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Quantum simulation with adiabatic annealing can provide insight into difficult problems that are impossible to study with classical computers. However, it deteriorates when the systems scale up due to the shrinkage of the excitation gap and thus places an annealing rate bottleneck for high success probability. Here, we accelerate quantum simulation using digital multi-qubit gates that entangle primary system qubits with the ancillary qubits. The practical benefits originate from tuning the ancillary gauge degrees of freedom to enhance the quantum algorithm's original functionality in the system subspace. For simple but nontrivial short-ranged, infinite long-ranged transverse-field Ising models, and the hydrogen molecule model after qubit encoding, we show improvement in the time to solution by one hundred percent but with higher accuracy through exact state-vector numerical simulation in a digital-analog setting. The findings are further supported by time-averaged Hamiltonian theory.

Hybrid variational quantum algorithms (VQAs) are promising for solving practical problems such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers. However, with typical random ansatz or quantum alternating operator ansatz, derived variational quantum algorithms become a black box for model interpretation. In this paper we construct a quantum regression algorithm wherein the quantum state directly encodes the classical data table and the variational parameters correspond directly to the regression coefficients which are real numbers by construction, providing a high degree of model interpretability and minimal cost to optimize with the right expressiveness. Instead of assuming the state preparation is given by granted, we discuss the state preparation with different encoders and their time complexity and overall resource cost. We can take advantage of the encoded data structure to cut down the algorithm time complexity. To the best of our knowledge, we show for the first time explicitly how the linkage of the classical data structure can be taken advantage of directly through quantum subroutines by construction. For nonlinear regression, our algorithm can be extended by building nonlinear features into the training data as demonstrated by numerical results. In addition, we demonstrate that the model trainability is achievable only when the number of features $M$ is much less than the number of records $L$ for the encoded data structure to justify $L\gg M$ in our resource estimation.

Quantum computing offers a new paradigm for advancing high-energy physics research by enabling novel methods for representing and reasoning about fundamental quantum mechanical phenomena. Realizing these ideals will require the development of novel computational tools for modeling and simulation, detection and classification, data analysis, and forecasting of high-energy physics (HEP) experiments. While the emerging hardware, software, and applications of quantum computing are exciting opportunities, significant gaps remain in integrating such techniques into the HEP community research programs. Here we identify both the challenges and opportunities for developing quantum computing systems and software to advance HEP discovery science. We describe opportunities for the focused development of algorithms, applications, software, hardware, and infrastructure to support both practical and theoretical applications of quantum computing to HEP problems within the next 10 years., Comment: A contribution to the 2021 Snowmass Proceedings, Computational Frontier, Topical Group on Quantum Computing

In practical decoy-state quantum key distribution, the raw key length is finite. Thus, deviation of the estimated single photon yield and single photon error rate from their respective true values due to finite sample size can seriously lower the provably secure key rate $R$. Current method to obtain a lower bound of $R$ follows an indirect path by first bounding the yields and error rates both conditioned on the type of decoy used. These bounds are then used to deduce the single photon yield and error rate, which in turn are used to calculate a lower bound of the key rate $R$. Here we report an improved version of McDiarmid inequality in statistics and show how use it to directly compute a lower bound of $R$ via the so-called centering sequence. A novelty in this work is the optimization of the bound through the freedom of choosing possible centering sequences. The provably secure key rate of realistic 100~km long quantum channel obtained by our method is at least twice that of the state-of-the-art procedure when the raw key length $\ell_\text{raw}$ is $\approx 10^5$ to $10^6$. In fact, our method can improve the key rate significantly over a wide range of raw key length from about $10^5$ to $10^{11}$. More importantly, it is achieved by pure theoretical analysis without altering the experimental setup or the post-processing method. In a boarder context, this work introduces powerful concentration inequality techniques in statistics to tackle physics problem beyond straightforward statistical data analysis especially when the data are correlated so that tools like the central limit theorem are not applicable., Comment: 14 pages, 1 table, superseding the result reported in arXiv:1806.05063, to appear in New J Phys

