Machine learning methods for quantum mechanics
Exploratory implementations of possible algorithms for simulating small quantum mechanical systems on a classical computer.
Lawerence, Scott↗
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Assessing the theory-data tension in neutrino-induced charged pion production: the effect of final-state nucleon distortion
Pion production on nuclei constitutes a significant part of the total cross section in experiments involving few-GeV neutrinos. Combined analyses of data on deuterium and heavier nuclei points to tensions between the bubble chamber data and the data of the MINER$\nu$A experiment, which are often ascribed to unspecified nuclear effects. To understand the origin of these tensions, a microscopic quantum mechanical framework is needed to compute nuclear matrix elements. We use the local approximation to the relativistic distorted wave impulse approximation (RDWIA) to assess the role of final-state nucleon distortion. To perform this comparison under conditions relevant to neutrino experiments, we compute cross sections for the MINER$\nu$A and T2K charged pion production datasets. The inclusion of nucleon distortion leads to a reduction of the cross section up to 10%, but to no significant change in shape of the flux-averaged cross sections. Results with and without distortion compare favorably to experimental data, with the exception of the low-$Q^2$ MINER$\nu$A $\pi^+$ data. We point out that hydrogen target data from BEBC is also overpredicted at low-$Q^2$, and that the discrepancy is similar in shape and magnitude to what is found in comparison to MINER$\nu$A data. Including nucleon distortion alone cannot explain the overprediction of low-$Q^2$ cross sections measured by MINER$\nu$A. The similar overprediction of BEBC data on hydrogen means that it is impossible to ascribe this discrepancy solely to a nuclear effect. Axial couplings and their $Q^2$ dependence should ideally be derived from more precise data on hydrogen and deuterium.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Computational Determination of the Refractive Index of TATB, LLM-105, β-HMX, & α-RDX
In this study, we use Materials Studio CASTEP, an ab initio quantum mechanical (QM) program employing density functional theory (DFT), to compute the refractive index (RI) of solid energetic materials, specifically, PETN (tetragonal phase), TATB, LLM-105, β-HMX, and α-RDX. The use of quantum mechanical DFT methods affords the investigation of the optical mate rial properties of a system without the need for any experimental input. The RI values of PETN and TATB have been experimentally determined previously and are compared here to the QM derived RI values as validation of the theoretical approach in determining material optical proper ties. To date, experimental measurements to determine the RI values for LLM-105 have yet to be determined. This fact obviates the need to determine LLM-105 RI values using quantum mechanical means.
36 MATERIALS SCIENCE↗
Relative State Counting for Semiclassical Black Holes
It has been shown that entropy differences between certain states of perturbative quantum gravity can be computed without specifying an ultraviolet completion. This is analogous to the situation in classical statistical mechanics, where entropy differences are defined but absolute entropy is not. Unlike in classical statistical mechanics, however, the entropy differences computed in perturbative quantum gravity do not have a clear physical interpretation. Here we construct a family of perturbative black hole states for which the entropy difference can be interpreted as a relative counting of states. Conceptually, this Letter begins with the algebra of mass fluctuations around a fixed black hole background, and points out that while this is a type I algebra, it is not a factor and therefore has no canonical definition of entropy. As in previous work, coupling the mass fluctuations to quantum matter embeds the mass algebra within a type II factor, in which entropy differences (but not absolute entropies) are well defined. It is then shown that for microcanonical wave functions of mass fluctuation, the type II entropy difference equals the logarithm of the dimension of the extra Hilbert space that is needed to map one microcanonical window to another using gauge-invariant unitaries. The Letter closes with comments on type II entropy difference in a more general class of states, where the von Neumann entropy difference does not have a physical interpretation, but “one-shot” entropy differences do. Published by the American Physical Society 2024
Akers, Chris (ORCID:0000000227929827)↗
Dynamical logical qubits in the Bacon-Shor code
The Bacon-Shor code is a quantum error correcting subsystem code composed of weight-2 check operators that admits a single logical qubit, and has distance 𝑑 on a 𝑑×𝑑 square lattice. We show that when viewed as a Floquet code, by choosing an appropriate measurement schedule of the check operators, it can additionally host several dynamical logical qubits. Specifically, we identify a period-4 measurement schedule of the check operators that preserves logical information between the instantaneous stabilizer groups. Such a schedule not only measures the usual stabilizers of the Bacon-Shor code, but also measures and promotes gauge operators of the parent subsystem code to additional temporary stabilizers that protect the dynamical logical qubits against errors. We show that the code distance of these Floquet-Bacon-Shor codes scales as Θ(𝑑/√𝑘) on an 𝑛=𝑑×𝑑 lattice with 𝑘 dynamical logical qubits, along with the logical qubit of the parent subsystem code. Unlike the usual Bacon-Shor code, the Floquet-Bacon-Shor code family introduced here can therefore saturate the subsystem bound 𝑘𝑑=𝑂(𝑛). Moreover, several errors are shown to be self-corrected purely by the measurement schedule itself. This work provides insights into the design space for dynamical codes and expands the known approaches for constructing Floquet codes.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DeePKS + ABACUS as a Bridge between Expensive Quantum Mechanical Models and Machine Learning Potentials
