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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Exponential concentration in quantum kernel methods

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Quantum error thresholds for gauge-redundant digitizations of lattice field theories

In the quantum simulation of lattice gauge theories, gauge symmetry can be either fixed or encoded as a redundancy of the Hilbert space. While gauge-fixing reduces the number of qubits, keeping the gauge redundancy can provide code space to mitigate and correct quantum errors by checking and restoring Gauss’s law. In this work, we consider the correctable errors for generic finite gauge groups and design the quantum circuits to detect and correct them. We calculate the error thresholds below which the gauge-redundant digitization with Gauss’s law error correction has better fidelity than the gauge-fixed digitization involving only gauge-invariant states. Our results provide guidance for fault-tolerant quantum simulations of lattice gauge theories. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Nonlinear multi-magnon scattering in artificial spin ice

Abstract Magnons, the quantum-mechanical fundamental excitations of magnetic solids, are bosons whose number does not need to be conserved in scattering processes. Microwave-induced parametric magnon processes, often called Suhl instabilities, have been believed to occur in magnetic thin films only, where quasi-continuous magnon bands exist. Here, we reveal the existence of such nonlinear magnon-magnon scattering processes and their coherence in ensembles of magnetic nanostructures known as artificial spin ice. We find that these systems exhibit effective scattering processes akin to those observed in continuous magnetic thin films. We utilize a combined microwave and microfocused Brillouin light scattering measurement approach to investigate the evolution of their modes. Scattering events occur between resonance frequencies that are determined by each nanomagnet’s mode volume and profile. Comparison with numerical simulations reveals that frequency doubling is enabled by exciting a subset of nanomagnets that, in turn, act as nanosized antennas, an effect that is akin to scattering in continuous films. Moreover, our results suggest that tunable directional scattering is possible in these structures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Emergence of the polydeterminant in QCD

A generalization of the determinant appears in particle physics in effective Lagrangian interaction terms that model the chiral anomaly in quantum chromodynamics (Giacosa et al. in Phys Rev D 97(9):091901, 2018, Phys Rev D 109(7):L071502, 2024), in particular in connection to mesons. This polydeterminant function, known in the mathematical literature as a mixed discriminant, associates N distinct N x N complex matrices into a complex number and reduces to the usual determinant when all matrices are taken as equal. Here, we explore the main properties of the polydeterminant applied to (quantum) fields by using a formalism and a language close to high-energy physics approaches. We discuss its use as a tool to write down novel chiral anomalous Lagrangian terms and present an explicit illustrative model for mesons. Finally, the extension of the polydeterminant as a function of tensors is shown.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Quantum computing and quantum information storage

Quantum storage, transmission, and processing is the future of information technology. Here, the promise of quantum hardware stems from the inherent complexity of an entangled quantum system—the size of the wave-function scales exponentially with the number of particles, whether represented in real space or in a parameter space. In contrast, a classical N-body system can be completely represented by only 6N variables (positions and momenta of all particles). This complexity of quantum systems creates a yet-unsolved challenge of modeling quantum systems by means of classical computing—the curse of dimensionality. Indeed, although we can easily write the Schrödinger equation for any system of interacting nuclei and electrons, we can only solve it exactly on classical computers for very small systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Learning energy-based representations of quantum many-body states

Efficient representation of quantum many-body states on classical computers is a problem of practical importance. An ideal representation of a quantum state combines a succinct characterization informed by the structure and symmetries of the system along with the ability to predict the physical observables of interest. Several machine-learning approaches have been recently used to construct such classical representations, which enable predictions of observables and account for physical symmetries. However, the structure of a quantum state typically gets lost unless a specialized is employed based on prior knowledge of the system. Moreover, most such approaches give no information about what states are easier to learn in comparison with others. Here, we propose a generative energy-based representation of quantum many-body states derived from Gibbs distributions used for modeling the thermal states of classical spin systems. Based on the prior information on a family of quantum states, the energy function can be specified by a small number of parameters using an explicit low-degree polynomial or a generic parametric family such as neural nets and can naturally include the known symmetries of the system. Our results show that such a representation can be efficiently learned from data using exact algorithms in a form that enables the prediction of expectation values of physical observables. Importantly, the structure of the learned energy function provides a natural explanation for the difficulty of learning an energy-based representation of a given class of quantum states when measured in a certain basis. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1997

