Benchmarking multi-qubit gates in neutral atom systems

Multi-qubit gates are unitary operators generated by many-body Hamiltonians which act non-trivially on >2 (if not all) qubits. They can be naturally implemented in, for example, Rydberg atoms trapped in a tweezer array. They expand the control toolbox of quantum devices, making it over-complete and thus bolstering the optimization of experimental errors when designing a circuit. Moreover, they also carry the potential to achieve practical quantum advantage faster than with circuits using 1 and 2-qubit gates [1]. However, benchmarking such gates is challenging for two reasons: multi-qubit gates are represented by exponentially large unitary matrices, and therefore the corresponding process tomography is not scalable and this unitary cannot always be calculated theoretically, sometimes desirably so, leaving no reference to benchmark experimental data against. Therefore, developing new approaches to benchmarking multi-qubit gates is highly desirable.

Here, we develop a set of benchmarking techniques for multi-qubit gates that are effective against locally generated errors, i.e., errors that are generated by short-range coupling terms or by locally occurring losses/decay processes. We consider the reduced Choi matrix of the multi-qubit gate that represents the restricted process as seen by a subsystem consisting of one or two qubits. The reduced Choi matrix of unitary multi-qubit gates has several properties that are violated if the gate becomes non-unitary due to errors. For instance, it is doubly stochastic, i.e., both of its partial traces are equal to the identity matrix. This condition is violated if the system is coupled to a thermal bath. We show that such properties can be used to benchmark a multi-qubit gate [3].

From an experimental perspective, implementing such benchmarking techniques requires a reliable reduced process tomography. Although the number of parameters in this tomography does not scale with the system size, they are already significantly demanding on the experimental scale, in terms of the number of measurements. In order the speed up this reduced process tomography we develop experimental protocols based on ideas from quantum metrology, where we use entanglement to optimize the convergence rate of the sampling errors [2].