Shortly after the discovery of topological band insulators, the topological Kondo insulators (TKIs) have also been theoretically predicted. The latter has ignited revival interest in the properties of Kondo insulators. Currently, the feasibility of topological nature in SmB$_6$ has been intensively analyzed by several complementary probes. Here by starting with a minimal-orbital Anderson lattice model, we explore the local electronic structure in a Kondo insulator. We show that the two strong topological regimes sandwiching the weak topological regime give rise to a single Dirac cone, which is located near the center or corner of the surface Brillouin zone. We further find that, when a single impurity is placed on the surface, low-energy resonance states are induced in the weak scattering limit for the strong TKI regimes and the resonance level moves monotonically across the hybridization gap with the strength of impurity scattering potential; while low energy states can only be induced in the unitary scattering limit for the weak TKI regime, where the resonance level moves universally toward the center of the hybridization gap. These impurity induced low-energy quasiparticles will lead to characteristic signatures in scanning tunneling microscopy/spectroscopy, which has recently found success in probing into exotic properties in heavy fermion systems., Comment: 8 pages with 4 eps figures embedded, references updated

Since the recent discovery of plutonium-based superconductors such as PuCoIn$_{\rm 5}$, systematic studies of the electronic properties for plutonium compounds are providing insight into the itinerancy-localization crossover of Pu 5$f$ electrons. We are particularly interested in understanding the Fermi surface properties of PuIn$_{3}$ compound, which serves as the building block for the PuCoIn$_{\rm 5}$ superconductor. Motivated by the first observation of quantum oscillation and renewed interest in the de-Hass van-Alphen (dHvA) measurements on PuIn$_{\rm 3}$, we study the Fermi surface (FS) topology and the band dispersion in both paramagnetic and antiferromagnetic state of PuIn$_{\rm 3}$, based on density functional theory with generalized gradient approximation. We compare the results with its isostructural paramagnetic compound PuSn$_{\rm 3}$. We show the detailed Fermi surfaces of compounds PuIn$_{\rm 3}$ and PuSn$_{\rm 3}$ and conclude that the FS topology of an antiferromagnetic PuIn$_3$ agrees better with dHvA measurements. In addition, we show the magnetization of the antiferromagnetic order can alter the angle dependence and values of the effective mass for the dHvA orbits. We point out the accurate determination of the magnetic order orientation with respect to the crystal orientation is crucial to advance the understanding of the electronic structures of the PuIn$_{\rm 3}$ compound., Comment: 13 pages, 26 figures

We derive the normal modes for a rotating Coulomb ion crystal in a Penning trap, quantize the motional degrees of freedom, and illustrate how they can by driven by a spin-dependent optical dipole force to create a quantum spin simulator on a triangular lattice with hundreds of spins. The analysis for the axial modes (oscillations perpendicular to the two-dimensional crystal plane) follow a standard normal-mode analysis, while the remaining planar modes are more complicated to analyze because they have velocity-dependent forces in the rotating frame. After quantizing the normal modes into phonons, we illustrate some of the different spin-spin interactions that can be generated by entangling the motional degrees of freedom with the spin degrees of freedom via a spin-dependent optical dipole force. In addition to the well-known power-law dependence of the spin-spin interactions when driving the axial modes blue of phonon band, we notice certain parameter regimes in which the level of frustration between the spins can be engineered by driving the axial or planar phonon modes at different energies. These systems may allow for the analog simulation of quantum spin glasses with large numbers of spins., Comment: 20 pages, 17 figures

The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed matter systems, potentially including high-temperature superconductivity. However, many properties of exotic strongly correlated spin systems (e.g., spin liquids) have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N~30 particles. Feynman divined that a quantum simulator - a special-purpose "analog" processor built using quantum particles (qubits) - would be inherently adept at such problems. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach. However, simulations of quantum magnetism allowing controlled, tunable interactions between spins localized on 2D and 3D lattices of more than a few 10's of qubits have yet to be demonstrated, owing in part to the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin-spin interaction J_ij on a naturally occurring 2D triangular crystal lattice of hundreds of spin-1/2 particles (9Be+ ions stored in a Penning trap), a computationally relevant scale more than an order of magnitude larger than existing experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction J_ij ~ 1/d_ij^a, where a is tunable over 0

We demonstrate spectroscopy and thermometry of individual motional modes in a mesoscopic 2D ion array using entanglement-induced decoherence as a method of transduction. Our system is a $\sim$400 $\mu$m-diameter planar crystal of several hundred $^9$Be$^+$ ions exhibiting complex drumhead modes in the confining potential of a Penning trap. Exploiting precise control over the $^9$Be$^+$ valence electron spins, we apply a homogeneous spin-dependent optical dipole force to excite arbitrary transverse modes with an effective wavelength approaching the interparticle spacing ($\sim$20 \nolinebreak$\mu$m). Center-of-mass displacements below 1 nm are detected via entanglement of spin and motional degrees of freedom., Comment: 12 pages, 7 figures (includes Supplementary Material)

