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Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have utilized classical simulations based on tensor network techniques, and their limitations shed light on the improvements to quantum hardware required to frustrate classical simulability. In particular, quantum computers having in excess of $\sim 50$ qubits are primarily vulnerable to classical simulation due to restrictions on their gate fidelity and their connectivity, the latter determining how many gates are required (and therefore how much infidelity is suffered) in generating highly-entangled states. Here, we describe recent hardware upgrades to Quantinuum's H2 quantum computer enabling it to operate on up to $56$ qubits with arbitrary connectivity and $99.843(5)\%$ two-qubit gate fidelity. Utilizing the flexible connectivity of H2, we present data from random circuit sampling in highly connected geometries, doing so at unprecedented fidelities and a scale that appears to be beyond the capabilities of state-of-the-art classical algorithms. The considerable difficulty of classically simulating H2 is likely limited only by qubit number, demonstrating the promise and scalability of the QCCD architecture as continued progress is made towards building larger machines., Comment: Includes minor updates to the text and an updated author list to include researchers who made technical contributions in upgrading the machine to 56 qubits but were left off the original version by mistake

We implement logically encoded three-qubit circuits for the quantum Fourier transform (QFT), using the [[7,1,3]] Steane code, and benchmark the circuits on the Quantinuum H2-1 trapped-ion quantum computer. The circuits require multiple logical two-qubit gates, which are implemented transversally, as well as logical non-Clifford single-qubit rotations, which are performed by non-fault-tolerant state preparation followed by a teleportation gadget. First, we benchmark individual logical components using randomized benchmarking for the logical two-qubit gate, and a Ramsey-type experiment for the logical $T$ gate. We then implement the full QFT circuit, using two different methods for performing a logical control-$T$, and benchmark the circuits by applying it to each basis state in a set of bases that is sufficient to lower bound the process fidelity. We compare the logical QFT benchmark results to predictions based on the logical component benchmarks.

Calculating the equilibrium properties of condensed matter systems is one of the promising applications of near-term quantum computing. Recently, hybrid quantum-classical time-series algorithms have been proposed to efficiently extract these properties from a measurement of the Loschmidt amplitude $\langle \psi| e^{-i \hat H t}|\psi \rangle$ from initial states $|\psi\rangle$ and a time evolution under the Hamiltonian $\hat H$ up to short times $t$. In this work, we study the operation of this algorithm on a present-day quantum computer. Specifically, we measure the Loschmidt amplitude for the Fermi-Hubbard model on a $16$-site ladder geometry (32 orbitals) on the Quantinuum H2-1 trapped-ion device. We assess the effect of noise on the Loschmidt amplitude and implement algorithm-specific error mitigation techniques. By using a thus-motivated error model, we numerically analyze the influence of noise on the full operation of the quantum-classical algorithm by measuring expectation values of local observables at finite energies. Finally, we estimate the resources needed for scaling up the algorithm., Comment: 18 pages, 12 figures

The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here, we perform an extensive numerical investigation of QAOA on the low autocorrelation binary sequences (LABS) problem, which is classically intractable even for moderately sized instances. We perform noiseless simulations with up to 40 qubits and observe that the runtime of QAOA with fixed parameters scales better than branch-and-bound solvers, which are the state-of-the-art exact solvers for LABS. The combination of QAOA with quantum minimum finding gives the best empirical scaling of any algorithm for the LABS problem. We demonstrate experimental progress in executing QAOA for the LABS problem using an algorithm-specific error detection scheme on Quantinuum trapped-ion processors. Our results provide evidence for the utility of QAOA as an algorithmic component that enables quantum speedups., Comment: Journal-accepted version

Non-Abelian topological order (TO) is a coveted state of matter with remarkable properties, including quasiparticles that can remember the sequence in which they are exchanged. These anyonic excitations are promising building blocks of fault-tolerant quantum computers. However, despite extensive efforts, non-Abelian TO and its excitations have remained elusive, unlike the simpler quasiparticles or defects in Abelian TO. In this work, we present the first unambiguous realization of non-Abelian TO and demonstrate control of its anyons. Using an adaptive circuit on Quantinuum's H2 trapped-ion quantum processor, we create the ground state wavefunction of $D_4$ TO on a kagome lattice of 27 qubits, with fidelity per site exceeding $98.4\%$. By creating and moving anyons along Borromean rings in spacetime, anyon interferometry detects an intrinsically non-Abelian braiding process. Furthermore, tunneling non-Abelions around a torus creates all 22 ground states, as well as an excited state with a single anyon -- a peculiar feature of non-Abelian TO. This work illustrates the counterintuitive nature of non-Abelions and enables their study in quantum devices., Comment: 6 + 20 pages, 6 + 5 figures, 3 tables v2: Changed title, added a reference

