Abstract
We present a new and simplified two-qubit randomized benchmarking procedure that operates only in the symmetric subspace of a pair of qubits and is well suited for benchmarking trapped-ion systems. By performing benchmarking only in the symmetric subspace, we drastically reduce the experimental complexity, number of gates required, and run time. The protocol is demonstrated on trapped ions using collective single-qubit rotations and the Molmer-Sorenson (MS) interaction to estimate an entangling gate error of $2(1) \times 10^{-3}$. We analyze the expected errors in the MS gate and find that population remains mostly in the symmetric subspace. The errors that mix symmetric and anti-symmetric subspaces appear as leakage and we characterize them by combining our protocol with recently proposed leakage benchmarking. Generalizations and limitations of the protocol are also discussed.
Highlights
Like any complex machine, the construction of a largescale quantum computer will require a rapid design-and-test cycle of individual components and their assemblage
In addition to developing the theory behind subspace randomized benchmarking (SRB), we demonstrate the procedure in a trapped ion system
The Clifford gates are selected in randomized benchmarking (RB) for two reasons: (1) it is efficient to simulate their evolution by the Gottesman-Knill theorem [22] and (2)
Summary
The construction of a largescale quantum computer will require a rapid design-and-test cycle of individual components and their assemblage. In the case of multiqubit gate benchmarking, one disadvantage of the protocol is the requirement for individual addressing While this demand is needed for universal quantum computation, it can impose a significant engineering requirement on the design-and-test cycle, especially in trapped-ion systems. We use leakage benchmarking [18,19,20] to identify errors that may drive population outside of this subspace We show that these different methods can be combined into a single procedure and each effect can be individually measured. This analysis can identify many common errors, and we consider several examples numerically.
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