Novel Highly Parallel and Systolic Architectures Using Quantum Dot-Based Hardware

VLSI technology has made possible the integration of massive number of components (processors, memory, etc.) into a single chip. In VLSI design, memory and processing power are relatively cheap and the main emphasis of the design is on reducing the overall interconnection complexity since data routing costs dominate the power, time, and area required to implement a computation. Communication is costly because wires occupy the most space on a circuit and it can also degrade clock time. In fact, much of the complexity (and hence the cost) of VLSI design results from minimization of data routing. The main difficulty in VLSI routing is due to the fact that crossing of the lines carrying data, instruction, control, etc. is not possible in a plane. Thus, in order to meet this constraint, the VLSI design aims at keeping the architecture highly regular with local and short interconnection. As a result, while the high level of integration has opened the way for massively parallel computation, practical and full exploitation of such a capability in many applications of interest has been hindered by the constraints on interconnection pattern. More precisely. the use of only localized communication significantly simplifies the design of interconnection architecture but at the expense of somewhat restricted class of applications. For example, there are currently commercially available products integrating; hundreds of simple processor elements within a single chip. However, the lack of adequate interconnection pattern among these processing elements make them inefficient for exploiting a large degree of parallelism in many applications.

Fijany, Amir↗
DOE OSTI2023

Error statistics and scalability of quantum error mitigation formulas

Quantum computing promises advantages over classical computing in many problems. Nevertheless, noise in quantum devices prevents most quantum algorithms from achieving the quantum advantage. Quantum error mitigation provides a variety of protocols to handle such noise using minimal qubit resources. While some of those protocols have been implemented in experiments for a few qubits, it remains unclear whether error mitigation will be effective in quantum circuits with tens to hundreds of qubits. In this paper, we apply statistics principles to quantum error mitigation and analyse the scaling behaviour of its intrinsic error. We find that the error increases linearly O(ϵN) with the gate number N before mitigation and sublinearly O(ϵ'N γ ) after mitigation, where γ ≈ 0.5, ϵ is the error rate of a quantum gate, and ϵ' is a protocol-dependent factor. The $\sqrt{N}$ scaling is a consequence of the law of large numbers, and it indicates that error mitigation can suppress the error by a larger factor in larger circuits. We propose the importance Clifford sampling as a key technique for error mitigation in large circuits to obtain this result.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Designing Energy-Efficient Quantum Computers Through Prediction and Reduction of Cooling Requirements for Cryogenic Electronics

Quantum computing has been identified as a “wild card” by the International Energy Agency in predicting future global data center energy usage. This is primarily because both uncertainty in the extent to which quantum computing will be adopted, and uncertainty in the power consumption of individual quantum data centers. Unlike the classical counterparts, quantum computers need to be maintained at near absolute zero, requiring energy-intensive cryogenic cooling systems. Therefore, as quantum computers scale up from existing 50 qubit technology demonstrations to the 10,000 to 100,000 qubit systems that will be able to solve complex problems, the energy consumption of both the electronics and the required cooling systems will also increase. To predict this scaling, this work analyzes the energy requirements for both computation and cooling of quantum hardware. We show that the energy requirements for cooling of quantum computers is determined by several computing system parameters, including the number and type of physical qubits, the operating temperature, the packaging efficiency of the system, and the split between circuits operating at cryogenic temperatures and those operating at room temperature. The energy requirements can then be found based on thermal system parameters such as cooling efficiency and cryostat heat transfer. Analysis of these parameters shows that the energy required for cooling is significantly larger than that required for computation, a reversal from energy usage patterns seen in conventional computing. The results and discussions provide a road-map for creating energy efficient quantum computers through the selection of computer architectures and cryogenic system configurations that minimize cooling requirements.

energy efficiency↗
DOE OSTI2023

Numerical evidence against advantage with quantum fidelity kernels on classical data

