Randomized benchmarking of quantum gates

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 / 2 pulse of 0.00482͑17͒ in a particular experiment. We expect this error probability to be readily improved with straightforward technical modifications.

Characterizing quantum gates via randomized benchmarking

“…[25] we provided a scalable (in the number n of qubits comprising the system) and robust method for benchmarking the full set of Clifford gates by a single parameter using randomization techniques. The concept of using randomization methods for benchmarking quantum gates, commonly called randomized benchmarking (RB), was introduced previously in [18,26]. The simplicity of these protocols has motivated experimental implementations in atomic ions for different types of traps [26][27][28], NMR [29], superconducting qubits [30,31], and atoms in optical lattices [32].…”

Experimental quantum verification in the presence of temporally correlated noise

“…11 Despite their differences, these protocols share the common theme that they were originally developed and mathematically formalised assuming that error processes are statistically independent and do not exhibit strong correlations in time. 1,2,10 Even in highly controlled laboratory environments there are a range of noise sources that, when applied to a qubit concurrent with logical gate operations, produce effective error models that diverge significantly from the assumptions underlying most QCVV protocols. For example, slow variations in ambient magnetic fields or drifts in amplifier gain can produce temporally correlated noise processes, often characterised through a power spectral density possessing large weight at low frequencies.…”

Autonomous calibration of single spin qubit operations

“…Hence, a significant speed up in the total time of calibration and its fidelity precision may potentially be achieved by employing fast and simplified tomography methods, for instance randomised benchmarking. 30 In addition to the autonomous calibration, our demonstrated closed-loop optimisation features stabilisation mechanism against experimental drifts, for instance due to fluctuations of the magnetic field strength and the resulting frequency detuning. Our procedure presented in this letter is not limited for application to single-qubit operations only.…”