Randomized benchmarking of quantum gates

TLDR

Scalable quantum computing requires elementary gates with error rates below 10⁻⁴, but standard process tomography is limited by state preparation, measurement errors, inefficient scaling, and fails to detect error compounding in long sequences, making experimental verification of such low errors challenging. The authors propose a randomized benchmarking technique that estimates computationally relevant gate errors without relying on accurate state preparation and measurement. This method uses long sequences of randomly chosen gates to verify that error behavior remains stable during extended computations. Applying the technique to trapped atomic ion qubits, they measured a one‑qubit error probability per randomized π/2 pulse of 0.00482(17), which they anticipate can be readily improved with straightforward technical modifications.

Abstract

A key requirement for scalable quantum computing is that elementary quantum gates can be implemented with sufficiently low error. One method for determining the error behavior of a gate implementation is to perform process tomography. However, standard process tomography is limited by errors in state preparation, measurement and one-qubit gates. It suffers from inefficient scaling with number of qubits and does not detect adverse error-compounding when gates are composed in long sequences. An additional problem is due to the fact that desirable error probabilities for scalable quantum computing are of the order of 0.0001 or lower. Experimentally proving such low errors is challenging. We describe a randomized benchmarking method that yields estimates of the computationally relevant errors without relying on accurate state preparation and measurement. Since it involves long sequences of randomly chosen gates, it also verifies that error behavior is stable when used in long computations. We implemented randomized benchmarking on trapped atomic ion qubits, establishing a one-qubit error probability per randomized $\ensuremath{\pi}/2$ pulse of 0.00482(17) in a particular experiment. We expect this error probability to be readily improved with straightforward technical modifications.