Recently, the development of machine learning (ML) potentials has made it possible to perform large-scale and long-time molecular simulations with the accuracy of quantum mechanical (QM) models. However, for different levels of QM methods, such as density functional theory (DFT) at the meta-GGA level and/or with exact exchange, quantum Monte Carlo, etc., generating a sufficient amount of data for training an ML potential has remained computationally challenging due to their high cost. In this work, we demonstrate that this issue can be largely alleviated with Deep Kohn–Sham (DeePKS), an ML-based DFT model. DeePKS employs a computationally efficient neural network-based functional model to construct a correction term added upon a cheap DFT model. Upon training, DeePKS offers closely matched energies and forces compared with high-level QM method, but the number of training data required is orders of magnitude less than that required for training a reliable ML potential. As such, DeePKS can serve as a bridge between expensive QM models and ML potentials: one can generate a decent amount of high-accuracy QM data to train a DeePKS model and then use the DeePKS model to label a much larger amount of configurations to train an ML potential. Further, this scheme for periodic systems is implemented in a DFT package ABACUS, which is open source and ready for use in various applications.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Demonstration of Quantum Energy Teleportation on Superconducting Quantum Hardware
Teleporting physical quantities to remote locations remains a key challenge for quantum information science and technology. Quantum teleportation has enabled the transfer of quantum information, but teleportation of quantum physical quantities has not yet been realized. Here we report the realization and observation of quantum energy teleportation on real superconducting quantum hardware. We achieve this by using several IBM superconducting quantum computers. The results are consistent with the exact solution of the theory and are improved by the mitigation of measurement error. Quantum energy teleportation requires only local operations and classical communication. Furthermore, our results provide a realistic benchmark that is fully achievable with current quantum computing and communication technologies.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems
Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory. This article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light–matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (quantum electrodynamical-materials).
74 ATOMIC AND MOLECULAR PHYSICS↗
Interplay between Catalyst Corrosion and Homogeneous Reactive Oxygen Species in Electrochemical Ozone Production
In this study, electrochemical ozone production (EOP), a six-electron water oxidation reaction, offers promising avenues for creating value-added oxidants and disinfectants. However, progress in this field is slowed by a dearth of understanding of fundamental reaction mechanisms. In this work, we combine experimental electrochemistry, spectroscopic detection of reactive oxygen species (ROS), oxygen-anion chemical ionization mass spectrometry, and computational quantum chemistry calculations to determine a plausible reaction mechanism on nickel- and antimony-doped tin oxide (Ni/Sb–SnO 2 , NATO), one of the most selective EOP catalysts. Antimony doping is shown to increase the conductivity of the catalyst, leading to improved electrochemical performance. Spectroscopic analysis and electrochemical experiments combined with quantum chemistry predictions reveal that hydrogen peroxide (H 2 O 2 ) is a critical reaction intermediate. We propose that leached Ni 4+ cations catalyze hydrogen peroxide into solution phase hydroperoxyl radicals ( • OOH); these radicals are subsequently oxidized to ozone. Isotopic product analysis shows that ozone is generated catalytically from water and corrosively from the catalyst oxide lattice without regeneration of lattice oxygens. Further quantum chemistry calculations and thermodynamic analysis suggest that the electrochemical corrosion of tin oxide itself might generate hydrogen peroxide, which is then catalyzed to ozone. The proposed pathways explain both the roles of dopants in NATO and its lack of stability. Our study interrogates the possibility that instability and electrochemical activity are intrinsically linked through the formation of ROS. In doing so, we provide the first mechanism for EOP that is consistent with computational and experimental results and highlight the central challenge of instability as a target for future research efforts.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
Quantum Information Encoding and Decoding for Quantum Sensi
