Simulations of non-local spin interaction in atomic magnetometers using LANL’s D-Wave 2X
This report describes findings from LANL's D-Wave 2X simulation study.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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Charge d-wave topological insulator
Formation of a condensate of singlet electron-hole pairs in a two-dimensional metal lattice with the nesting of the Fermi contour is investigated. A numerical solution is obtained for the self-consistency equation for the insulating order parameter depending on the ratio of the coupling constants in the s- and d-wave channels of electron-hole pairing. Solutions with the pure orbital symmetry of s- and d-type are found, as well as solutions with the mixed s + d-symmetry. It is shown that in a wide range of values of the s- and d-wave coupling constants, the two-dimensional insulating order with the orbital symmetry <##> } d } x 2 −<!-- ??? --> y 2 $ d{sub {x^2 - y^2 }} $ d{sub x{sup 2}−y{sup 2}} </##> can compete with pure ordered s- and d{sub xy}-states and mixed s + d-states. Time reversal symmetry breaking under an established real order with <##> } d } x 2 −<!-- ??? --> y 2 $ d{sub {x^2 - y^2 }} $ d{sub x{sup 2}−y{sup 2}} </##>-wave symmetry may generate the imaginary component of the order parameter with symmetry d{sub xy} and cause a rise in topologically nontrivial d + id-wave ordering similar to the quantum Hall state in the absence of external magnetic field.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
D-Wave Electron-H, -He+, and -Li2+ Elastic Scattering and Photoabsorption in P States of Two-Electron Systems
In previous papers [A. K. Bhatia, Phys. Rev. A 85, 052708 (2012); 86, 032709 (2012); 87, 042705 (2013)] electron-H, -He+, and -Li2+ P-wave scattering phase shifts were calculated using the variational polarized orbital theory. This method is now extended to the singlet and triplet D-wave scattering in the elastic region. The long-range correlations are included in the Schrodinger equation by using the method of polarized orbitals variationally. Phase shifts are compared to those obtained by other methods. The present calculation provides results which are rigorous lower bonds to the exact phase shifts. Using the presently calculated D-wave and previously calculated S-wave continuum functions, photoionization of singlet and triplet P states of He and Li+ are also calculated, along with the radiative recombination rate coefficients at various electron temperatures.
D-wave↗
Finding Maximum Cliques on the D-Wave Quantum Annealer
This work assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is quite small (usually around 45 vertices), we also consider decomposition algorithms intended for larger graphs and analyze their performance. For smaller graphs that fit DW, we provide formulations of the maximum clique problem as a quadratic unconstrained binary optimization (QUBO) problem, which is one of the two input types (together with the Ising model) acceptable by the machine, and compare several quantum implementations to current classical algorithms such as simulated annealing, Gurobi, and third-party clique finding heuristics. We further estimate the contributions of the quantum phase of the quantum annealer and the classical post-processing phase typically used to enhance each solution returned by DW. We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms. On the other hand, for instances specifically designed to fit well the DW qubit interconnection network, we observe substantial speed-ups in computing time over classical approaches.
97 MATHEMATICS AND COMPUTING↗
Rapid Response: D-Wave Effort Debrief Welcome, Logistics
The main objects of this project is to develop a diverse and sizable workforce, community, interest within LANL for D-Wave and Quantum Computing; identify promising application areas/problems for future projects; and complement other D-Wave work at LANL (LDRD DR, ASC).
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A regression algorithm for accelerated lattice QCD that exploits sparse inference on the D-Wave quantum annealer
We propose a regression algorithm that utilizes a learned dictionary optimized for sparse inference on a D-Wave quantum annealer. In this regression algorithm, we concatenate the independent and dependent variables as a combined vector, and encode the high-order correlations between them into a dictionary optimized for sparse reconstruction. On a test dataset, the dependent variable is initialized to its average value and then a sparse reconstruction of the combined vector is obtained in which the dependent variable is typically shifted closer to its true value, as in a standard inpainting or denoising task. Here, a quantum annealer, which can presumably exploit a fully entangled initial state to better explore the complex energy landscape, is used to solve the highly non-convex sparse coding optimization problem. The regression algorithm is demonstrated for a lattice quantum chromodynamics simulation data using a D-Wave 2000Q quantum annealer and good prediction performance is achieved. The regression test is performed using six different values for the number of fully connected logical qubits, between 20 and 64. The scaling results indicate that a larger number of qubits gives better prediction accuracy.
