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At least 307 records · Page 17

Efficient quantum circuits based on the quantum natural gradient

Efficient preparation of arbitrary entangled quantum states is crucial for quantum computation. This is particularly important for noisy intermediate-scale quantum simulators relying on variational hybrid quantum-classical algorithms. To that end, we propose symmetry-conserving modified quantum approximate optimization algorithm (SCom-QAOA) circuits. The depths of these circuits depend not only on the desired fidelity to the target state but also on the amount of entanglement the state contains. The parameters of the SCom-QAOA circuits are optimized using the quantum natural gradient method based on the Fubini-Study metric. The SCom-QAOA circuit transforms an unentangled state into a ground state of a gapped one-dimensional Hamiltonian with a circuit depth that depends not on the system size but rather on the finite correlation length. In contrast, the circuit depth grows proportionally to the system size for preparing low-lying states of critical one-dimensional systems. Even in the latter case, SCom-QAOA circuits with depth less than the system size were sufficient to generate states with fidelity in excess of 99%, which is relevant for near-term applications. The proposed scheme enlarges the set of the initial states accessible for variational quantum algorithms and widens the scope of investigation of nonequilibrium phenomena in quantum simulators. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Porting Classical Approaches for Quantum Simulations to Quantum Computers

Simulating quantum many-body systems is one of the most promising problems in which we might anticipate that quantum computers should show quantum advantage. Unfortunately, there is still a gap between this promise and actual practice. New quantum algorithms need to be developed and the current quantum algorithms have various difficulties - e.g efficient state preparation - which must be overcome and improved upon. In many cases, classical approaches need to be ported over to quantum devices. In this project we have developed a suite of new quantum algorithms which makes progress in this regard. We developed a new optimization scheme for variational quantum eigensolvers, UBOS, which mitigates problems with local minimas and barren plateaus while improving convergence to the ground state by an order of magnitude. We developed a new way to utilize qubitization to find ground states of nearly frustration-free Hamiltonians faster than all previous methods. We developed a series of state preparation techniques which helps initialize parameterized quantum circuits into reasonable starting points on which quantum algorithms are then applied. In addition to the development of novel algorithms, it is critical to have classical simulation techniques for approximately simulating quantum circuits which can be used to benchmark and understand quantum algorithms. Toward that end, we developed a novel POVM formalism to simulate quantum circuits as well as exemplify the massive parallelization of tensor network methodologies. Finally, we developed physical understanding of entanglement phase transitions such as many-body localization and random tensor networks.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Finding New Math Identities by Computer

Recently a number of interesting new mathematical identities have been discovered by means of numerical searches on high performance computers, using some newly discovered algorithms. These include the following: pi = ((sup oo)(sub k=0))(Sigma) (1 / 16) (sup k) ((4 / 8k+1) - (2 / 8k+4) - (1 / 8k+5) - (1 / 8k+6)) and ((17 pi(exp 4)) / 360) = ((sup oo)(sub k=1))(Sigma) (1 + (1/2) + (1/3) + ... + (1/k))(exp 2) k(exp -2), zeta(3, 1, 3, 1, ..., 3, 1) = (2 pi(exp 4m) / (4m+2)! where m = number of (3,1) pairs. and where zeta(n1,n2,...,nr) = (sub k1 (is greater than) k2 (is greater than) ... (is greater than) kr)(Sigma) (1 / (k1 (sup n1) k2 (sup n2) ... kr (sup nr). The first identity is remarkable in that it permits one to compute the n-th binary or hexadecimal digit of pu directly, without computing any of the previous digits, and without using multiple precision arithmetic. Recently the ten billionth hexadecimal digit of pi was computed using this formula. The third identity has connections to quantum field theory. (The first and second of these been formally established; the third is affirmed by numerical evidence only.) The background and results of this work will be described, including an overview of the algorithms and computer techniques used in these studies.

Bailey, David H.↗

Physics-Reinforced Machine Learning Algorithms for Multiscale Closure Model Discovery

The central objective of this project was to address the challenge of modeling and simulating complex multiscale turbulence phenomena by leveraging physics-guided machine learning (PGML) and hybrid modeling approaches. By integrating physics-based methods with data-driven models, the research focused on achieving robust and scalable solutions for geophysical turbulence, enhancing numerical weather prediction and climate research tools. The project resulted in significant advancements in computational modeling paradigms, predictive tools for reduced-order modeling, and innovative algorithms for fluid dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

How Well Can Quantum Embedding Method Predict the Reaction Profiles for Hydrogenation of Small Li Clusters?