The lifetime of Ba$^+$ ions confined in a Paul trap is found, under typical conditions, to be limited by chemical reactions with residual background gas. An integrated ion trap and time-of-flight mass spectrometer are used to analyze the reactions of the trapped Ba$^+$ ions with three common gases in an ultrahigh vacuum system (H$_2$, CO$_2$ and H$_2$O). It is found that the products of these reactions can all be photodissociated by a single ultraviolet laser at 225~nm, thereby allowing the recovery of the Ba$^+$ ions and leading to an increase of the effective trap lifetime. For a Coulomb crystal, the lifetime increased from roughly 6~hours to 2~days at room temperature. It is suggested that higher enhancement factors are possible in systems with stronger traps. In addition, photodissociation wavelengths for other common trapped ion systems are provided., Comment: 6 pages, 4 figures, 1 table

The Ni-base superalloy 718 is the most widely used material for turbomachinery in the aerospace industry and land-based turbines. Although the relationship between processing and the resulting properties is well known, an understanding of the specific deformation mechanisms activated across its application temperature range is required to create more mechanistically accurate property models. Direct atomic-scale imaging observations with high angle annular dark-field scanning transmission electron microscopy, complemented by phase-field modeling informed by generalized stacking fault surface calculations using density functional theory, were employed to understand the shear process of ${\gamma}''$ and ${\gamma}'/{\gamma}''$ co-precipitates after 1 \% macroscopic strain at lower temperature (ambient and $427 {\deg}C$). Experimentally, intrinsic stacking faults were observed in the ${\gamma}''$, whereas the ${\gamma}'$ was found to exhibit anti-phase boundaries or superlattice intrinsic stacking faults. Additionally, the atomically flat ${\gamma}'/{\gamma}''$ interfaces in the co-precipitates were found to exhibit offsets after shearing, which can be used as tracers for the deformation events. Phase-field modeling shows that the developing fault-structure is dependent on the direction of the Burgers vector of the $a/2 \langle110\rangle$ matrix dislocation (or dislocation group) due to the lower crystal symmetry of the ${\gamma''}$ phase. The interplay between ${\gamma}'$ and ${\gamma}''$ phases results in unique deformation pathways of the co-precipitate and increases the shear resistance. Consistent with the experimental observations, the simulation results indicate that complex shearing mechanisms are active in the low-temperature deformation regime and that multiple $a/2 \langle110\rangle$ dislocations of non-parallel Burgers vectors may be active on the same slip plane., Comment: 32 pages, 17+6 figures, submitted to Acta Materiallia

The effects of various heat treatments on the microstructure and hardness of new Ni56Ti41Hf3 and Ni56Ti36Hf8 (atomic %) alloys were studied to evaluate the suitability of these materials for tribological applications. A solid-solution strengthening effect due to Hf atoms was observed for the solution annealed (SA) Ni56Ti36Hf8 alloy (716 HV), resulting in a comparable hardness to the Ni56Ti41Hf3 alloy containing 54 vol.% of Ni4Ti3 precipitates (707 HV). In the Ni56Ti41Hf3 alloy, the maximum hardness (752 HV), achieved after aging at 300C for 12 h, was attributed to dense, semi-coherent precipitation of the Ni4Ti3 phase. Unlike the lenticular morphology usually observed within binary NiTi alloys, a blocky Ni4Ti3 morphology formed within Ni56Ti36Hf3 due to a smaller lattice mismatch in the direction normal to the habit plane at the precipitate/matrix interface. The maximum hardness for Ni56Ti36Hf8 (769 HV) was obtained after applying an intermediate aging step (300C for 12 h) followed by normal aging (550C for 4 h). This two-step aging treatment induces dense nanoscale precipitation of two interspersed precipitate phases, namely H-phase and a new cubic Ni-rich precipitate phase, resulting in the highest hardness exhibited yet by this family alloys. The composition of cubic Ni-rich precipitates was measured using atom probe tomography to be approximately Ni61.5Ti31Hf7.5, while HAADF-STEM revealed a 54 atom motif cubic structure (a= 8.87 Angstroms), and electron diffraction showed that the structure belongs to the pm-3m (No. 221) space group.