Quantum machine learning techniques are commonly considered one of the most promising candidates for demonstrating practical quantum advantage. In particular, quantum kernel methods have been demonstrated to be able to learn certain classically intractable functions efficiently if the kernel is well aligned with the target function. In the more general case, quantum kernels are known to suffer from exponential “flattening” of the spectrum as the number of qubits grows, preventing generalization and necessitating the control of the inductive bias by hyperparameters. We show that the general-purpose hyperparameter-tuning techniques proposed to improve the generalization of quantum kernels lead to the kernel becoming well approximated by a classical kernel, removing the possibility of quantum advantage. We provide extensive numerical evidence for this phenomenon utilizing multiple previously studied quantum feature maps and both synthetic and real data. Our results show that unless novel techniques are developed to control the inductive bias of quantum kernels, they are unlikely to provide a quantum advantage on classical data that lacks special structure.

Quantum Information, Science & Technology↗
DOE OSTI2022

Quantum time dynamics employing the Yang-Baxter equation for circuit compression

Quantum time dynamics (QTD) is considered a promising problem for quantum supremacy on near-term quantum computers. However, QTD quantum circuits grow with increasing time simulations. This study focuses on simulating the time dynamics of one-dimensional (1D) integrable spin chains with nearest-neighbor interactions. We have proved the existence of a reflection symmetry in the quantum circuit employed for simulating the time evolution of certain classes of 1D Heisenberg model Hamiltonians by virtue of the quantum Yang-Baxter equation, and how this symmetry can be exploited to compress and produce a shallow quantum circuit. With this compression scheme, the depth of the quantum circuit becomes independent of step size and only depends on the number of spins. We show that the depth of the compressed circuit is rigorously a linear function of the system size for the studied Heisenberg model Hamiltonians in the present work. As a consequence, the number of CNOT gates in the compressed circuit only scales quadratically with the system size, which allows for the simulations of time dynamics of very large 1D spin chains. We derive the compressed circuit representations for different special cases of the Heisenberg Hamiltonian. We compare and demonstrate the effectiveness of this approach by performing simulations on quantum computers.

1-dimensional spin chains↗
DOE OSTI2020

Efficient Scalable Tomography of Many-Qubit Quantum Processors

Quantum computing has the potential to realize powerful and revolutionary applications. A quantum computer can, in theory, solve certain problems exponentially faster than its classical counterparts. The current state of the art devices, however, are too small and noisy to practically realize this goal. An important tool for the advancement of quantum hardware, called model-based characterization, seeks to learn what types of noise are exhibited in a quantum processor. This technique, however, is notoriously difficult to scale up to even modest numbers of qubit, and has been limited to just 2 qubits until now. In this report, we present a novel method for performing model-based characterization, or tomography, on a many-qubit quantum processor. We consider up to 10 qubits, but the technique is expected to scale to even larger systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fast decay of classification error in variational quantum circuits

Variational quantum circuits (VQCs) have shown great potential in near-term applications. However, the discriminative power of a VQC, in connection to its circuit architecture and depth, is not understood. To unleash the genuine discriminative power of a VQC, we propose a VQC system with the optimal classical post-processing—maximum-likelihood estimation on measuring all VQC output qubits. Via extensive numerical simulations, we find that the error of VQC quantum data classification typically decays exponentially with the circuit depth, when the VQC architecture is extensive—the number of gates does not shrink with the circuit depth. This fast error suppression ends at the saturation towards the ultimate Helstrom limit of quantum state discrimination. On the other hand, non-extensive VQCs such as quantum convolutional neural networks are sub-optimal and fail to achieve the Helstrom limit, demonstrating a trade-off between ansatz complexity and classification performance in general. To achieve the best performance for a given VQC, the optimal classical post-processing is crucial even for a binary classification problem. To simplify VQCs for near-term implementations, we find that utilizing the symmetry of the input properly can improve the performance, while oversimplification can lead to degradation.

Zhang, Bingzhi↗
NASA NTRS1998

Nested Quantum Search and NP-Complete Problem

A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order square-root of d, where d is the dimension of the search space, whereas any classical algorithm scales as O(d).