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Theory of d-Wave High Temperature Superconductivity in the Cuprates Involving Non-linear Lattice Modes
The transition mechanism in high temperature cuprate superconductors is an outstanding puzzle. A previous suggestion on the role of non-linear local lattice instability modes on the microscopic pairing mechanism in high temperature cuprate superconductors (Lee, J. Supercond. Nov. Magn. 23(3), 333; 2009) is re-examined to provide a viable mechanism for superconductivity in these cuprates via an unusual lattice vibration in which an electron is predominantly interacting with a non-linear Q{sub 2} mode of the oxygen clusters in the CuO{sub 2} planes. It is shown that the interaction has explicit d-wave symmetry and leads to an indirect coupling of d-wave symmetry between electrons. As a follow-up of Lee (J. Supercond. Nov. Magn. 23(3), 333; 2009), in this paper, we report detailed derivation of the superconducting gap equation and numerical solutions for the transition temperature as inherently integrated into the so-called extended Hubbard model (EHM). A unique feature in the EHM is that the transition temperature has an inherent k-dependence. In addition, superconducting gap solutions are restrained to specific regions in the first Brillouin zone (1BZ). It is very feasible to expect that the EHM naturally inherits a huge parameter space in which experimentally measured results, such as the well-known superconducting dome and the phase diagram from electronic Raman scattering (Sacuto et al., Rep. Prog. Phys. 76(2), 022502; 2013) can be accommodated. The EHM model hence offers a viable venue to search for or confirm any signature in k-point-sensitive experimental measurements.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Global phase diagram of D-wave superconductivity in the square-lattice t-J model
The Hubbard and closely related t-J models are exciting platforms for unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calculations using the grand canonical ensemble, we address open issues regarding the ground-state phase diagram of the extended t-J model on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the pure t-J model with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ( δ = 0.1 to 0.2 ), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping t 2 suppresses pair and charge density waves, resulting in a uniform d-wave SC phase in both electron- and hole-doped cuprate model systems. Our work validates the t-J model as a proper minimum model for the emergence of superconductivity in cuprate superconductors.
Chen, Feng (ORCID:000000018196030X)↗
Higgs Mode in the d -Wave Superconductor Bi 2 Sr 2 CaCu 2 O 8 + x Driven by an Intense Terahertz Pulse
We investigated the terahertz (THz)-pulse driven nonlinear response in the d-wave cuprate superconductor Bi 2 Sr 2 CaCu 2 O 8+x (Bi2212) using a THz pump near-infrared probe scheme in the time domain. We have observed an oscillatory behavior of the optical reflectivity that follows the THz electric field squared and is strongly enhanced below T c . The corresponding third-order nonlinear effect exhibits both A 1g and B 1g symmetry components, which are decomposed from polarization-resolved measurements. Comparison with a BCS calculation of the nonlinear susceptibility indicates that the A 1g component is associated with the Higgs mode of the d-wave order parameter.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Concealed d -wave pairs in the s ± condensate of iron-based superconductors
Significance Inspired by the hidden spin entanglement in superfluid Helium-3B, we propose that orbitally entangled Cooper pairs of d -wave character lie within the s -wave condensate of iron-based superconductors. This order is revealed when the topologically nontrivial helical nature of the band structure is taken into account. The hidden d-wave character lowers the Coulomb repulsion energy and accounts for the observed phase transition from a fully gapped s -wave to a nodal octet superconductor within a single pairing mechanism. We predict that this entangled superconductor will display a shift in the orbital character of its quasiparticles on pair condensation, and will form Andreev edge states at the domain wall between its s -wave and an octet phase.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
A Rigorous Comparison of the D-Wave 2X QPU to Established B-QP Solution Methods [Slides]
This document compares the D-wave 2X QPU to other B-QP solution methods for use in optimization applications.
97 MATHEMATICS AND COMPUTING↗
Amplitude mode oscillations in pump-probe photoemission spectra from a d -wave superconductor
Recent developments in the techniques of ultrafast pump-probe photoemission have made possible the search for collective modes in strongly correlated systems out of equilibrium. Including inelastic scattering processes and a retarded interaction, we simulate time- and angle-resolved photoemission spectroscopy (trARPES) to study the amplitude mode of a d-wave superconductor, a collective mode excited through the nonlinear light-matter coupling to the pump pulse. We find that the amplitude mode oscillations of the d-wave order parameter occur in phase at a single frequency that is twice the quasi-steady-state maximum gap size after pumping. As a result, we comment on the necessary conditions for detecting the amplitude mode in trARPES experiments.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Robust d-Wave Superconductivity in the Square-Lattice t–J Model
Unravelling competing orders emergent in doped Mott insulators and their interplay with unconventional superconductivity is one of the major challenges in condensed matter physics. Here, to explore the possible superconducting state in a doped Mott insulator, we study the square-lattice t-J model with both the nearest-neighbor and next-nearest-neighbor electron hoppings and spin interactions. By using the state-of-the-art density matrix renormalization group calculation with imposing charge U(1) and spin SU(2) symmetries on the six-leg cylinders, we establish a quantum phase diagram including three phases: a stripe charge density wave phase, a superconducting phase without static charge order, and a superconducting phase coexistent with a weak charge stripe order. Crucially, we demonstrate that the superconducting phase has a power-law pairing correlation that decays much slower than the charge density and spin correlations, which is a quasi-1D descendant of the uniform d-wave superconductor in two dimensions. These findings reveal that enhanced charge and spin fluctuations with optimal doping is able to produce robust d-wave superconductivity in doped Mott insulators, providing a foundation for connecting theories of superconductivity to models of strongly correlated systems.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Ground state of the three-dimensional BCS d -wave superconductor
