Brian K. McFarland

Topological phases are governed by discrete symmetries that protect boundary modes against local perturbations. When translational periodicity is absent, the bulk states also become localized, so that a topological edge state can no longer be distinguished from them by spatial localization alone. Here, we investigate the topological edge state (TES) and bulk eigenstates of the anisotropic quantum Rabi model (AQRM) in a trapped-ion quantum simulator. The AQRM hosts a topological phase in a one-dimensional synthetic lattice, whose translational symmetry is broken by the non-uniform couplings scaling with the site index. While both the TES and bulk states show localized distributions, we find that the TES exhibits well-defined chirality and near-complete spin--boson separability as signatures of the topological phase, in contrast to the bulk states. Phase-space tomography further reveals that the bosonic component of the TES is a squeezed vacuum state, with squeezing up to 6.45 dB. These results identify the TES through its intrinsic topological signatures and establish eigenstate-level characterization as a route to probing topological phenomena.

Hybrid continuous-discrete-variable quantum processors can represent bosonic degrees of freedom directly in oscillator modes, or qumodes, while using qubits for control, readout, and nonlinear operations. Recently proposed trigonometric continuous-variable (CV) gate sets promote periodic functions of oscillator quadratures to elementary operations, making them natural primitives for compact variables, rotor models, lattice gauge theories, and anharmonic dynamics. Here we experimentally demonstrate and benchmark one-qumode cosine gates, and perform a mode-resolved marginal benchmark of two-qumode cosine-gate implementations, on the QSCOUT trapped-ion quantum platform. Our implementation uses collective motional modes of three- and four-ion $^{171}{\rm Yb}^{+}$ chains and realizes finite-step trigonometric-gate circuits through hybrid qubit-qumode operations and conditional phase-space displacements. In contrast to previous theoretical and compilation work, we focus on the gate-level characterization of the trigonometric primitives. We measure Fock-space transition probabilities, study their dependence on gate parameters and Trotter step number, and compare with simulations incorporating thermal initialization and motional dephasing. We also derive ideal gate matrix elements and phase-space diagnostics, connecting the measurements to the non-Gaussian structure generated by these gates. These results establish trigonometric CV gates as reusable building blocks for bosonic Hamiltonian simulations and hybrid quantum algorithms requiring intrinsically non-polynomial operations.

Highly-localized light-matter interactions are necessary for scaling trapped-ion architectures. In hyperfine qubits, counterpropagating beams generate entangling gates by coupling with motion, but this effect is undesirable during single-qubit operations. For that reason, single-qubit gates are traditionally implemented with copropagating beams, and the coexistence of two beam geometries adds hardware and computational overhead. In an effort towards collective performance improvement with minimal overhead, we design and implement pulse-amplitude and dephasing robust dynamically corrected gates using Space Curve Quantum Control (SCQC) and compare them against the constant-amplitude gate implementation. We perform gate set tomography on a four-qubit trapped-ion register, and we discover more than 50% error reduction when robust pulses are used. We find that counterpropagating robust gates often outperform their copropagating counterparts and reach error rates as low as $(3.59 \pm 1.25)\cdot 10^{-3}$, using diamond distance as a metric. This value establishes a laser-driven-gate error reference and is merely an order of magnitude higher than the best reported $\textit{microwave}$ gate on a $\textit{single}$ ion. Additional experiments reveal that robust pulses can effectively suppress non-Markovian errors that grow during runtime. Our work challenges the widely accepted belief that copropagating gates should be preferred for their weak motional coupling and invites the adoption of high-performance robust pulses that suppress multiple noise sources of the trapped-ion error budget.

We present an approach based on tensor networks for distributed quantum computing simulation of chemical wavepacket dynamics in a continuous variable representation. The central idea is that the tensor-network representation of the multidimensional time-evolution operator naturally induces an elevated Hilbert space where the dynamics decomposes into a set of independent lower-dimensional propagations. This transformation converts an entangled quantum evolution into a set of parallel computational tasks that can be executed asynchronously across heterogeneous quantum and classical computing architectures. The resulting formalism establishes a direct connection between tensor-network decompositions, uniformly controlled quantum circuits, and asynchronous distributed quantum computing. The approach is developed with a goal towards hybrid quantum/classical implementation, and is appropriate for a general heterogeneous mixture of quantum hardware systems. The experimental realization of the asynchronously distributed quantum processes that arise from the tensor-network decomposition are carried out on the Sandia National Laboratories' trapped-ion quantum computer, where the circuits are compiled using native partial-entangling $XX(θ)$ gates, reducing the expected two-qubit gate infidelity by more than 30\% relative to conventional fully entangling decompositions. We demonstrate the methodology by quantum computing the vibrational spectra of a small protonated water cluster that shows critical quantum nuclear behavior. Such water cluster systems have been found to be challenging for experimental action spectroscopy and for theory, and here, for the first time, we provide results for vibrational spectroscopy that are in agreement with the respective classical results to within 4cm$^{-1}$, thus allowing for the potential for spectroscopic accuracy from quantum computations.