NP-complete problems quantum search algorithm tree↗
DOE OSTI2022

Coherent Many-Body Oscillations Induced by a Superposition of Broken Symmetry States in the Wake of a Quantum Phase Transition

It is now widely accepted that quenches through the critical region of quantum phase transitions result in post-transition states populated with topological defects—analogs of the classical topological defects. However, consequences of the very nonclassical fact that the state after a quench is a superposition of distinct, broken-symmetry vacua with different numbers and locations of defects have remained largely unexplored. Here, we identify coherent quantum oscillations induced by such superpositions in observables complementary to the one involved in symmetry breaking. These oscillations satisfy Kibble-Zurek dynamical scaling laws with the quench rate, with an instantaneous oscillation frequency set primarily by the gap of the system. In addition to the obvious fundamental significance of a superposition of different broken symmetry states, quantum coherent oscillations can be used to verify unitarity and test for imperfections of the experimental implementations of quantum simulators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Neutrinoless double beta decay via light neutralinos in R-parity violating supersymmetry

We perform a study of neutrinoless double beta (0νββ) decay mediated by the lightest neutralino of arbitrary mass in the minimal supersymmetric Standard Model (MSSM) under the presence of R-parity violating trilinear interactions. In this scenario, the exchange of the lightest neutralino can result in 0νββ decay of either long-range or short-range behaviour, depending on the neutralino mass. Using nuclear matrix elements calculated in the interacting boson model, we use an interpolation between the long- and short-range behaviours with an approximate formula. The non-observation of 0νββ decay is then used to place constraints on the supersymmetry parameter space, compatible with constraints from collider experiments. We compare these constraints to bounds from pion decays, CKM unitarity and big bang nucleosynthesis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Neutrino masses and magnetic moments of electron and muon in the Zee Model

We explore parameter space in the Zee Model to resolve the long-standing tension of the electron and muon anomalous magnetic moment (AMM). The model comprises a second Higgs doublet and a charged singlet at electroweak scale and generates Majorana neutrino masses at one-loop level; the neutral partner of the SU(2) L doublet contributes to the AMM of electron and muon via one loop and two-loop corrections. We propose two minimal flavor structures that can explain these anomalies while fitting the neutrino oscillation data. We find that the neutral Higgs resides in the mass range of roughly 10–300 GeV or 1–30 GeV, depending on the flavor structures. The model is consistent with constraints from colliders, electroweak precision data, and lepton flavor violation. To be comprehensive, we examine the constraints from the electric dipole moment (EDM) and find a region of parameter space that gives a sizable contribution to muon EDM while simultaneously giving corrections to muon AMM. In addition to the light scalar, the two charged scalars with masses as low as 100 GeV can induce nonstandard neutrino interactions ε ee as large as 8%, potentially hinting at new physics. We also investigate the projected capability of future lepton colliders to probe the currently allowed parameter space consistent with both electron and muon AMMs via direct searches in the ℓ + ℓ – → ℓ + ℓ – (H→ℓ + ℓ – )channel.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

High-resolution absorption spectroscopy of room-temperature and jet-cooled ammonia between 59,000 and 93,000 cm -1

Here, we present new high-resolution photoabsorption spectra of ammonia spanning the region between 59,000 cm -1 and 93,000 cm -1 that were recorded by using the Fourier Transform Spectrometer at the Synchrotron SOLEIL. This region extends from just above the Franck-Condon envelope for the $\tilde{A}$ 1 $A$ 2 " ← $\tilde{X}$ 1 $A$ 1 ' transition to well above the NH 3 + $\tilde{X}$ + 2 $A$ 2 " ionization threshold. The spectra were recorded at a measured resolution of 0.23 cm -1 in both a room-temperature cell (293 K) and in a slit-jet supersonic expansion (~70 K). The absolute photoabsorption cross section with an uncertainty of ±5% is also reported for the room-temperature spectrum. The present resolution is a factor of 10 – 100 times higher than in other recently reported broad band spectra of ammonia, and many of the observed bands show partially resolved rotational structure. We have attempted to assign this structure for a number of these bands. The oscillator strengths extracted from the data are in good agreement with previous measurements but, in the case of structured bands, the present higher resolution measurements return higher peak absorption cross sections, that increase further when the sample is cooled. The present higher resolution spectra suggest that a number of previous vibronic band assignments that were based on quantum defect considerations may require some revision. Finally, we discuss the substantial differences between the photoabsorption and photoionization data just above the first ionization threshold.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