Control and Readout of a 13-level Trapped Ion Qudit

To implement useful quantum algorithms which demonstrate quantum advantage, we must scale currently demonstrated quantum computers up significantly. Leading platforms such as trapped ions face physical challenges in including more information carriers. A less explored avenue for scaling up the computational space involves utilizing the rich energy level structure of a trapped ion to encode multi-level qudits rather than two-level qubits. Here we show control and single-shot readout of qudits with up to 13 computational states, using protocols which can be extended directly to manipulate qudits of up to 25 levels in our chosen information host, $^{137}\text{Ba}^{+}$. This represents more than twice as many computational states per qudit compared with prior work in trapped ions. In addition to the preparation and readout protocols we demonstrate, universal quantum computation requires other quantum logic primitives such as entangling gates. These primitives have been demonstrated for lower qudit dimensions and can be directly generalized to the higher dimensions we employ. Hence, our advance opens an avenue towards using high-dimensional qudits for large-scale quantum computation. We anticipate efficiently utilizing available energy states in a trapped ion to play a significant and complementary role in tackling the challenge in scaling up the computational space of a trapped ion quantum computer. A qudit architecture also offers other practical benefits, which include affording relaxed fault tolerance thresholds for quantum error correction, providing an avenue for efficient quantum simulation of higher spin systems, and more efficient qubit gates

Practical trapped-ion protocols for universal qudit-based quantum computing

The notion of universal quantum computation can be generalized to multi-level qudits, which offer advantages in resource usage and algorithmic efficiencies. Trapped ions, which are pristine and well-controlled quantum systems, offer an ideal platform to develop qudit-based quantum information processing. Previous work has not fully explored the practicality of implementing trapped-ion qudits accounting for known experimental error sources. Here, we describe a universal set of protocols for state preparation, single-qudit gates, a new generalization of the M\o{}lmer-S\o{}rensen gate for two-qudit gates, and a measurement scheme which utilizes shelving to a meta-stable state. We numerically simulate known sources of error from previous trapped ion experiments, and show that there are no fundamental limitations to achieving fidelities above $99\%$ for three-level qudits encoded in $^{137}\mathrm{Ba}^+$ ions. Our methods are extensible to higher-dimensional qudits, and our measurement and single-qudit gate protocols can achieve $99\%$ fidelities for five-level qudits. We identify avenues to further decrease errors in future work. Our results suggest that three-level trapped ion qudits will be a useful technology for quantum information processing

Quantum Catalysis of Magnetic Phase Transitions in a Quantum Simulator

We control quantum fluctuations to create the ground state magnetic phases of a classical Ising model with a tunable longitudinal magnetic field using a system of 6 to 10 atomic ion spins. Due to the long-range Ising interactions, the various ground state spin configurations are separated by multiple first-order phase transitions, which in our zero temperature system cannot be driven by thermal fluctuations. We instead use a transverse magnetic field as a quantum catalyst to observe the first steps of the complete fractal devil's staircase, which emerges in the thermodynamic limit and can be mapped to a large number of many-body and energy-optimization problems.Comment: New data in Fig. 3, and much of the paper rewritte

Cold Matter Assembled Atom-by-Atom

The realization of large-scale fully controllable quantum systems is an exciting frontier in modern physical science. We use atom-by-atom assembly to implement a novel platform for the deterministic preparation of regular arrays of individually controlled cold atoms. In our approach, a measurement and feedback procedure eliminates the entropy associated with probabilistic trap occupation and results in defect-free arrays of over 50 atoms in less than 400 ms. The technique is based on fast, real-time control of 100 optical tweezers, which we use to arrange atoms in desired geometric patterns and to maintain these configurations by replacing lost atoms with surplus atoms from a reservoir. This bottom-up approach enables controlled engineering of scalable many-body systems for quantum information processing, quantum simulations, and precision measurements.Comment: 12 pages, 9 figures, 3 movies as ancillary file

