existing randomized benchmarking schemes enables an efficient means of characterizing universal gate sets for quantum information processing in a way that is independent of state-preparation and measurement errors. In particular, our protocol enables direct benchmarking of the $T$ gate (sometime called $π/8$-gate) even for the gate-dependent error model that is expected in leading approaches to fault-tolerant quantum computation.
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Tradeoffs on the volume of fault-tolerant circuits
Anirudh Krishna, Gilles Zémor
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2510.03057
- arXiv
- 2510.03057
Dating back to the seminal work of von Neumann [von Neumann, Automata Studies, 1956], it is known that error correcting codes can overcome faulty circuit components to enable robust computation. Choosing an appropriate code is non-trivial as it must balance several requirements. Increasing the rate of the code reduces the relative number of redundant bits used in the fault-tolerant circuit, while increasing the distance of the code ensures robustness against faults. If the rate and distance were the only concerns, we could use asymptotically optimal codes as is done in communication settings. However, choosing a code for computation is challenging due to an additional requirement: The code needs to facilitate accessibility of encoded information to enable computation on encoded data. This seems to conflict with having large rate and distance. We prove that this is indeed the case, namely that a code family cannot simultaneously have constant rate, growing distance and short-depth gadgets to perform encoded CNOT gates. As a consequence, achieving good rate and distance may necessarily entail accepting very deep circuits, an undesirable trade-off in certain architectures and applications.
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