This two-year theory project focused on theoretical investigations of novel paradigms for quantum sensing, building on information encoding and techniques from quantum error correction, quantum computing and other quantum information domains. The outcomes facilitate quantum information technology development, especially at the interface of quantum computing and quantum sensing. The results of the project show new use cases and new paradigms for quantum sensing beyond what has so far been considered. One outcome shows how quantum sensing opens new opportunities for fundamental physics such as the capability of single graviton detection. Another outcome reveals a new application of NISQ quantum computers with error correction for metrology, building on recent advances in practical quantum error correction implementation. The third outcome of the project creates new paradigms of back-action-evading sensing inspired by collective quantum information encoding, which achieves quantum sensing beyond the quantum limit without the use of entanglement.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
QCOR; A Language Extension Specification for the Heterogeneous Quantum-Classical Model of Computation
Quantum computing (QC) is an emerging computational paradigm that leverages the laws of quantum mechanics to perform elementary logic operations. Existing programming models for QC were designed with fault-tolerant hardware in mind, envisioning stand-alone applications. However, the susceptibility of near-term quantum computers to noise limits their stand-alone utility. To better leverage limited computational strengths of noisy quantum devices, hybrid algorithms have been suggested whereby quantum computers are used in tandem with their classical counterparts in a heterogeneous fashion. This modus operandi calls out for a programming model and a high-level programming language that natively and seamlessly supports heterogeneous quantum-classical hardware architectures in a single-source-code paradigm. Motivated by the lack of such a model, we introduce a language extension specification, called QCOR, which enables single-source quantum-classical programming. Programs written using the QCOR library–based language extensions can be compiled to produce functional hybrid binary executables. After defining QCOR’s programming model, memory model, and execution model, we discuss how QCOR enables variational, iterative, and feed-forward QC. Additionally, QCOR approaches quantum-classical computation in a hardware-agnostic heterogeneous fashion and strives to build on best practices of high-performance computing. The high level of abstraction in the language extension is intended to accelerate the adoption of QC by researchers familiar with classical high-performance computing.
97 MATHEMATICS AND COMPUTING↗
Impacts of noise and structure on quantum information encoded in a quantum memory
As larger, higher-quality quantum devices are built and demonstrated in quantum information applications, such as quantum computation and quantum communication, the need for high-quality quantum memories to store quantum states becomes ever more pressing. Future quantum devices likely will use a variety of physical hardware, some being used primarily for processing of quantum information and others for storage. Here we study the correlation of the structure of quantum information with physical noise models of various possible quantum memory implementations. Through numerical simulation of different noise models and approximate analytical formulas applied to a variety of interesting quantum states, we provide comparisons between quantum hardware with different structure, including both qubit- and qudit-based quantum memories. Our findings point to simple, experimentally relevant formulas for the relative lifetimes of quantum information in different quantum memories and have relevance to the design of hybrid quantum devices.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
SPARC-X: Quantum simulations at extreme scale - reactive dynamics from first principles
We have developed the massively parallel electronic structure code SPARC-X: a computational framework for performing Kohn-Sham Density Functional Theory (DFT) calculations that can scale linearly with the number of atoms in the system, while being able to leverage petascale and emerging exascale parallel computers to study chemical phenomena at unprecedented length and time scales. SPARC-X exploits a recent breakthrough in electronic structure methodologies: systematically improvable, strictly local, orthonormal, discontinuous real-space bases that efficiently and systematically capture the local chemistry of the system. With further adaptation using new machine-learning techniques and the use of the massively parallel Spectral Quadrature (SQ) electronic structure method, the algorithmic complexity and prefactor associated with DFT calculations involving semilocal as well as hybrid functionals are dramatically reduced. Using petascale computational resources, SPARC-X enables quantum mechanical simulations at length and time scales previously accessible only by empirical approaches, e.g., 1,000,000 atoms for a few picoseconds using semilocal functionals or 1,000 atoms for a few picoseconds using hybrid functionals. Using exascale resources, the sizes and times targeted are two orders of magnitude larger. Such a capability has applications in a wide variety of chemical sciences, including reactive interfaces where large length- and/or long time-scales are needed and traditional force fields fail. This is particularly important in dynamic catalysis, where bond breaking and formation must be understood in detail. We developed, tested, and employed the SPARC-X framework to understand the photocatalytic properties of TiO 2 nanoparticles, revealing finite size effects that cannot be captured with standard model systems or functionals. This integrated development and application strategy ensures that SPARC-X remains a robust, efficient, and scalable software package for quantum simulations on current petascale and emerging exascale computing resources.