Linear Paul traps have been used recently to simulate the transverse field Ising model with long-range spin-spin couplings. We study the intrinsic effects of phonon creation (from the initial phonon ground state) on the spin-state probability and spin entanglement for such quantum spin simulators. While it has often been assumed that phonon effects are benign because they play no role in the pure Ising model, they can play a significant role when a transverse field is added to the model. We use a many-body factorization of the quantum time-evolution operator of the system, adiabatic perturbation theory and exact numerical integration of the Schr\"odinger equation in a truncated spin-phonon Hilbert space followed by a tracing out of the phonon degrees of freedom to study this problem. We find that moderate phonon creation often makes the probabilities of different spin states behave differently from the static spin Hamiltonian. In circumstances in which phonon creation is minor, the spin dynamics state probabilities converge to the static spin Hamiltonian prediction at the cost of reducing the spin entanglement. We show how phonon creation can severely impede the observation of kink transitions in frustrated spin systems when the number of ions increases. Many of our results also have implications for quantum simulation in a Penning trap., Comment: 21 pages, 11 figures, final version accepted by Physical Review A

A quantum simulator is a well controlled quantum system that can simulate the behavior of another quantum system which may require exponentially large classical computing resources to understand otherwise. In the 1980s, Feynman proposed the use of quantum logic gates on a standard controllable quantum system to efficiently simulate the behavior of a model Hamiltonian. Recent experiments using trapped ions and neutral atoms have realized quantum simulation of Ising model in presence of external magnetic fields, and showed almost arbitrary control in generating non-trivial Ising coupling patterns. Here we use laser-cooled trapped 171-Yb+ ions to simulate the emergence of magnetism in a system of interacting spins by implementing a fully-connected non-uniform ferromagnetic Ising model in a transverse magnetic field. To link this quantum simulation to condensed matter physics, we measure scalable correlation functions and order parameters appropriate for the description of larger systems, such as various moments of the magnetization. By increasing the Ising coupling strengths compared with the external field, the crossover from paramagnetism to ferromagnetic order sharpens as the system is scaled up from N = 2 to 9 trapped ion spins. This points toward the onset of a quantum phase transition that should become infinitely sharp as the system approaches the macroscopic scale. We compare the measured ground state order to theory, which may become intractable for non-uniform Ising couplings as the number of spins grows beyond 20- 30 and even NP complete for a fully-connected frustrated Ising model, making this experiment an important benchmark for large-scale quantum simulation., Comment: 7 pages, 4 figures

We study the spinless and spinful extended Hubbard models with repulsive interactions on the kagome and the decorated honeycomb ("star") lattice. Using Hartree-Fock mean-field theory, we show that interaction-driven insulating phases with non-trivial topological invariants (Chern number or $Z_2$ invariant) exist for an experimentally reasonable range of parameters. These phases occur at filling fractions which involve either Dirac points or quadratic band crossing points in the non-interacting limit. We present comprehensive mean-field phase diagrams for these lattices and discuss the competition between topologically non-trivial phases and numerous other ordered states, including various charge, spin, and bond orderings. Our results suggest that $Z_2$ topological insulators should be found in a number of systems with either little or no intrinsic spin-orbit coupling., Comment: 16 pages, 12 figures

We compute how phonon creation affects the fidelity of the quantum spin dynamics in trapped ion simulators. A rigorous treatment of the quantum dynamics is made by employing an exact operator factorization of the evolution operator. Although it is often assumed that phonon creation modifies the dynamics of the spin evolution, for an Ising spin-spin interaction in an external magnetic field, phonons have \textit{no effect} on the probabilities of spin product states measured in the direction of the Ising model axis. Phonons play a much more important role in influencing the effective spin dynamics for Heisenberg or XY model spin simulators or for other observables, like witness operators in the Ising model., Comment: 4 pages

We derive an effective action for the vortex position degree-of-freedom in a superfluid by integrating out condensate phase and density fluctuation environmental modes. When the quantum dynamics of environmental fluctuations is neglected, we confirm the occurrence of the vortex Magnus force and obtain an expression for the vortex mass. We find that this adiabatic approximation is valid only when the superfluid droplet radius $R$, or the typical distance between vortices, is very much larger than the coherence length $\xi$. We go beyond the adiabatic approximation numerically, accounting for the quantum dynamics of environmental modes and capturing their dissipative coupling to condensate dynamics. For the case of an optical-lattice superfluid we demonstrate that vortex motion damping can be adjusted by tuning the ratio between the tunneling energy $J$ and the on-site interaction energy $U$. We comment on the possibility of realizing vortex Landau level physics., Comment: 14 pages, 10 figures, accepted by PRA with corrected references and typos