Quantum computing leverages the principles of quantum mechanics in novel ways to tackle complex chemistry problems that cannot be accurately addressed using traditional quantum chemistry methods. However, the high computational cost and available number of physical qubits with high fidelity limit its application to small chemical systems. This work employed a quantum-classical framework which features a quantum active space-embedding approach to perform simulations of chemical reactions that require up to 14 qubits. This framework was applied to prototypical example metal hydrogenation reactions: the coupling between hydrogen and Li 2 , Li 3 , and Li 4 clusters. Particular attention was paid to the computation of barriers and reaction energies. The predicted reaction profiles compare well with advanced classical quantum chemistry methods, demonstrating the potential of the quantum embedding algorithm to map out reaction profiles of realistic gas-phase chemical reactions to ascertain qualitative energetic trends. Additionally, the predicted potential energy curves provide a benchmark to compare against both current and future quantum embedding approaches.

36 MATERIALS SCIENCE↗

A Perspective on Quantum Computing Applications in Quantum Chemistry Using 25-100 Logical Qubits

The intersection of quantum computing and quantum chemistry represents a promising frontier for achieving quantum utility in domains of both scientific and societal relevance. Owing to the exponential growth of classical resource requirements for simulating quantum systems, quantum chemistry has long been recognized as a natural candidate for quantum computation. This perspective focuses on identifying scientifically meaningful use cases where early fault-tolerant quantum computers, which are considered to be equipped with approximately 25-100 logical qubits, could deliver tangible impact. While recent advances in classical computing have pushed the boundaries of tractable simulations to unprecedented scales, this logical-qubit regime represents the first window where quantum devices can pursue qualitatively distinct strategies, such as polynomial-scaling phase estimation, direct simulation of quantum dynamics, and active-space embedding, that remain challenging for classical solvers, such as multireference charge-transfer and conical-intersection states central to photochemistry and materials design. We highlight near-term opportunities in algorithm and software design, discuss representative chemical problems suited for quantum acceleration, and propose strategic roadmaps and collaborative pathways for advancing practical quantum utility in quantum chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Efficient use of quantum computers for collider physics

Most observables at particle colliders involve physics at a wide variety of distance scales. Due to asymptotic freedom of the strong interaction, the physics at short distances can be calculated reliably using perturbative techniques, while long distance physics is non-perturbative in nature. Factorization theorems separate the contributions from different scales, allowing to identify the pieces that can be determined perturbatively from those that require non-perturbative information, and if the non-perturbative pieces can be reliably determined, one can use experimental measurements to extract the short distance effects, sensitive to possible new physics. Without the ability to compute the non-perturbative ingredients from first principles one typically identifies observables for which the non-perturbative information is universal in the sense that it can be extracted from some experimental observables and then used to predict other observables. In this paper we argue that the future ability to use quantum computers to calculate non-perturbative matrix elements from first principles will allow to make predictions for observables with non-universal non-perturbative long-distance physics.

Algorithms and Theoretical Developments↗

Assessment of Quantum ML Applicability for Climate Actions: Comparison of the Variational Quantum Classifier and the Quantum Support Vector Classifier with Classical ML Models

Climate change refers to significant and long-term alterations in the Earth’s climate patterns, typically resulting from human activities that increase greenhouse gas emissions. Addressing climate change is not merely an option but a necessity, demanding creative solutions and efforts from individuals, researchers, communities, and governments. Despite the capabilities of machine learning (ML) with data-driven solutions promising to combat climate change-related problems, they face challenges stemming from traditional computational methods and prolonged training times, impeding their practical utility. Recent strides in quantum computing have permeated diverse domains, spanning from manufacturing engineering and pharmaceutical discovery to the latest frontier of detecting climate anomalies. With the potential to substantially reduce time and computational complexity, quantum computing shows promise in addressing climate change impacts. Its distinctive features will enable the concurrent exploration of expansive solution spaces, making it well-suited for analyzing extensive climate datasets, simulating intricate climate models, optimizing resource allocation, and discerning patterns in climate data for mitigation and adaptation endeavors. This study explores the potential of using Quantum machine learning (QML) techniques on climate and weather data obtained from NASA Giovannis. We used two QML algorithms, the Quantum Support Vector Classifier (QSVC) and the Variational Quantum Classifier (VQC) models, using the IBM Qiskit ML 0.7.2 ecosystem. We used an actual 127-Qubit IBM Quantum Computer (IBM 127-qubit Eagle) in this study. The methodology and results sections describe the experiences gained from applying and evaluating quantum ML results on climate and weather data obtained from NASA satellites as a novel practical application of quantum computing.

