Source-linked AI summary
Characterizing Universal Gate Sets via Dihedral Benchmarking
Arnaud Carignan-Dugas, Joel J. Wallman, Joseph Emerson
TL;DR
Characterizing non-Clifford errors matters because their implementation can have error rates unlike Clifford gates, while quantum process tomography scales exponentially and cannot distinguish gate errors from SPAM. The paper extends randomized benchmarking to dihedral groups without the usual 2-design constraint and combines it with existing schemes for direct T-gate characterization; simulations show precise estimates in a high-contrast error regime but a loose bound when error levels match.
Problem
Quantum process tomography scales exponentially with qubit number and cannot separate gate errors from state-preparation and measurement errors, while non-Clifford gates can have different error rates from Clifford gates.
Source: p. 1Method
The protocol benchmarks average fidelity for dihedral-group operations without the usual 2-design constraint and combines with standard and interleaved randomized benchmarking to characterize the T gate directly.
Source: p. 1Results
0.9902(3) is the simulated T-gate fidelity estimate when Clifford fidelity is 1−10−6 and T-gate fidelity is 1−10−2; with both at 0.99, the estimate is 0.966 and the bound is [0.928, 0.995].
Source: p. 4Takeaways & Limitations
The D8 and D4 protocols enable efficient and precise benchmarking of the T gate in leading fault-tolerant quantum-computing proposals.
Source: p. 4In the similar-error regime, the interleaved protocol’s bound is loose, spanning [0.928, 0.995]; this is an open problem for interleaved randomized benchmarking generally.
Source: p. 4
Abstract
from arXiv · showhide
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 $\pi/8$-gate) even for the gate-dependent error model that is expected in leading approaches to fault-tolerant quantum computation.