Enhancing the fidelity of two-qubit gates by measurements

Dynamical decoupling techniques are the method of choice for increasing gate fidelities. While these methods have produced very impressive results in terms of decreasing local noise and increasing the fidelities of single-qubit operations, dealing with the noise of two-qubit gates has proven more challenging. The main obstacle is that the noise time scale is shorter than the two-qubit gate itself, so that refocusing methods do not work. We present a measurement- and feedback-based method to suppress two-qubit-gate noise, which cannot be suppressed by conventional methods. We analyze in detail this method for an error model, which is relevant for trapped-ion quantum information.

Figure 1

The general scheme. The source of the protocol is a low-fidelity two-qubit gate with a specific error model with a single error operator. (a) The first step is to utilize this two-qubit gate together with single-qubit operations to create efficient two-qubit measurements, which are used in (b) the next step to create high-fidelity two-qubit gates.

Figure 2

A detailed description of the scheme that includes all the required qubits and operations. MS denotes the Mølmer-Sørensen gate. The first step is a ${\sigma }_{Z,1}{\sigma }_{Z,A1}$ measurement, the second is a ${\sigma }_{X,2}{\sigma }_{X,A1}$ measurement, and the last one is a ${\sigma }_{Z,A1}$ measurement. Depending on the measurement outcomes, a correction $(c_1$ and $c_2$ boxes) is applied on qubits 1 and 2.

Figure 3

Given a threshold $T,$ the single-qubit error $e_2$ determines a new threshold for the original cnot error, such that the infidelity of our cnot will be below $T.$ The plot shows this new threshold as a function of $e_2$ for $T={10}^{-4}.$ For each value of single-qubit error a different number of maximal repetitions is required: The brown (top) curve represents seven repetitions, the blue (middle) curve corresponds to five repetitions, and the yellow (bottom) curve represents three repetitions.