97 MATHEMATICS AND COMPUTING↗
Equivalence of quantum barren plateaus to cost concentration and narrow gorges
Optimizing parameterized quantum circuits (PQCs) is the leading approach to make use of near-term quantum computers. However, very little is known about the cost function landscape for PQCs, which hinders progress towards quantum-aware optimizers. In this work, we investigate the connection between three different landscape features that have been observed for PQCs: (1) exponentially vanishing gradients (called barren plateaus (BPs)), (2) exponential cost concentration about the mean, and (3) the exponential narrowness of minima (called narrow gorges). Here we analytically prove that these three phenomena occur together, i.e., when one occurs then so do the other two. A key implication of this result is that one can numerically diagnose BPs via cost differences rather than via the computationally more expensive gradients. More broadly, our work shows that quantum mechanics rules out certain cost landscapes (which otherwise would be mathematically possible), and hence our results could be interesting from a quantum foundations perspective.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Logical gates embedding in artificial spin ice
The realization and study of arrays of interacting magnetic nanoislands, such as artificial spin ices, have reached mature levels of control that allow design and demonstration of exotic, collective behaviors not seen in natural materials. Advances in the direct manipulation of their local, binary moments also suggest a use as nanopatterned, interacting memory media, for computation within a magnetic memory. Recent experimental work has demonstrated the possibility of building logic gates from clusters of interacting magnetic domains, and yet the possibility of large scale integration of such gates can prove problematic even at the theoretical level. Here we introduce theoretically complete sets of logical gates, in principle realizable in an experiment, and we study the feasibility of their integration into tree-like circuits. By evaluating the fidelity control parameter between their collective behavior and their expected logic functionality we determine conditions for integration. Also, we test our numerical results against the presence of disorder in the couplings, showing that the design gate structure is robust to small coupling perturbations, and thus possibly to small imperfections in the fabrication of the islands.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Hardware-Conscious Optimization of the Quantum Toffoli Gate
While quantum computing holds great potential in combinatorial optimization, electronic structure calculation, and number theory, the current era of quantum computing is limited by noisy hardware. Many quantum compilation approaches can mitigate the effects of imperfect hardware by optimizing quantum circuits for objectives such as critical path length. Few approaches consider quantum circuits in terms of the set of vendor-calibrated operations (i.e., native gates) available on target hardware. This manuscript expands the analytical and numerical approaches for optimizing quantum circuits at this abstraction level. We present a procedure for combining the strengths of analytical native gate-level optimization with numerical optimization. Although we focus on optimizing Toffoli gates on the IBMQ native gate set, the methods presented are generalizable to any gate and superconducting qubit architecture. Our optimized Toffoli gate implementation demonstrates an 18% reduction in infidelity compared with the canonical implementation as benchmarked on IBM Jakarta with quantum process tomography. Assuming the inclusion of multi-qubit cross-resonance (MCR) gates in the IBMQ native gate set, we produce Toffoli implementations with only six multi-qubit gates, a 25% reduction from the canonical eight multi-qubit implementations for linearly connected qubits.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
CFD Analysis of RLUOB Zone 1 HEPA Filter Plenum and Testing Manifolds
The purpose of this computational fluid dynamics (CFD) analysis is to ensure that Camfil Farr’s upstream and downstream injection and sampling manifolds can meet or exceed the requirements outlined in the ASME AG-1 1997 a(2000) Code on Nuclear Air and Gas Treatment for the testing of HEPA and adsorbent filters. This paper will present a numerical simulation of airflow in the Radiological Laboratory Utility Office Building (RLUOB) zone 1 HEPA filter plenum and testing manifolds using the commercial CFD software ANSYS FLUENT 2020R1. The CFD analysis focuses on the investigation of the air flow distribution and air-aerosol mixing uniformity. The evaluation was done for all steps of the modeling process: grid generation, physics setup, simulation, and post-processing. The mass flow rate in each section of the zone 1 injection and sampling manifolds is also reported.
42 ENGINEERING↗
Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics
Sampling from known probability distributions is a ubiquitous task in computational science, underlying calculations in domains from linguistics to biology and physics. Generative machine-learning (ML) models have emerged as a promising tool in this space, building on the success of this approach in applications such as image, text, and audio generation. Often, however, generative tasks in scientific domains have unique structures and features—such as complex symmetries and the requirement of exactness guarantees—that present both challenges and opportunities for ML. This Perspective outlines the advances in ML-based sampling motivated by lattice quantum field theory, in particular for the theory of quantum chromodynamics. Enabling calculations of the structure and interactions of matter from our most fundamental understanding of particle physics, lattice quantum chromodynamics is one of the main consumers of open-science supercomputing worldwide. Here, the design of ML algorithms for this application faces profound challenges, including the necessity of scaling custom ML architectures to the largest supercomputers, but also promises immense benefits, and is spurring a wave of development in ML-based sampling more broadly. In lattice field theory, if this approach can realize its early promise it will be a transformative step towards first-principles physics calculations in particle, nuclear and condensed matter physics that are intractable with traditional approaches.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