arXiv subjects

P. Aaron Lott

Publications and source records attributed to P. Aaron Lott.

14 recordsLinked to original sources

arXiv2026

Sequential Reservoir Computing for Efficient High-Dimensional Spatiotemporal Forecasting

Forecasting high-dimensional spatiotemporal systems remains computationally challenging for recurrent neural networks (RNNs) and long short-term memory (LSTM) models due to gradient-based training and memory bottlenecks. Reservoir Computing (RC) mitigates these challenges by replacing backpropagation with fixed recurrent layers and a convex readout optimization, yet conventional RC architectures still scale poorly with input dimensionality. We introduce a Sequential Reservoir Computing (Sequential RC) architecture that decomposes a large reservoir into a series of smaller, interconnected reservoirs. This design reduces memory and computational costs while preserving long-term temporal dependencies. Using both low-dimensional chaotic systems (Lorenz63) and high-dimensional physical simulations (2D vorticity and shallow-water equations), Sequential RC achieves 15-25% longer valid forecast horizons, 20-30% lower error metrics (SSIM, RMSE), and up to three orders of magnitude lower training cost compared to LSTM and standard RNN baselines. The results demonstrate that Sequential RC maintains the simplicity and efficiency of conventional RC while achieving superior scalability for high-dimensional dynamical systems. This approach provides a practical path toward real-time, energy-efficient forecasting in scientific and engineering applications.

cs.LG↗

arXiv2025

The USRA Feynman Quantum Academy: If You Give a Student a Quantum Internship

In the rapidly expanding field of quantum computing, one key aspect to maintain ongoing progress is ensuring that early career scientists interested in the field get appropriate guidance and opportunity to advance their work, and in return that institutions and enterprises with a stake in quantum computing have access to a qualified pool of talent. Internship programs at the graduate level are the perfect vehicle to achieve this. In this paper, we review the trajectory of the USRA Feynman Quantum Academy Internship Program over the last 8 years, placing it in the context of the current push to prepare the quantum workforce of the future, and highlighting the caliber of the work it produced.

physics.ed-ph↗

arXiv2025

Pushing the Boundary of Quantum Advantage in Hard Combinatorial Optimization with Probabilistic Computers

Recent demonstrations on specialized benchmarks have reignited excitement for quantum computers, yet whether they can deliver an advantage for practical real-world problems remains an open question. Here, we show that probabilistic computers (p-computers), when co-designed with hardware to implement powerful Monte Carlo algorithms, provide a compelling and scalable classical pathway for solving hard optimization problems. We focus on two key algorithms applied to 3D spin glasses: discrete-time simulated quantum annealing (DT-SQA) and adaptive parallel tempering (APT). We benchmark these methods against the performance of a leading quantum annealer on the same problem instances. For DT-SQA, we find that increasing the number of replicas improves residual energy scaling, in line with expectations from extreme value theory. We then show that APT, when supported by non-local isoenergetic cluster moves, exhibits a more favorable scaling and ultimately outperforms DT-SQA. We demonstrate these algorithms are readily implementable in modern hardware, projecting that custom Field Programmable Gate Arrays (FPGA) or specialized chips can leverage massive parallelism to accelerate these algorithms by orders of magnitude while drastically improving energy efficiency. Our results establish a new, rigorous classical baseline, clarifying the landscape for assessing a practical quantum advantage and presenting p-computers as a scalable platform for real-world optimization challenges.

quant-ph↗

arXiv2024

How to Build a Quantum Supercomputer: Scaling from Hundreds to Millions of Qubits

In the span of four decades, quantum computation has evolved from an intellectual curiosity to a potentially realizable technology. Today, small-scale demonstrations have become possible for quantum algorithmic primitives on hundreds of physical qubits. Nevertheless, there are significant outstanding challenges in quantum hardware, fabrication, software architecture, and algorithms on the path towards a full-stack scalable quantum computing technology. Here, we provide a comprehensive review of these scaling challenges. We show how to facilitate scaling by adopting existing semiconductor technology to build much higher-quality qubits, employing systems engineering approaches, and performing distributed heterogeneous quantum-classical computing. We provide a detailed resource and sensitivity analysis for quantum applications on surface-code error-corrected quantum computers given current, target, and desired hardware specifications based on superconducting qubits, accounting for a realistic distribution of errors. We provide comprehensive resource estimates for several utility-scale applications including quantum chemistry calculations, catalyst design, NMR spectroscopy, and Fermi-Hubbard simulation. We show that orders of magnitude enhancement in performance could be obtained by a combination of hardware improvements and tight quantum-HPC integration. Furthermore, we introduce high-performance architectures for quantum-probabilistic computing with custom-designed accelerators to tackle today's industry-scale classical optimization, machine learning, and quantum simulation tasks in a cost-effective manner.

