Essential to the functionality of qubit-based sensors are control protocols, which shape their response in frequency space. However, in common control routines out-of-band spectral leakage complicates interpretation of the sensor’s signal. In this work, we leverage discrete prolate spheroidal sequences (a.k.a. Slepian sequences) to synthesize provably optimal narrowband controls ideally suited to spectral estimation of a qubit’s noisy environment. Experiments with trapped ions demonstrate how spectral leakage may be reduced by orders of magnitude over conventional controls when a near resonant driving field is modulated by Slepians, and how the desired narrowband sensitivity may be tuned using concepts from RF engineering. We demonstrate that classical multitaper techniques for spectral analysis can be ported to the quantum domain and combined with Bayesian estimation tools to experimentally reconstruct complex noise spectra. We then deploy these techniques to identify previously immeasurable frequency-resolved amplitude noise in our qubit’s microwave synthesis chain.
Entangling operations are among the most important primitive gates employed in quantum computing and it is crucial to ensure high-fidelity implementations as systems are scaled up. We experimentally realize and characterize a simple scheme to minimize errors in entangling operations related to the residual excitation of mediating bosonic oscillator modes that both improves gate-robustness and provides scaling benefits in larger systems. The technique employs discrete phase shifts in the control field driving the gate operation, determined either analytically or numerically, to ensure all modes are de-excited at arbitrary user-defined times. We demonstrate an average gate fidelity of 99.4(2)% across a wide range of parameters in a system of 171 Yb + trapped ion qubits, and observe a reduction of gate error in the presence of common experimental error sources. Our approach provides a unified framework to achieve robustness against both static and time-varying laser amplitude and frequency detuning errors. We verify these capabilities through systemidentification experiments revealing improvements in error-susceptibility achieved in phase-modulated gates.The ability to perform robust, high fidelity entangling gates in multi-qubit systems is a key requirement for realizing scalable quantum information processing 1 . In several hardware architectures, qubits are entangled through shared bosonic oscillator modes via an interaction that is moderated by an external driving field. The Mølmer-Sørensen (MS) gate in trapped ions 2-4 and the resonator-induced phase gate in superconducting circuits 5-7 are both of this type. In addition, interactions simultaneously employing multiple bosonic modes have been explored to improve gate fidelities 8 and probe novel types of interactions 9 in superconducting circuits.A major source of error for oscillator-mediated gates is residual qubit-oscillator entanglement at the end of the operation 10 . This detrimental effect can arise due to the presence of quasi-static or time-varying noise on the driving field, slow drifts in experimental parameters such as the qubit and oscillator frequencies, or the presence of spectator modes that are not properly accounted for in the gate construction. In trapped ion systems, various schemes have been demonstrated that minimize this residual coupling 11-15 , with some also incorporating the ability to simultaneously decouple from multiple modes 16-21 . Their common feature is a temporal modulation of the driving field, modifying the trajectories of the joint qubit-oscillator states in each oscillator's phase space.In this work, we experimentally demonstrate a new class of phase-modulated (ΦM) entangling gates using trapped ions in the presence of multi-mode motional spectra. Specifically, we implement an MS-type interaca) These three authors contributed equally to this work. b) Current address: Fachrichtung Physik, Universität des Saarlandes, tion and employ discrete phase shifts of the driving field to suppress dominant gate errors. Using both an ana...
Laser-cooled atomic ions form ordered structures in radiofrequency ion traps and in Penning traps. Here we demonstrate in a Penning trap the creation and manipulation of a wide variety of ion Coulomb crystals formed from small numbers of ions. The configuration can be changed from a linear string, through intermediate geometries, to a planar structure. The transition from a linear string to a zigzag geometry is observed for the first time in a Penning trap. The conformations of the crystals are set by the applied trap potential and the laser parameters, and agree with simulations. These simulations indicate that the rotation frequency of a small crystal is mainly determined by the laser parameters, independent of the number of ions and the axial confinement strength. This system has potential applications for quantum simulation, quantum information processing and tests of fundamental physics models from quantum field theory to cosmology.
Classical control noise is ubiquitous in qubit devices, making its accurate spectral characterization essential for designing optimized error suppression strategies at the physical level. Here, we focus on multiplicative Gaussian amplitude control noise on a driven qubit sensor and show that sensing protocols using optimally band-limited Slepian modulation offer substantial benefit in realistic scenarios. Special emphasis is given to laying out the theoretical framework necessary for extending non-parametric multitaper spectral estimation to the quantum setting by highlighting key points of contact and differences with respect to the classical formulation. In particular, we introduce and analyze two approaches (adaptive vs. single-setting) to quantum multitaper estimation, and show how they provide a practical means to both identify fine spectral features not otherwise detectable by existing protocols and to obtain reliable prior estimates for use in subsequent parametric estimation, including high-resolution Bayesian techniques. We quantitatively characterize the performance of both singleand multitaper Slepian estimation protocols by numerically reconstructing representative spectral densities, and demonstrate their advantage over dynamical-decoupling noise spectroscopy approaches in reducing bias from spectral leakage as well as in compensating for aliasing effects while maintaining a desired sampling resolution. arXiv:1803.05538v2 [quant-ph]
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