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Genesis: A Compiler Framework for Hamiltonian Simulation on Hybrid CV-DV Quantum Computers

We introduce Genesis, the first compiler designed to support Hamiltonian Simulation on hybrid continuous-variable (CV) and discrete-variable (DV) quantum computing systems. Genesis is a two-level compilation system. At the first level, it decomposes an input Hamiltonian into basis gates using the native instruction set of the target hybrid CV-DV quantum computer. At the second level, it tackles the mapping and routing of qumodes/qubits to implement long-range interactions for the gates decomposed from the first level. Rather than a typical implementation that relies on SWAP primitives similar to qubit-based (or DV-only) systems, we propose an integrated design of connectivity-aware gate synthesis and beamsplitter SWAP insertion tailored for hybrid CV-DV systems. We also introduce an OpenQASM-like domain-specific language (DSL) named CVDV-QASM to represent Hamiltonian in terms of Pauli-exponentials and basic gate sequences from the hybrid CVDV gate set. Genesis has successfully compiled several important Hamiltonians, including the Bose-Hubbard model, Z2−Higgs model, Hubbard-Holstein model, Heisenberg model and Electron-vibration coupling Hamiltonians, which are critical in domains like quantum field theory, condensed matter physics, and quantum chemistry. Our implementation is available at Genesis-CVDV-Compiler https://github.com/ruadapt/Genesis-CVDV-Compiler

Chen, Henry↗

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows

Herein we demonstrate that the reformulation of renormalization group (RG) flow equations as nonlinear heat equations has severe implications on the understanding of RG flows in general. We demonstrate by explicitly constructing an entropy function for a zero-dimensional Z 2 -symmetric model that the dissipative character of generic nonlinear diffusion equations is also hard-coded in the functional RG equation. This renders RG flows manifestly irreversible, revealing the semigroup property of RG transformations on the level of the flow equation itself. Additionally, we argue that the dissipative character of RG flows, its irreversibility and the entropy production during the RG flow may be linked to the existence of a so-called C– / A-function. In total, this introduces an asymmetry in the so-called RG time—in complete analogy to the thermodynamic arrow of time—and allows for an interpretation of infrared actions as equilibrium solutions of dissipative RG flows equations. The impossibility of resolving microphysics from macrophysics is evident in this framework. Furthermore, we directly link the irreversibility and the entropy production in RG flows to an explicit numerical entropy production, which is manifest in diffusive and non-linear partial differential equations (PDEs) and a standard mathematical tool for the analysis of PDEs. Using exactly solvable zero-dimensional Z 2 -symmetric models, we explicitly compute the (numerical) entropy production related to the total variation nonincreasing property of the PDE during RG flows toward the infrared limit. Finally, we discuss generalizations of our findings and relations to the C– / A-theorem as well as how our work may help to construct truncations of RG flow equations in the future, including numerically stable schemes for solving the corresponding PDEs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Solvable 3D Kondo Lattice Exhibiting Pair Density Wave, Odd-Frequency Pairing, and Order Fractionalization

The Kondo lattice model plays a key role in our understanding of quantum materials, but a lack of small parameters has posed a long-standing problem. We present a 3 dimensional S= 1 2 Kondo lattice model describing a spin liquid within an electron sea. Strong correlations in the spin liquid are treated exactly, enabling a controlled analytical approach. Like a Peierls or BCS phase, a logarithmically divergent susceptibility leads to an instability into a new phase at arbitrarily small Kondo coupling. Our solution captures a plethora of emergent phenomena, including odd-frequency pairing, pair density wave formation and order fractionalization. The ground-state state is a pair density wave with a fractionalized charge e, S = 1/2 order parameter, formed between electrons and Majorana fermions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Factorization of Binary Matrices: Rank Relations, Uniqueness and Model Selection of Boolean Decomposition

The application of binary matrices are numerous. Representing a matrix as a mixture of a small collection of latent vectors via low-rank decomposition is often seen as an advantageous method to interpret and analyze data. In this work, we examine the factorizations of binary matrices using standard arithmetic (real and nonnegative) and logical operations (Boolean and $\mathbb{Z}$ 2 ). We examine the relationships between the different ranks, and discuss when factorization is unique. In particular, we characterize when a Boolean factorization X = W$\land$H has a unique W, a unique H (for a fixed W), and when both W and H are unique, given a rank constraint. We introduce a method for robust Boolean model selection, called BMFk, and show on numerical examples that BMFk not only accurately determines the correct number of Boolean latent features but reconstruct the pre-determined factors accurately.

97 MATHEMATICS AND COMPUTING↗

Fragmentation cross sections of 28Si at 14.5 GeV/nucleon

We used CR39 plastic nuclear track detectors (C12H18O7) in combination with automatic track measurement techniques to determine total charge changing and partial cross sections for the production of fragments of charge ZF = 6 to ZF = 13 in collisions of 28Si beam nuclei at 14.5 GeV/nucleon in targets H, C, CR39, (C18H38O), Al, Cu, Ag, and Pb. By application of factorization rules, measured partial cross sections are separated into pure nuclear and electromagnetic components. The cross sections for electromagnetic dissociation agree with theoretical models. The results are consistent with a Z2 dependence of virtual photon spectra.