Dipole-phonon quantum logic (DPQL) leverages the interaction between polar molecular ions and the motional modes of a trapped-ion Coulomb crystal to provide a potentially scalable route to quantum information science. Here, we study a class of candidate molecular ions for DPQL, the cationic alkaline-earth monoxides and monosulfides, which possess suitable structure for DPQL and can be produced in existing atomic ion experiments with little additional complexity. We present calculations of DPQL operations for one of these molecules, CaO$^+$, and discuss progress towards experimental realization. We also further develop the theory of DPQL to include state preparation and measurement and entanglement of multiple molecular ions., Comment: 10 pages, 6 figures

Dislocation structures, chemical segregation, {\gamma ^{\prime}, {\gamma ^{\prime \prime}}, {\delta} precipitates and Laves phase were quantified within the microstructures of Inconel 718 (IN718) produced by laser powder bed fusion additive manufacturing (AM) and subjected to standard, direct aging, and modified multi-step heat treatments. Additionally, heat-treated samples still attached to the build plates vs. those removed were also documented for a standard heat treatment. The effects of the different resulting microstructures on room temperature strengths and elongations to failure is revealed. Knowledge derived from these process structure property relationships was used to engineer a super solvus solution anneal at 1020 degC for 15 minutes, followed by aging at 720 degC for 24 hours heat treatment for AM-IN718 that eliminates Laves and {\delta} phases, preserves AM specific dislocation cells that are shown to be stabilized by MC carbide particles, and precipitates dense {\gamma ^{\prime} and {\gamma ^{\prime \prime}} nanoparticle populations. This 'optimized for AM-IN718 heat treatment' results in superior properties relative to wrought/additively manufactured, then industry standard heat treated IN718: relative increases of 7/10 percent in yield strength, 2/7 percent in ultimate strength, and 23/57 percent in elongation to failure are realized, respectively, regardless of as-built vs. machined surface finishes., Comment: After peer-review and minor revisions

We study an excited atom-polar molecular ion chemical reaction (Ca$^*$ + BaCl$^+$) at low temperature by utilizing a hybrid atom-ion trapping system. The reaction rate and product branching fractions are measured and compared to model calculations as a function of both atomic quantum state and collision energy. At the lowest collision energy we find that the chemical dynamics dramatically differ from capture theory predictions and are primarily dictated by the radiative lifetime of the atomic quantum state instead of the underlying excited-state interaction potential. We provide a simple rule for calculating at what temperature this regime, where the collision complex lifetime is longer than the radiative lifetime of the quantum state, is reached. This effect, which greatly suppresses the reactivity of short-lived excited states, provides a means for directly probing reaction range. It also naturally suppresses unwanted chemical reactions in hybrid trapping experiments, allowing longer molecular ion coherence and interrogation times., Comment: 13 pages, 5 figures

An important physical process unique to neutral-ion systems is the charge-transfer (CT) reaction. Here, we present measurements of and models for CT processes between co-trapped ultracold Ca atoms and Yb ions under well-controlled conditions. The theoretical analysis reveals the existence of three reaction mechanisms when lasers from a magneto-optical trap (MOT) and an additional catalyst laser are present. Besides the direct CT involving existent excited Ca population in the MOT, the second pathway is controlled by MOT-induced CT, whereas the third one mostly involves the additional red-detuned laser., Comment: 9 pages, 4 figures

Using a recently developed method for precisely controlling collision energy, we observe a dramatic suppression of inelastic collisions between an atom and ion (Ca + Yb$^+$) at low collision energy. This suppression, which is expected to be a universal phenomenon, arises when the spontaneous emission lifetime of the excited state is comparable to or shorter than the collision complex lifetime. We develop a technique to remove this suppression and engineer excited-state interactions. By dressing the system with a strong catalyst laser, a significant fraction of the collision complexes can be excited at a specified internuclear separation. This technique allows excited-state collisions to be studied, even at ultracold temperature, and provides a general method for engineering ultracold excited-state interactions., Comment: 6 pages, 4 figures

Near-field and far-field high-energy diffraction microscopy and microcomputed tomography X-ray techniques were used to study a bulk single crystal nickel-titanium shape memory alloy sample subjected to thermal cycling under a constant applied load. Three-dimensional in situ reconstructions of the austenite microstructure are presented, including the structure and distribution of emergent grain boundaries. After one cycle, the subgrain structure is significantly refined, and heterogeneous {\Sigma}3 and {\Sigma}9 grain boundaries emerge. The low volume and uneven dispersion of the emergent {\Sigma} boundaries across the volume show why previous transmission electron microscopy investigations of {\Sigma} grain boundary formation were inconsistent., Comment: accepted in Scripta Materialia