quant-ph↗

arXiv2024

Design and execution of quantum circuits using tens of superconducting qubits and thousands of gates for dense Ising optimization problems

We develop a hardware-efficient ansatz for variational optimization, derived from existing ansatze in the literature, that parametrizes subsets of all interactions in the Cost Hamiltonian in each layer. We treat gate orderings as a variational parameter and observe that doing so can provide significant performance boosts in experiments. We carried out experimental runs of a compilation-optimized implementation of fully-connected Sherrington-Kirkpatrick Hamiltonians on a 50-qubit linear-chain subsystem of Rigetti Aspen-M-3 transmon processor. Our results indicate that, for the best circuit designs tested, the average performance at optimized angles and gate orderings increases with circuit depth (using more parameters), despite the presence of a high level of noise. We report performance significantly better than using a random guess oracle for circuits involving up to approx 5000 two-qubit and approx 5000 one-qubit native gates. We additionally discuss various takeaways of our results toward more effective utilization of current and future quantum processors for optimization.

quant-ph↗

arXiv2024

A Multilevel Approach For Solving Large-Scale QUBO Problems With Noisy Hybrid Quantum Approximate Optimization

Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the existing quantum processing units (QPUs) are relatively small, and canonical mappings of QUBO via the Ising model require one qubit per variable, rendering direct large-scale optimization infeasible. In classical optimization, a general strategy for addressing many large-scale problems is via multilevel/multigrid methods, where the large target problem is iteratively coarsened, and the global solution is constructed from multiple small-scale optimization runs. In this work, we experimentally test how existing QPUs perform as a sub-solver within such a multilevel strategy. We combine and extend (via additional classical processing) the recent Noise-Directed Adaptive Remapping (NDAR) and Quantum Relax $\&$ Round (QRR) algorithms. We first demonstrate the effectiveness of our heuristic extensions on Rigetti's transmon device Ankaa-2. We find approximate solutions to $10$ instances of fully connected $82$-qubit Sherrington-Kirkpatrick graphs with random integer-valued coefficients obtaining normalized approximation ratios (ARs) in the range $\sim 0.98-1.0$, and the same class with real-valued coefficients (ARs $\sim 0.94-1.0$). Then, we implement the extended NDAR and QRR algorithms as subsolvers in the multilevel algorithm for $6$ large-scale graphs with at most $\sim 27,000$ variables. The QPU (with classical post-processing steps) is used to find approximate solutions to dozens of problems, at most $82$-qubit, which are iteratively used to construct the global solution. We observe that quantum optimization results are competitive regarding the quality of solutions compared to classical heuristics used as subsolvers within the multilevel approach.

quant-ph↗

arXiv2024

Assessing and Advancing the Potential of Quantum Computing: A NASA Case Study

Quantum computing is one of the most enticing computational paradigms with the potential to revolutionize diverse areas of future-generation computational systems. While quantum computing hardware has advanced rapidly, from tiny laboratory experiments to quantum chips that can outperform even the largest supercomputers on specialized computational tasks, these noisy-intermediate scale quantum (NISQ) processors are still too small and non-robust to be directly useful for any real-world applications. In this paper, we describe NASA's work in assessing and advancing the potential of quantum computing. We discuss advances in algorithms, both near- and longer-term, and the results of our explorations on current hardware as well as with simulations, including illustrating the benefits of algorithm-hardware co-design in the NISQ era. This work also includes physics-inspired classical algorithms that can be used at application scale today. We discuss innovative tools supporting the assessment and advancement of quantum computing and describe improved methods for simulating quantum systems of various types on high-performance computing systems that incorporate realistic error models. We provide an overview of recent methods for benchmarking, evaluating, and characterizing quantum hardware for error mitigation, as well as insights into fundamental quantum physics that can be harnessed for computational purposes.