NASA Discipline Number 04-10↗

Breaking mirror twin color

We investigate simple extensions of the Mirror Twin Higgs model in which the twin color gauge symmetry and the discrete Z2 mirror symmetry are spontaneously broken. This is accomplished in a minimal way by introducing a single new colored triplet, sextet, or octet scalar field and its twin along with a suitable scalar potential. This spontaneous Z2 breaking allows for a phenomenologically viable alignment of the electroweak vacuum, and leads to dramatic differences between the visible and mirror sectors with regard to the residual gauge symmetries at low energies, color confinement scales, and particle spectra. In particular, several of our models feature a remnant SU(2) or SO(3) twin color gauge symmetry with a very low confinement scale in comparison to ΛQCD. Furthermore, couplings between the colored scalar and matter provide a new dynamical source of twin fermion masses, and due to the mirror symmetry, these lead to a variety of correlated visible sector effects that can be probed through precision measurements and collider searches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A predictive mirror twin Higgs with small Z2 breaking

The twin Higgs mechanism is a solution to the little hierarchy problem in which the top partner is neutral under the Standard Model (SM) gauge group. The simplest mirror twin Higgs (MTH) model — where a Z 2 symmetry copies each SM particle — has too many relativistic degrees of freedom to be consistent with cosmological observations. We demonstrate that MTH models can have an observationally viable cosmology if the twin mass spectrum leads to twin neutrino decoupling before the SM and twin QCD phase transitions. Our solution requires the twin photon to have a mass of ~20 MeV and kinetically mix with the SM photon to mediate entropy transfer from the twin sector to the SM. This twin photon can be robustly discovered or excluded by future experiments. Additionally, the residual twin degrees of freedom present in the early Universe in this scenario would be detectable by future observations of the cosmic microwave background.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

ℤ2 × ℤ2 Equivariant Quantum Neural Networks: Benchmarking against Classical Neural Networks

This paper presents a comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNNs) and Quantum Neural Networks (QNNs), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENNs) and Deep Neural Networks (DNNs). We evaluate the performance of each network with three two-dimensional toy examples for a binary classification task, focusing on model complexity (measured by the number of parameters) and the size of the training dataset. Our results show that the Z2×Z2 EQNN and the QNN provide superior performance for smaller parameter sets and modest training data samples.

Dong, Zhongtian (ORCID:0000000210003454)↗

Quantum order by disorder in frustrated spin nanotubes

Here we investigate quantum order by disorder in a frustrated spin nanotube formed by wrapping a J1–J2 Heisenberg model at 45° around a cylinder. Using Schwinger boson theory and density matrix renormalization group (DMRG), we have computed the ground-state phase diagram to reveal a Z2 phase in which collinear spin stripes form a right- or left-handed helix around the nanotube. We have derived an analytic estimate for the critical η c = J 1 /2J 2 of the Z 2 -helical phase transition, which is in agreement with the DMRG results. By evaluating the entanglement spectrum and nonlocal string order parameters we discuss the topology of the Z 2 -helical phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Novel local symmetries and chiral-symmetry-broken phases in S = 1/2 triangular-lattice Heisenberg model

Using a nonmean-field approach the triangular-lattice S = 1/2 Heisenberg antiferromagnet with nearest- and next-nearest-neighbor couplings is shown undergo an Ising-type phase transition into a chiral-symmetry-broken phase (Kalmeyer-Laughlin-like state) at small T. Removal of next-nearest-neighbor coupling introduces a local Z2 symmetry, thereby suppressing any finite-T chiral order.

Baskaran, G.↗

Footprints of Kitaev spin liquid in the Fano lineshape of Raman-active optical phonons

We develop a theoretical description of the Raman spectroscopy in the spin-phonon-coupled Kitaev system and show that it can provide observable signatures of fractionalized excitations characteristic of the underlying spin-liquid phase. In particular, we obtain the explicit form of the phonon modes and construct the coupling Hamiltonian based on the D 3d symmetry. We then systematically compute the Raman intensity and show that the spin-phonon coupling renormalizes phonon propagators and generates the salient Fano lineshape. We find that the temperature evolution of the Fano lineshape displays two crossovers, and the low-temperature crossover shows pronounced magnetic-field dependence. We thus identify the observable effect of the Majorana fermions and the Z2 gauge fluxes encoded in the Fano lineshape. Our results are consistent with the phonon Raman scattering experiments in the candidate material α-RuCl 3 .

