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We report on the fault-tolerant operation of logical qubits on a neutral atom quantum computer, with logical performance surpassing physical performance for multiple circuits including Bell states (12x error reduction), random circuits (15x), and a prototype Anderson Impurity Model ground state solver for materials science applications (up to 6x, non-fault-tolerantly). The logical qubits are implemented via the [[4, 2, 2]] code (C4). Our work constitutes the first complete realization of the benchmarking protocol proposed by Gottesman 2016 [1] demonstrating results consistent with fault-tolerance. In light of recent advances on applying concatenated C4/C6 detection codes to achieve error correction with high code rates and thresholds, our work can be regarded as a building block towards a practical scheme for fault tolerant quantum computation. Our demonstration of a materials science application with logical qubits particularly demonstrates the immediate value of these techniques on current experiments.

We present the design and vacuum performance of a compact room-temperature trapped ion system for quantum computing, consisting of a ultra-high vacuum (UHV) package, a micro-fabricated surface trap and a small form-factor ion pump. The system is designed to maximize mechanical stability and robustness by minimizing the system size and weight. The internal volume of the UHV package is only 2 cm$^3$, a significant reduction in comparison with conventional vacuum chambers used in trapped ion experiments. We demonstrate trapping of $^{174}$Yb$^+$ ions in this system and characterize the vacuum level in the UHV package by monitoring both the rates of ion hopping in a double-well potential and ion chain reordering events. The calculated pressure in this vacuum package is about 1.5e-11 Torr, which is sufficient for the majority of current trapped ion experiments.

This paper we define a new Puzzle called Proof-of-Interaction and we show how it can replace, in the Bitcoin protocol, the Proof-of-Work algorithm.

We report on progress towards implementing mixed ion species quantum information processing for a scalable ion trap architecture. Mixed species chains may help solve several problems with scaling ion trap quantum computation to large numbers of qubits. Initial temperature measurements of linear Coulomb crystals containing barium and ytterbium ions indicate that the mass difference does not significantly impede cooling at low ion numbers. Average motional occupation numbers are estimated to be $\bar{n} \approx 130$ quanta per mode for chains with small numbers of ions, which is within a factor of three of the Doppler limit for barium ions in our trap. We also discuss generation of ion-photon entanglement with barium ions with a fidelity of $F \ge 0.84$, which is an initial step towards remote ion-ion coupling in a more scalable quantum information architecture. Further, we are working to implement these techniques in surface traps in order to exercise greater control over ion chain ordering and positioning.

We present a measurement of the branching fractions for decay from the long-lived $5D_{5/2}$ level in \Ba. The branching fraction for decay into the $6S_{1/2}$ ground state was found to be $0.846(25)_{\mathrm{stat}}(4)_{\mathrm{sys}}$. We also report an improved measurement of the $5D_{5/2}$ lifetime, $\tau_{5D_{5/2}}=31.2(0.9)$~s. Together these measurements provide the first experimental determination of transition rates for decay out of the $5D_{5/2}$ level. The low ($<7 \times 10^{-12}$~Torr) pressure in the ion trap in which these measurements were made simplified data acquisition and analysis. Comparison of the experimental results with theoretical predictions of the transition rates shows good agreement., Comment: 5 pages, 4 figures

We report on the demonstration of ion-photon entanglement and Bell inequality violation in a system of trapped 138Ba+ ions. Entanglement between the Zeeman sublevels of the ground state of a single 138Ba+ ion and the polarization state of a single 493 nm photon emitted by the ion with a fidelity of $0.84\pm0.01$ was achieved, along with a Bell signal of 2.3, exceeding the classical limit of 2 by over eight standard deviations. This system is a promising candidate for a loophole-free Bell inequality violation test as the wavelengths of the transitions of 138Ba+ are in the visible region and thus suitable for long range transmission over fiber optic cable., Comment: 5 pages, 3 figures, 1 table

We report an improved measurement of the Land\'e g factor of the 5D5/2 state of singly ionized barium. Measurements were performed on single Doppler-cooled 138Ba+ ions in linear Paul traps using two similar, independent apparatuses. Transitions between Zeeman sublevels of the 6S1/2 and 5D5/2 states were driven with two independent, stabilized radio-frequency synthesizers using a dedicated electrode within each ion trap chamber. State detection within each Zeeman manifold was achieved with a frequency-stabilized fiber laser operating at 1.76 microns. By calculating the ratio of the two Zeeman splittings, and using the measured Land\'e g factor of the 6S1/2 state, we find a value of 1.200371(4stat)(6sys) for g of 5D5/2., Comment: Five pages, 3 figures

We present experimental and theoretical analysis of quantum fluctuation in a vacuum field in the presence of orthogonal linearly polarized pump field propagating through a Rb vapor cell. Previously reported theoretical and experimental studies provided somewhat contradictory conclusions regarding the possibility to observe the "squeezed vacuum" -- the reduction of vacuum fluctuations below standard quantum limit -- in this system. Here, using the D1 transitions of Rb in a cell without buffer as as an example, we demonstrate that vacuum squeezing is corrupted by incoherent processes (such as spontaneous emission, elastic scattering, etc.), and its observation is only possible in a specific small region of the experimental parameter space. Numerical simulations, in good agreement with the experiment, demonstrate that the two excited state hyperfine levels play a crucial role in the squeezing and excess noise production. The significant influence of far-detuned atoms on the field fluctuations at low noise frequencies imposes the explicit consideration of the full velocity distribution of the atomic vapor., Comment: 6 pages, 6 figures