Earth Observational Data↗

Unorthodox parallelization for Bayesian quantum state estimation

Quantum state tomography (QST) allows for the reconstruction of quantum states through measurements and some inference technique under the assumption of repeated state preparations. Bayesian inference provides a promising platform to achieve both efficient QST and accurate uncertainty quantification, yet is generally plagued by the computational limitations associated with long Markov chains. In this work, we present a novel Bayesian QST approach that leverages modern distributed parallel computer architectures to efficiently sample a D-dimensional Hilbert space. Using a parallelized preconditioned Crank–Nicholson Metropolis–Hastings algorithm, we demonstrate our approach on simulated data and experimental results from IBM Quantum systems up to four qubits, showing significant speedups through parallelization. Although highly unorthodox in pooling independent Markov chains, our method proves remarkably practical, with validation ex post facto via diagnostics like the intrachain autocorrelation time. We conclude by discussing scalability to higher-dimensional systems, offering a path toward efficient and accurate Bayesian characterization of large quantum systems.

Bayesian inference↗

The black hole interior from non-isometric codes and complexity

Quantum error correction has given us a natural language for the emergence of spacetime, but the black hole interior poses a challenge for this framework: at late times the apparent number of interior degrees of freedom in effective field theory can vastly exceed the true number of fundamental degrees of freedom, so there can be no isometric (i.e. inner-product preserving) encoding of the former into the latter. In this paper we explain how quantum error correction nonetheless can be used to explain the emergence of the black hole interior, via the idea of “non-isometric codes protected by computational complexity”. We show that many previous ideas, such as the existence of a large number of “null states”, a breakdown of effective field theory for operations of exponential complexity, the quantum extremal surface calculation of the Page curve, post-selection, “state-dependent/state-specific” operator reconstruction, and the “simple entropy” approach to complexity coarse-graining, all fit naturally into this framework, and we illustrate all of these phenomena simultaneously in a soluble model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Performance evaluations of signed and unsigned noisy approximate quantum Fourier arithmetic

The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route toward a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor’s algorithm, weighted-sum optimization problems in data processing and machine learning, and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM’s superconducting-qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands’ superposed integer states. We analyze performance and identify the most effective approximation depths for unsigned quantum addition and quantum multiplication within the given context. We then perform a similar analysis of signed addition and compare to the unsigned results. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges—relevant to signed, unsigned, modular and non-modular versions—that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. Here, we analyze the performance trends in our results and speculate on possible future developments within this computational paradigm.

Computational models↗

Properties of the contraction map for holographic entanglement entropy inequalities

We present a deterministic way of finding contraction maps for candidate holographic entanglement entropy inequalities modulo choices due to actual degeneracy. We characterize its complexity and give an argument for the completeness of the contraction map proof method as a necessary and sufficient condition for the validity of an entropy inequality for holographic entanglement.

97 MATHEMATICS AND COMPUTING↗

Report for the ASCR Workshop on Basic Research Needs in Quantum Computing and Networking - 2023

Employing quantum mechanical resources in computing and networking opens the door to new computation and communication models and potential disruptive advantages over classical counterparts. However, quantifying and realizing such advantages face extensive scientific and engineering challenges. Investments by the Department of Energy (DOE) have driven progress toward addressing such challenges. Quantum algorithms have been recently developed, in some cases offering asymptotic exponential advantages in speed or accuracy, for fundamental scientific problems such as simulating physical systems, solving systems of linear equations, or solving differential equations. Empirical demonstrations on nascent quantum hardware suggest better performance than classical analogs on specialized computational tasks favorable to the quantum computing systems. However, demonstration of an end-to-end, substantial and rigorously quantifiable quantum performance advantage over classical analogs remains a grand challenge, especially for problems of practical value. The definition of requirements for quantum technologies to exhibit scalable, rigorous, and transformative performance advantages for practical applications also remains an outstanding open question, namely, what will be required to ultimately demonstrate practical quantum advantage?

97 MATHEMATICS AND COMPUTING↗

Accelerating resonant spectroscopy simulations using multishifted biconjugate gradient

Resonant spectroscopies, which involve intermediate states with finite lifetimes, provide important insights into collective excitations in quantum materials that are otherwise inaccessible. However, theoretical understanding in this area is often limited by the numerical challenges of solving Kramers-Heisenberg-type response functions for large-scale systems. To address this, we introduce a multishifted biconjugate gradient algorithm that exploits the shared structure of Krylov subspaces across spectra with varying incident energies, effectively reducing the computational complexity to that of linear spectroscopies. Both mathematical proofs and numerical benchmarks confirm that this algorithm substantially accelerates spectral simulations, achieving constant complexity independent of the number of incident energies, while ensuring accuracy and stability. This development provides a scalable, versatile framework for simulating advanced spectroscopies in quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Impact of dynamics, entanglement and Markovian noise on the fidelity of few-qubit digital quantum simulation