We determine the mean-field ground state of the three-dimensional rotationally symmetric d-wave (ℓ = 2) superconductor at weak coupling. It is a noninert state, invariant under the symmetry C 2 only, which breaks time-reversal symmetry almost maximally, and features a high but again less-than-maximal average magnetization. The state obtained by minimization of the expanded sixth-order Ginzburg–Landau free energy is found to be an excellent approximation to the true ground state. Here, the coupling to a parasitic s-wave component has only a minuscule quantitative and no qualitative effect on the ground state.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Computing molecular excited states on a D-Wave quantum annealer
Abstract The possibility of using quantum computers for electronic structure calculations has opened up a promising avenue for computational chemistry. Towards this direction, numerous algorithmic advances have been made in the last five years. The potential of quantum annealers, which are the prototypes of adiabatic quantum computers, is yet to be fully explored. In this work, we demonstrate the use of a D-Wave quantum annealer for the calculation of excited electronic states of molecular systems. These simulations play an important role in a number of areas, such as photovoltaics, semiconductor technology and nanoscience. The excited states are treated using two methods, time-dependent Hartree–Fock (TDHF) and time-dependent density-functional theory (TDDFT), both within a commonly used Tamm–Dancoff approximation (TDA). The resulting TDA eigenvalue equations are solved on a D-Wave quantum annealer using the Quantum Annealer Eigensolver (QAE), developed previously. The method is shown to reproduce a typical basis set convergence on the example $$\hbox {H}_2$$ H 2 molecule and is also applied to several other molecular species. Characteristic properties such as transition dipole moments and oscillator strengths are computed as well. Three potential energy profiles for excited states are computed for $$\hbox {NH}_3$$ NH 3 as a function of the molecular geometry. Similar to previous studies, the accuracy of the method is dependent on the accuracy of the intermediate meta-heuristic software called qbsolv.
74 ATOMIC AND MOLECULAR PHYSICS↗
Directly visualizing the sign change of d-wave superconducting gap in Bi 2 Sr 2 CaCu 2 O 8+δ by phase-referenced quasiparticle interference
The superconducting state is formed by the condensation of Cooper pairs and protected by the superconducting gap. The pairing interaction between the two electrons of a Cooper pair determines the gap function. Thus, it is pivotal to detect the gap structure for understanding the mechanism of superconductivity. In cuprate superconductors, it has been well established that the gap may have a d-wave function. This gap function has an alternative sign change in the momentum space. It is however hard to visualize this sign change. Here we report the measurements of scanning tunneling spectroscopy in Bi 2 Sr 2 CaCu 2 O 8+δ and conduct the analysis of phase-referenced quasiparticle interference (QPI). We see the seven basic scattering vectors that connect the octet ends of the banana-shaped contour of Fermi surface. The phase-referenced QPI clearly visualizes the sign change of the d -wave gap. Lastly, our results illustrate an effective way for determining the sign change of unconventional superconductors.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Electronic structure with direct diagonalization on a D-wave quantum annealer
Quantum chemistry is regarded to be one of the first disciplines that will be revolutionized by quantum computing. Although universal quantum computers of practical scale may be years away, various approaches are currently being pursued to solve quantum chemistry problems on near-term gate-based quantum computers and quantum annealers by developing the appropriate algorithm and software base. This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. The approach is based on the matrix formulation, efficiently uses qubit resources based on a power-of-two encoding scheme and is hardware-dominant relying on only one classically optimized parameter. We demonstrate the use of D-Wave hardware for obtaining ground and excited electronic states across a variety of small molecular systems. The approach can be adapted for use by a vast majority of electronic structure methods currently implemented in conventional quantum-chemical packages. The results of this work will encourage further development of software such as qbsolv which has promising applications in emerging quantum information processing hardware and has expectation to address large and complex optimization problems intractable for classical computers.
97 MATHEMATICS AND COMPUTING↗
ARPES-parameterized Hubbard approach to d-wave cuprate superconductors
In the last decade, the Angle Resolved Photoemission Spectroscopy (ARPES) has achieved important advances in both energy and angular resolutions, providing a direct measurement of the single-particle dispersion relation and superconducting gap. These dispersion relation data allow a full determination of the self-energy, first and second neighbor parameters in the Hubbard model. This model and its generalizations offer a simple and general way to describe the electronic correlation in solids. In particular, the parameters of correlated hopping interactions, responsible of the d-wave superconductivity in the generalized Hubbard model, are determined from ARPES data and the critical temperature within the mean-field approximation. In this work, we determine the model parameters for Bi{sub 2}Sr{sub 2−x}La{sub x}CuO{sub 6+δ} and study its d-wave superconducting gap as a function of temperature by solving numerically two coupled integral equations. Finally, the calculated electronic specific heat is compared with experimental results.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