36 MATERIALS SCIENCE↗

Thermal Line Shift and Broadening of Ho(3+) in Y3AI5O12 and Lu3AIO12

The interaction between the active ion and the host lattice manifests itself in two distinct ways: the static interaction with the crystal field that causes the splitting of the free ion energy levels and the active interaction through the surrounding phonon system that produces temperature dependent characteristics in the optical spectrum of the ion (e.g. line broadening and line shift). The strength of the splitting depends heavily on the electronic configuration of the atom. The model give by McCumber and Sturge describes the thermal effects on line width and position above 77 K with Raman scattering of Debye model phonons. These processes predict a Lorentzian line shape. However, below 77 K the principal contributions are from crystal inhomogeneities that result in a Gaussian line shape. We have investigated the experimental Stark levels as well as the thermal effects on the line width and the position of trivalent holmium ions in both yttrium aluminum garnet, Y3Al5O12 (YAG) and lutetium aluminum garnet, Lu3Al5O12 (LuAG) crystals. We have compared the Stark levels of the (5)I(6) state, and the thermal line shift and broadening of an isolated transition (Z2 to X13) between the (5)I(8) and (5)I(6) stark levels in these crystals. This transition occurs in the near infrared region at approximately 1117 nm.

Snoke, Elizabeth R.↗

[EC5-Space Suit Assembly Team- Internship]

There were three main projects in this internship. The first pertained to the Bearing Dust Cycle Test, in particular automating the test to allow for easier administration. The second concerned modifying the communication system setup in the Z2 suit, where speakers and mics were adjusted to allow for more space in the helmet. And finally, the last project concerned the tensile strength testing of fabrics deemed as candidates for space suit materials and desired to be sent off for radiation testing. The major duties here are split up between the major projects detailed above. For the Bearing Dust Cycle Test, the first objective was to find a way to automate administration of the test, as the previous version was long and tedious to perform. In order to do this, it was necessary to introduce additional electronics and perform programming to control the automation. Once this was done, it would be necessary to update documents concerning the test setup, procedure, and potential hazards. Finally, I was tasked with running tests using the new system to confirm system performance. For the Z2 communication system modifications, it was necessary to investigate alternative speakers and microphones which may have better performance than those currently used in the suit. Further, new speaker and microphone positions needed to be identified to keep them out of the way of the suit user. Once this was done, appropriate hardware (such as speaker or microphone cases and holders) could be prototyped and fabricated. For the suit material strength testing, the first task was to gather and document various test fabrics to identify the best suit material candidates. Then, it was needed to prepare samples for testing to establish baseline measurements and specify a testing procedure. Once the data was fully collected, additional test samples would be prepared and sent off-site to undergo irradiation before being tested again to observe changes in strength performance. For the Bearing Dust Cycle Test, automation was achieved through use of a servo motor and code written in LabVIEW. With this a small electrical servo controller was constructed and added to the system. For the Z2 communication modifications speaker cases were developed and printed, and new speakers and mics were selected. This allowed us to move the speakers and mics to locations to remain out of the suit users way. For the suit material strength testing, five material candidates were identified and test samples were created. These samples underwent testing, and baseline test results were gathered, though these results are currently being investigated for accuracy. The main process efficiency developed during the course of this internship comes from automation of the Bearing Dust Cycle Test. In particular, many hours of human involvement and precise operation are replaced with a simple motor setup. Thus it is no longer required to man the test, saving valuable employee time. This internship has confirmed a few things for me, namely that I both want to work as an engineer for an aerospace firm and that in particular I want to work for the Johnson Space Center. I am also confirmed in my desire to work with electronics, though I was surprised to enjoy prototyping 3D CAD design as much as I did. Therefore, I will make an effort to build my skills in this area so that I can continue to design mechanical models. In fact, I found the process of hands-on prototyping to be perhaps the most fun aspect of my time working here. This internship has also furthered my excitement for continual education, and I will hopefully be pursuing a masters in my field in the near future.

Maicke, Andrew↗

Superspin renormalization and slow relaxation in random spin systems

We develop an excited-state real-space renormalization group (RSRG-X) formalism to describe the dynamics of conserved densities in randomly interacting spin-12 systems. Our formalism is suitable for systems with U(1) and Z2 symmetries, and we apply it to chains of randomly positioned spins with dipolar XX+YY interactions, as arise in Rydberg quantum simulators and other platforms. The formalism generates a sequence of effective Hamiltonians that provide approximate descriptions for dynamics on successively smaller energy scales. These effective Hamiltonians involve “superspins”: two-level collective degrees of freedom constructed from (anti)aligned microscopic spins. Conserved densities can then be understood as relaxing via coherent collective spin flips. For the well-studied simpler case of randomly interacting nearest-neighbor XX+YY chains, the superspins reduce to single spins. Our formalism also leads to a numerical method capable of simulating the dynamics up to an otherwise inaccessible combination of large system size and late time. Focusing on disorder-averaged infinite-temperature autocorrelation functions, in particular the spin survival probability Sp¯(t), we demonstrate quantitative agreement between our algorithm and exact diagonalization (ED) at low but nonzero frequencies. Such agreement holds for chains with nearest-neighbor, next-nearest-neighbor, and long-range dipolar interactions. Our results indicate decay of Sp¯(t) slower than any power law and feature no significant deviation from the ∼1/ln2(t) asymptote expected from the infinite-randomness fixed-point of the nearest-neighbor model. We also apply the RSRG-X formalism to two-dimensional long-range systems of moderate size and find slow late-time decay of Sp¯(t).

Zhao, Yi J↗