We report the quantum process tomography of a Mølmer-Sørensen entangling gate. The tomographic protocol relies on a single discriminatory transition, exploiting excess micromotion in the trap to realize all operations required to prepare all input states and analyze all output states. Using a master-slave diode lasers setup, we demonstrate a two-qubit entangling gate, with a fidelity of Bell state production of 0.985(10). We characterize its χ-process matrix, the simplest for an entanglement gate on a separable-states basis, and we observe that the dominant source of error is accurately modelled by a quantum depolarization channel.
PACS numbers:The ability to realize and characterize high-fidelity two-qubit gates is central for quantum information science as, together with single-qubit rotations, they constitute the building blocks for quantum computation [1]. The detailed characterization of these gates is therefore crucial. Quantum Process Tomography (QPT) is an important method to fully characterize linear quantum processes. In particular, QPT of two-qubit entangling gates has been used to characterize CNOT gates in linear-optic [2], NMR [3], as well as trapped ions [4,5], or a square root i-SWAP gate with superconducting qubits [6]. In trapped-ions experiments, Mølmer-Sørensen (MS) entangling gates [7] have become increasingly popular, both for quantum computation purposes [8,9] and for inducing effective spin-spin couplings that allow to simulate complex quantum many-body hamiltonians from condensed matter physics [10]. One of its main advantages as compared with other gate protocols is its first-order insensitivity to the phonon occupation number (i.e. temperature of the ion-crystal), which allowed, inter alia, the highest entangled state production fidelity reached to date (0.993(1) [11]), entanglement between ions in thermal motion [12], as well as the creation of a maximally entangled state of a large (N = 14) number of qubits [13]. In this letter, we first implement a new and simple protocol for QPT with trapped ions, which only requires a single discriminatory transition. The scheme is based on inhomogeneous micromotion in the trap that enables addressing single qubits in the chain [14][15][16]. Subsequently, we realize the tomographic reconstruction of a Mølmer-Sørensen interaction which, despite its growing importance, has not been process-analyzed yet.A quantum process is defined as a completely positive map E in the space of density matrices. Given a complete set of operators {A i } (such that j A † j A j = I), the * These authors contributed equally to this work. † Present email and address: nn270@cam.ac.uk, Cavendish Laboratory, University of Cambridge, J.J. Thomson Ave., Cambridge CB3 0HE, United Kingdom output state for an arbitrary input state ρ can be written as (for details see for instance [3,17,18])(1)Here {χ ab } is the process matrix (with 4 n × 4 n elements for n qubits), which contains the full information on the process E and is measured by QPT. A convenient set of input states for t...