Quantum algorithms have been proposed to accelerate the simulation of the chaotic dynamical systems that are ubiquitous in the physics of plasmas. Quantum computers without error correction might even use noise to their advantage to calculate the Lyapunov exponent by measuring the Loschmidt echo fidelity decay rate. For the first time, digital Hamiltonian simulations of the quantum sawtooth map, performed on the IBM-Q quantum hardware platform, show that the fidelity decay rate of a digital quantum simulation increases during the transition from dynamical localization to chaotic diffusion in the map. The observed error per CNOT gate increases by $1.5{\times }$ as the dynamics varies from localized to diffusive, while only changing the phases of virtual RZ gates and keeping the overall gate count constant. A gate-based Lindblad noise model that captures the effective change in relaxation and dephasing errors during gate operation qualitatively explains the effect of dynamics on fidelity as being due to the localization and entanglement of the states created. Specifically, highly delocalized states that are entangled with random phases show an increased sensitivity to dephasing and, on average, a similar sensitivity to relaxation as localized states. In contrast, delocalized unentangled states show an increased sensitivity to dephasing but a lower sensitivity to relaxation. This gate-based Lindblad model is shown to be a useful benchmarking tool by estimating the effective Lindblad coherence times during CNOT gates and finding a consistent $2\unicode{x2013}3{\times }$ shorter $T_2$ time than reported for idle qubits. Thus, the interplay of the dynamics of a simulation with the noise processes that are active can strongly influence the overall fidelity decay rate.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Scalability of a Low-Cost Multi-Teraflop Linux Cluster for High-End Classical Atomistic and Quantum Mechanical Simulations

Scalability of a low-cost, Intel Xeon-based, multi-Teraflop Linux cluster is tested for two high-end scientific applications: Classical atomistic simulation based on the molecular dynamics method and quantum mechanical calculation based on the density functional theory. These scalable parallel applications use space-time multiresolution algorithms and feature computational-space decomposition, wavelet-based adaptive load balancing, and spacefilling-curve-based data compression for scalable I/O. Comparative performance tests are performed on a 1,024-processor Linux cluster and a conventional higher-end parallel supercomputer, 1,184-processor IBM SP4. The results show that the performance of the Linux cluster is comparable to that of the SP4. We also study various effects, such as the sharing of memory and L2 cache among processors, on the performance.

Kikuchi, Hideaki↗

Machine Learning on Heterogeneous, Edge, and Quantum Hardware for Particle Physics (ML-HEQUPP)

The next generation of particle physics experiments will face a new era of challenges in data acquisition, due to unprecedented data rates and volumes along with extreme environments and operational constraints. Harnessing this data for scientific discovery demands real-time inference and decision-making, intelligent data reduction, and efficient processing architectures beyond current capabilities. Crucial to the success of this experimental paradigm are several emerging technologies, such as artificial intelligence and machine learning (AI/ML) and silicon microelectronics, and the advent of quantum algorithms and processing. Their intersection includes areas of research such as low-power and low-latency devices for edge computing, heterogeneous accelerator systems, reconfigurable hardware, novel codesign and synthesis strategies, readout for cryogenic or high-radiation environments, and analog computing. This white paper presents a community-driven vision to identify and prioritize research and development opportunities in hardware-based ML systems and corresponding physics applications, contributing towards a successful transition to the new data frontier of fundamental science.

Gonski, Julia [SLAC]↗

Dynamic Cooling on Contemporary Quantum Computers

We study the problem of dynamic cooling whereby a target qubit is cooled at the expense of heating up N − 1 further identical qubits by means of a global unitary operation. A standard back-of-the-envelope high-temperature estimate establishes that the target qubit temperature can be dynamically cooled by at most a factor of 1 / N . Here we provide the exact expression for the minimum temperature to which the target qubit can be cooled and reveal that there is a crossover from the high initial temperature regime, where the scaling is 1 / N , to a low initial temperature regime, where a much faster scaling of 1 / N occurs. This slow, 1 / N scaling, which was relevant for early high-temperature NMR quantum computers, is the reason dynamic cooling was dismissed as ineffectual around 20 years ago; the fact that current low-temperature quantum computers fall in the fast, 1 / N scaling regime, reinstates the appeal of dynamic cooling today. We further show that the associated work cost of cooling is exponentially more advantageous in the low-temperature regime. We discuss the implementation of dynamic cooling in terms of quantum circuits and examine the effects of hardware noise. We successfully demonstrate dynamic cooling in a three-qubit system on a real quantum processor. Since the circuit size grows quickly with N , scaling dynamic cooling to larger systems on noisy devices poses a challenge. We therefore propose a suboptimal cooling algorithm, whereby relinquishing a small amount of cooling capability results in a drastically reduced circuit complexity, greatly facilitating the implementation of dynamic cooling on near-future quantum computers. Published by the American Physical Society2024

Physics↗