Atom-by-atom assembly of defect-free one-dimensional cold atom arrays

The realization of large-scale fully controllable quantum systems is an exciting frontier in modern physical science. We use atom-by-atom assembly to implement a platform for the deterministic preparation of regular one-dimensional arrays of individually controlled cold atoms. In our approach, a measurement and feedback procedure eliminates the entropy associated with probabilistic trap occupation and results in defect-free arrays of over 50 atoms in less than 400 milliseconds. The technique is based on fast, real-time control of 100 optical tweezers, which we use to arrange atoms in desired geometric patterns and to maintain these configurations by replacing lost atoms with surplus atoms from a reservoir. This bottom-up approach may enable controlled engineering of scalable many-body systems for quantum information processing, quantum simulations, and precision measurements

Dynamics and Excited States of Quantum Many-body Spin Systems with Trapped Ions

Certain classes of quantum many-body systems, including those supporting phenomena like high-$T_c$ superconductivity and spin liquids, are believed to be fundamentally intractable to classical modeling. Quantum simulations, in which synthetic materials are engineered by inducing well-controlled quantum systems like ultracold atoms to obey many-body Hamiltonians of interest, are a promising new approach to study this type of physics. In this work, I present several advances toward this ultimate goal of large-scale, highly controllable quantum simulations of many-body spin physics. We simulate long-range Ising and XY spin models in the presence of transverse and longitudinal magnetic fields using chains of up to 18 ultracold $^{171}$Yb$^+$ ions held in a linear Paul trap, where two hyperfine levels in each ion encode spin-1/2 states. The tunable spin-spin interactions and effective magnetic fields are engineered using laser fields, and the individual spin states are directly imaged with state-dependent fluorescence. The results in this thesis address several of the ongoing challenges in the development of synthetic quantum matter platforms. One such challenge is establishing more flexible capabilities in the sorts of Hamiltonians we can model. By observing suppression of the ground state spin ordering, we have demonstrated our ability to continuously tune the interaction range in a power-law interaction pattern, and hence the amount of frustration present in the spin system. We have additionally begun developing tools to study particles of higher spin, which could eventually be used to create and study topological phases of matter. Another challenge is the necessity of identifying problems that the next generation of experiments, with flexible (but not arbitrary) controls and classically intractable (but not infinitely large) system sizes, can feasibly shed new light on. We have made measurements of how the range of interaction affects dynamics of spin correlations propagating through the chain, and the excellent agreement between our observations and numerical simulations indicate that at larger sizes, our experiment can meaningfully contribute to the open question of the fundamental speed limit on the transfer of information through such a spin chain. Finally, for classically intractable system sizes, it will be crucial to have multiple techniques at our disposal for validating our understanding of the exact microscopic model being implemented. We have developed and demonstrated an MRI-like spectroscopic technique for probing the energies of the many-body Hamiltonian, which serves as a new method for validating quantum simulations of the transverse Ising model. Our experiments can potentially be scaled up in the near future to study fully connected lattice spin models with several tens of spins, where classical computation begins to fail, and the results described in this thesis contribute to the effort to build experiments that can break new ground in the study of quantum many-body physics

Strong coupling of two individually controlled atoms via a nanophotonic cavity

We demonstrate photon-mediated interactions between two individually trapped atoms coupled to a nanophotonic cavity. Specifically, we observe collective enhancement when the atoms are resonant with the cavity and level repulsion when the cavity is coupled to the atoms in the dispersive regime. Our approach makes use of individual control over the internal states of the atoms and their position with respect to the cavity mode, as well as the light shifts to tune atomic transitions individually, allowing us to directly observe the anticrossing of the bright and dark two-atom states. These observations open the door for realizing quantum networks and studying quantum many-body physics based on atom arrays coupled to nanophotonic devices. ©2020 Keywords: cavity quantum electrodynamics; collective effects in quantum optics; hybrid quantum systems; quantum control; quantum optics; superradiance & subradianceCenter for Ultracold Atoms (grant no. PHY-1125846)National Science Foundation (grant no. PHY-1506284)AFOSR (grant no. FA9550-16-1-0323)Vannevar Bush Faculty Fellowship (grant no. N00014-15-1-2846)ARL CDQI (grant no. W911NF1520067