quant-ph↗

arXiv2024

Combinatorial Reasoning: Selecting Reasons in Generative AI Pipelines via Combinatorial Optimization

Recent Large Language Models (LLMs) have demonstrated impressive capabilities at tasks that require human intelligence and are a significant step towards human-like artificial intelligence (AI). Yet the performance of LLMs at reasoning tasks have been subpar and the reasoning capability of LLMs is a matter of significant debate. While it has been shown that the choice of the prompting technique to the LLM can alter its performance on a multitude of tasks, including reasoning, the best performing techniques require human-made prompts with the knowledge of the tasks at hand. We introduce a framework for what we call Combinatorial Reasoning (CR), a fully-automated prompting method, where reasons are sampled from an LLM pipeline and mapped into a Quadratic Unconstrained Binary Optimization (QUBO) problem. The framework investigates whether QUBO solutions can be profitably used to select a useful subset of the reasons to construct a Chain-of-Thought style prompt. We explore the acceleration of CR with specialized solvers. We also investigate the performance of simpler zero-shot strategies such as linear majority rule or random selection of reasons. Our preliminary study indicates that coupling a combinatorial solver to generative AI pipelines is an interesting avenue for AI reasoning and elucidates design principles for future CR methods.

cs.AI↗

arXiv2024

Hybrid quantum-classical reservoir computing for simulating chaotic systems

Forecasting chaotic systems is a notably complex task, which in recent years has been approached with reasonable success using reservoir computing (RC), a recurrent network with fixed random weights (the reservoir) used to extract the spatio-temporal information of the system. This work presents a hybrid quantum reservoir-computing (HQRC) framework, which replaces the reservoir in RC with a quantum circuit. The modular structure and measurement feedback in the circuit are used to encode the complex system dynamics in the reservoir states, from which classical learning is performed to predict future dynamics. The noiseless simulations of HQRC demonstrate valid prediction times comparable to state-of-the-art classical RC models for both the Lorenz63 and double-scroll chaotic paradigmatic systems and adhere to the attractor dynamics long after the forecasts have deviated from the ground truth.

quant-ph↗

arXiv2023

Quantum-Enhanced Greedy Combinatorial Optimization Solver

Combinatorial optimization is a broadly attractive area for potential quantum advantage, but no quantum algorithm has yet made the leap. Noise in quantum hardware remains a challenge, and more sophisticated quantum-classical algorithms are required to bolster their performance. Here, we introduce an iterative quantum heuristic optimization algorithm to solve combinatorial optimization problems. The quantum algorithm reduces to a classical greedy algorithm in the presence of strong noise. We implement the quantum algorithm on a programmable superconducting quantum system using up to 72 qubits for solving paradigmatic Sherrington-Kirkpatrick Ising spin glass problems. We find the quantum algorithm systematically outperforms its classical greedy counterpart, signaling a quantum enhancement. Moreover, we observe an absolute performance comparable with a state-of-the-art semidefinite programming method. Classical simulations of the algorithm illustrate that a key challenge to reaching quantum advantage remains improving the quantum device characteristics.

quant-ph↗

arXiv2023

Anomaly Detection in Aeronautics Data with Quantum-compatible Discrete Deep Generative Model

Deep generative learning cannot only be used for generating new data with statistical characteristics derived from input data but also for anomaly detection, by separating nominal and anomalous instances based on their reconstruction quality. In this paper, we explore the performance of three unsupervised deep generative models -- variational autoencoders (VAEs) with Gaussian, Bernoulli, and Boltzmann priors -- in detecting anomalies in flight-operations data of commercial flights consisting of multivariate time series. We devised two VAE models with discrete latent variables (DVAEs), one with a factorized Bernoulli prior and one with a restricted Boltzmann machine (RBM) as prior, because of the demand for discrete-variable models in machine-learning applications and because the integration of quantum devices based on two-level quantum systems requires such models. The DVAE with RBM prior, using a relatively simple -- and classically or quantum-mechanically enhanceable -- sampling technique for the evolution of the RBM's negative phase, performed better than the Bernoulli DVAE and on par with the Gaussian model, which has a continuous latent space. Our studies demonstrate the competitiveness of a discrete deep generative model with its Gaussian counterpart on anomaly-detection tasks. Moreover, the DVAE model with RBM prior can be easily integrated with quantum sampling by outsourcing its generative process to measurements of quantum states obtained from a quantum annealer or gate-model device.