Fault-tolerant quantum computing requires extremely precise knowledge and control of qubit dynamics during the application of a gate. We develop a data-driven learning protocol for characterizing quantum gates that builds off previous work on learning the Nakajima-Mori-Zwanzig (NMZ) formulation of open system dynamics from time series data, which allows detailed reconstruction of quantum evolution, including non-Markovian dynamics. We demonstrate this learning technique on three different systems: a simulation of a qubit whose dynamics are purely Markovian, a simulation of a driven qubit coupled to stochastic noise produced by an Ornstein-Uhlenbeck process, and trapped-ion experimental data of a driven qubit whose noise environment is not characterized ahead of time. Our technique is able to learn the generators of time evolution, or the NMZ operators, in all three cases and can learn the timescale in which the qubit dynamics can no longer be accurately described by a purely Markovian model. Our technique complements existing quantum gate characterization methods such as gate set tomography by explicitly capturing non-Markovianity in the gate generator, thus allowing for more thorough diagnosis of noise sources.

Continuously parameterized two-qubit gates are a key feature of state-of-the-art trapped-ion quantum processors as they have favorable error scalings and show distinct improvements in circuit performance over more restricted maximally entangling gatesets. In this work, we provide a comprehensive and pedagogical discussion on how to practically implement these continuously parameterized Mølmer-Sørensen gates on the Quantum Scientific Computing Open User Testbed (QSCOUT), a low-level trapped-ion processor. To generate the arbitrary entangling angles, $θ$, we simply scale the amplitude of light used to generate the entanglement. However, doing so requires careful consideration of amplifier saturation as well as the variable light shifts that result. As such, we describe a method to calibrate and cancel the dominant fourth-order effects, followed by a dynamic virtual phase advance during the gate to cancel any residual light shifts, and find a linear scaling between $θ$ and the residual light shift. Once, we have considered and calibrated these effects, we demonstrate performance improvement with decreasing $θ$. Finally, we describe nuances of hardware control to transform the XX-type interaction of the arbitrary-angle Mølmer-Sørensen gate into a phase-agnostic and crosstalk-mitigating ZZ interaction.

We analyze the use of the Solovay Kitaev (SK) algorithm to generate an ensemble of one qubit rotations over which to perform randomized compilation. We perform simulations to compare the trace distance between the quantum state resulting from an ideal one qubit $R_{Z}$ rotation and discrete SK decompositions. We find that this simple randomized gate synthesis algorithm can reduce the approximation error of these rotations in the absence of gate errors in simulation by at least a factor of two compared to a naive gate synthesis algorithm. We test the technique under the effects of a simple coherent noise model and find that it can mitigate coherent noise. We also run our algorithm on Sandia National Laboratories' QSCOUT trapped-ion device and find that randomization is able to help in the presence of realistic noise sources.

State-of-the-art noisy-intermediate-scale quantum (NISQ) processors are currently implemented across a variety of hardware platforms, each with their own distinct gatesets. As such, circuit compilation should not only be aware of, but also deeply connect to, the native gateset and noise properties of each. Trapped-ion processors are one such platform that provides a gateset that can be continuously parameterized across both one- and two-qubit gates. Here we use the Quantum Scientific Computing Open User Testbed (QSCOUT) to study noise-aware compilations focused on continuously parameterized two-qubit $\mathcal{ZZ}$ gates (based on the Mølmer-Sørensen interaction) using $\textbf{Superstaq}$, a quantum software platform for hardware-aware circuit compiler optimizations. We discuss the realization of $\mathcal{ZZ}$ gates with arbitrary angle on the all-to-all connected trapped-ion system. Then we discuss a variety of different compiler optimizations that innately target these $\mathcal{ZZ}$ gates and their noise properties. These optimizations include moving from a restricted maximally entangling gateset to a continuously parameterized one, swap mirroring to further reduce total entangling angle of the operations, focusing the heaviest $\mathcal{ZZ}$ angle participation on the best performing gate pairs, and circuit approximation to remove the least impactful $\mathcal{ZZ}$ gates. We demonstrate these compilation approaches on the hardware with randomized quantum volume circuits, observing the potential to realize a larger quantum volume as a result of these optimizations. Using differing yet complementary analysis techniques, we observe the distinct improvements in system performance provided by these noise-aware compilations and study the role of stochastic and coherent error channels for each compilation choice.