Emanuel Knill

Randomized benchmarking (RB) is a widely used strategy to assess the quality of available quantum gates in a computational context. RB involves applying known random sequences of gates to an initial state and using the statistics of a final measurement step to determine an effective depolarizing error per step of the sequence, which is a metric of gate quality. Here we investigate the advantages of fully randomized benchmarking, where a new random sequence is drawn for each experimental trial. The advantages of full randomization include smaller confidence intervals on the inferred step error, the ability to use maximum likelihood analysis without heuristics, straightforward optimization of the sequence lengths, and the ability to model and measure behaviors that go beyond the typical assumption of time-independent error rates. We discuss models of time-dependent or non-Markovian errors that generalize the basic RB model of a single exponential decay of the success probability. For any of these models, we implement a concrete protocol to minimize the uncertainty of the estimated parameters given a fixed time constraint on the complete experiment, and we implement a maximum likelihood analysis. We consider several previously published experiments and determine the potential for improvements with optimized full randomization. We experimentally observe such improvements in Clifford randomized benchmarking experiments on a single trapped ion qubit at the National Institute of Standards and Technology (NIST). For an experiment with uniform lengths and intentionally repeated sequences the step error was $2.42^{+0.30}_{-0.22}\times 10^{-5}$, and for an optimized fully randomized experiment of the same total duration the step error was $2.57^{+0.07}_{-0.06}\times 10^{-5}$. We find a substantial decrease in the uncertainty of the step error as a result of optimized fully randomized benchmarking.

Precise quantum control and measurement of several harmonic oscillators, such as the modes of the electromagnetic field in a cavity or of mechanical motion, are key for their use as quantum platforms. The motional modes of trapped ions can be individually controlled and have good coherence properties. However, achieving high-fidelity two-mode operations and nondestructive measurements of the motional state has been challenging. Here we demonstrate the coherent exchange of single motional quanta between spectrally separated harmonic motional modes of a trapped-ion crystal. The timing, strength, and phase of the coupling are controlled through an oscillating electric potential with suitable spatial variation. Coupling rates that are much larger than decoherence rates enable demonstrations of high fidelity quantum state transfer and beamsplitter operations, entanglement of motional modes, and Hong-Ou-Mandel-type interference. Additionally, we use the motional coupling to enable repeated non-destructive projective measurement of a trapped-ion motional state. Our work enhances the suitability of trapped-ion motion for continuous-variable quantum computing and error correction and may provide opportunities to improve the performance of motional cooling and motion-mediated entangling interactions.

We propose and demonstrate a protocol for high-fidelity indirect readout of trapped ion hyperfine qubits, where the state of a $^9\text{Be}^+$ qubit ion is mapped to a $^{25}\text{Mg}^+$ readout ion using laser-driven Raman transitions. By partitioning the $^9\text{Be}^+$ ground state hyperfine manifold into two subspaces representing the two qubit states and choosing appropriate laser parameters, the protocol can be made robust to spontaneous photon scattering errors on the Raman transitions, enabling repetition for increased readout fidelity. We demonstrate combined readout and back-action errors for the two subspaces of $1.2^{+1.1}_{-0.6} \times 10^{-4}$ and $0^{+1.9}_{-0} \times 10^{-5}$ with 68% confidence while avoiding decoherence of spectator qubits due to stray resonant light that is inherent to direct fluorescence detection.

Large-scale quantum computers will require quantum gate operations between widely separated qubits. A method for implementing such operations, known as quantum gate teleportation (QGT), requires only local operations, classical communication, and shared entanglement. We demonstrate QGT in a scalable architecture by deterministically teleporting a controlled-NOT (CNOT) gate between two qubits in spatially separated locations in an ion trap. The entanglement fidelity of our teleported CNOT is in the interval [0.845, 0.872] at the 95% confidence level. The implementation combines ion shuttling with individually-addressed single-qubit rotations and detections, same- and mixedspecies two-qubit gates, and real-time conditional operations, thereby demonstrating essential tools for scaling trapped-ion quantum computers combined in a single device.

Quantum simulation - the use of one quantum system to simulate a less controllable one - may provide an understanding of the many quantum systems which cannot be modeled using classical computers. Impressive progress on control and manipulation has been achieved for various quantum systems, but one of the remaining challenges is the implementation of scalable devices. In this regard, individual ions trapped in separate tunable potential wells are promising. Here we implement the basic features of this approach and demonstrate deterministic tuning of the Coulomb interaction between two ions, independently controlling their local wells. The scheme is suitable for emulating a range of spin-spin interactions, but to characterize the performance of our setup we select one that entangles the internal states of the two ions with 0.82(1) fidelity. Extension of this building-block to a 2D-network, which ion-trap micro-fabrication processes enable, may provide a new quantum simulator architecture with broad flexibility in designing and scaling the arrangement of ions and their mutual interactions. To perform useful quantum simulations, including those of intriguing condensed-matter phenomena such as the fractional quantum Hall effect, an array of tens of ions might be sufficient.