cs.LG↗

arXiv2021

Inter-generational comparison of quantum annealers in solving hard scheduling problems

We compare the performance of four quantum annealers, the D-Wave Two, 2X, 2000Q, and Advantage in solving an identical ensemble of a parametrized family of scheduling problems. These problems are NP-complete and, in fact, equivalent to vertex coloring problems. They are also practically motivated and closely connected to planning problems from artificial intelligence. We examine factors contributing to the performance differences while separating the contributions from hardware upgrades, support for shorter anneal times, and possible optimization of ferromagnetic couplings. While shorter anneal times can improve the time to solution (TTS) at any given problem size, the scaling of TTS with respect to the problem size worsens for shorter anneal times. In contrast, optimizing the ferromagnetic coupling improves both the absolute TTS and the scaling. There is a statistically significant improvement in performance between D-Wave Two and 2X and from all older generation annealers to Advantage, even when operated under identical anneal time and ferromagnetic couplings. However, the performance improvement from 2X to 2000Q requires the anneal time and ferromagnetic couplings to be optimized. Overall, owing to these inter-generational hardware improvements and optimizations, the scaling exponent reduces from $1.01 \pm 0.01$ on Two to $0.173 \pm 0.009$ on Advantage.

quant-ph↗

arXiv2021

Practical Verification of Quantum Properties in Quantum Approximate Optimization Runs

In order to assess whether quantum resources can provide an advantage over classical computation, it is necessary to characterize and benchmark the non-classical properties of quantum algorithms in a practical manner. In this paper, we show that using measurements in no more than 3 out of the possible $3^N$ bases, one can not only reconstruct the single-qubit reduced density matrices and measure the ability to create coherent superpositions, but also possibly verify entanglement across all $N$ qubits participating in the algorithm. We introduce a family of generalized Bell-type observables for which we establish an upper bound to the expectation values in fully separable states by proving a generalization of the Cauchy-Schwarz inequality, which may serve of independent interest. We demonstrate that a subset of such observables can serve as entanglement witnesses for QAOA-MaxCut states, and further argue that they are especially well tailored for this purpose by defining and computing an entanglement potency metric on witnesses. A subset of these observables also certify, in a weaker sense, the entanglement in GHZ states, which share the $\mathbb{Z}_2$ symmetry of QAOA-MaxCut. The construction of such witnesses follows directly from the cost Hamiltonian to be optimized, and not through the standard technique of using the projector of the state being certified. It may thus provide insights to construct similar witnesses for other variational algorithms prevalent in the NISQ era. We demonstrate our ideas with proof-of-concept experiments on the Rigetti Aspen-9 chip for ansatze containing up to 24 qubits.

quant-ph↗

arXiv2019

Scaling advantage in quantum simulation of geometrically frustrated magnets

The promise of quantum computing lies in harnessing programmable quantum devices for practical applications such as efficient simulation of quantum materials and condensed matter systems. One important task is the simulation of geometrically frustrated magnets in which topological phenomena can emerge from competition between quantum and thermal fluctuations. Here we report on experimental observations of relaxation in such simulations, measured on up to 1440 qubits with microsecond resolution. By initializing the system in a state with topological obstruction, we observe quantum annealing (QA) relaxation timescales in excess of one microsecond. Measurements indicate a dynamical advantage in the quantum simulation over the classical approach of path-integral Monte Carlo (PIMC) fixed-Hamiltonian relaxation with multiqubit cluster updates. The advantage increases with both system size and inverse temperature, exceeding a million-fold speedup over a CPU. This is an important piece of experimental evidence that in general, PIMC does not mimic QA dynamics for stoquastic Hamiltonians. The observed scaling advantage, for simulation of frustrated magnetism in quantum condensed matter, demonstrates that near-term quantum devices can be used to accelerate computational tasks of practical relevance.

quant-ph↗