arXiv subjects

Elijah Pelofske

Publications and source records attributed to Elijah Pelofske.

At least 19 recordsLinked to original sources

arXiv2026

Effects of Trotter Error, Digitization Error, and Initial State Overlap on Tapered Quantum Phase Estimation for Minimum Eigenvalue Computation

We numerically implement full quantum circuits of optimal tapered Quantum Phase Estimation (in the form of an implementable approximate bandwidth-limited DPSS taper) for the purpose of minimum eigenvalue computation, where the Hamiltonian time-evolution unitary is implemented using standard Trotterization, and the taper state is constructed using an optimized bandwidth-limited taper. We illustrate, on representative quantum Hamiltonians, with tractable exact classical numerical quantum circuit simulations, how tapered QPE performs with respect to optimal phase sampling rate, absolute error, Shannon entropy of the optimal phase distribution, when the tQPE algorithm parameters are changed. Those algorithm parameters are Trotter error, finite sampling, imperfect initial states, total evolution time, and digitization error (number of phase qubits). The reported numerical experiments include up to $\ell=10$ phase qubits of precision with $m=3$ additional phase-register error suppression qubits, on a $4$-qubit Heisenberg quantum magnet model Hamiltonian, using up to 12th-order Trotterization. We numerically show i) the steady-state optimal phase sampling rate is determined by the initial state overlap with the ground-state, ii) with respect to phase sampling probability, or overall eigenvalue sampling error rate, there is no strong evolution time dependence for tQPE unless there is high Trotter error, iii) the approximated time-evolution unitaries in tQPE, like in standard QPE, can result in substantial ringing, which leads to non-physical eigenvalue estimates.

quant-ph↗

arXiv2026

Probing Antiferromagnetic Hysteresis on Programmable Quantum Annealers

Using programmable analog quantum annealing processors, we implement a sampling-based magnetic hysteresis protocol to probe the counterintuitive notion of magnetic memory in antiferromagnetic models. A key component of this protocol responsible for the hysteresis is a transverse field, which enables state transitions, while the longitudinal magnetic field sweep is done via a longitudinal control field. We observe intriguing non-monotonic magnetization, alongside full saturation and reversal of the hysteresis curve, Barkhausen-like noise, as well as emergent magnetic domains mediated by quantum fluctuations that give rise to the magnetic memory effect in antiferromagnets.

quant-ph↗

arXiv2026

Numerical Experiments with Parameter Setting of Trotterized Quantum Phase Estimation for Quantum Hamiltonian Ground State Computation

We numerically investigate quantum circuit elementary-gate level instantiations of the standard Quantum Phase Estimation (QPE) algorithm for the task of computing the ground-state energy of a quantum magnet; the disordered fully-connected quantum Heisenberg spin glass model. We consider (classical simulations of) QPE circuit computations on relatively small quantum Hamiltonians ($3$ qubits) with up to $10$ phase bits of precision, using up to Trotter order $10$. We systematically study the inputs of QPE, specifically time evolution, Trotter order, Trotter steps, and initial state, and illustrate how these inputs practically determine how QPE operates. From this we outline a coherent set of quantum algorithm input and tuning guidelines. One of the notable properties we characterize is that QPE sampling of the optimal digitized phase converges to a fixed rate. This results in strong diminishing returns of optimal phase sampling rates which can occur when the Trotter error is surprisingly high.

quant-ph↗

arXiv2026

Entanglement Negativity in Noisy Quantum Volume Sampling

The Quantum Volume protocol uses scrambling random circuits to benchmark NISQ computers. Quantum Volume is generally well-regarded as a benchmark for small, noisy, quantum computers because it requires the quantum computer to implement many non-local entangling gates within a square-shaped circuit, which incentivizes high qubit count, long qubit coherence times, and low error rates on all hardware gates. Quantum Volume circuits inherently produce high-entanglement states that are fragile to errors and decoherence. The Quantum Volume benchmark measures an observable called heavy-output-probability (HOP), where an HOP of $0.5$ corresponds to complete loss of coherence, and in the limit of system size an HOP $\approx 0.84$ for a fully coherent quantum processor. Here, we numerically study the tradeoff between depolarizing noise, entanglement as quantified by the bipartite negativity measure, and HOP in quantum volume circuits. Our results contextualize prior small scale quantum volume demonstrations on quantum computers and highlight that under depolarizing noise, due to finite system size effects heavy output probabilities can be greater than $0.5$ while the bipartite negativity entanglement has been destroyed. This implies, although improbable, that a NISQ computer could pass the Quantum Volume benchmark test threshold of $2/3$ while the underlying quantum computation has no global entanglement -- albeit only for small $n$.

quant-ph↗

arXiv2026

Boltzmann Sampling of Frustrated J1 - J2 Ising Models with Programmable Quantum Annealers

One of the surprising, and potentially very useful, capabilities of analog quantum computers, such as D-Wave quantum annealers, is sampling from the Boltzmann, or Gibbs, distribution defined by a classical Hamiltonian. In this study, we thoroughly examine the ability of D-Wave quantum annealers to sample from the Boltzmann distribution defined by a canonical type of competing magnetic frustration $J_1$-$J_2$ model; the 1-dimensional ANNNI (axial next-nearest-neighbor Ising) model. Boltzmann sampling error rate is quantified for standard linear-ramp anneals ranging from $5$ nanosecond annealing times up to $2000$ microseconds on two different D-Wave quantum annealing processors. Interestingly, we find some analog hardware parameters which result in a very high accuracy (down to a TVD of $0.0003$) and low temperature sampling (down to $β=32.2$) in a frustrated region of the ANNNI model magnetic phase diagram. This bolsters the viability of current analog quantum computers for thermodynamic sampling applications of highly frustrated magnetic spin systems.

quant-ph↗

arXiv2026

Geometry-Induced Domain-Wall Pinning and $\mathbb{Z}_2$ Asymmetry in Nominally One-Dimensional Rydberg Arrays

We perform experiments on QuEra's neutral-Rydberg-atom Aquila quantum computer, using quasi-adiabatic evolution on 1-dimensional models. We use hardware fine-tuning to balance the measurement statistics close to zero net magnetization, in two different geometric outlines: one closed triangular model with 33 atoms, and one 47-atom square with an engineered atom vacancy. The nature of this processor restricts the geometry of the atoms that can be programmed to a 2D plane. We report effects not predicted by the pure 1D Ising model, such as pinning of domain walls and $\mathbb{Z}_2$ symmetry breaking due to the interplay between van der Waals interactions and the Rydberg blockade. In particular, atoms around the atom vacancy and at the vertices of the 1-dimensional square-outline model strongly prefer the Rydberg state, leading to the effective model having a ferromagnetic bond across the vacancy.

quant-ph↗

arXiv2026

A Validation Framework for Quantum Simulation of Spin Dynamics against Inelastic Neutron Scattering and Classical Simulation

Quantitative validation of quantum simulations of dynamical spin response remains challenging because experiment, classical simulation, and quantum simulation do not produce the same native observables. This problem has become increasingly important as quantum simulation protocols for dynamical response have progressed from theory to hardware-level benchmarking against neutron-scattering data, while the longer term goal is validation in regimes that may eventually become classically intractable, including in future fault-tolerant implementations. Here, we develop a cross-pipeline validation framework for quantum simulation, using inelastic neutron scattering and classical many-body simulation as complementary experimental and computational anchors, based on explicit forward and inverse observable maps, covariance- or resampling-based uncertainty propagation, robustness tests for structured distortion, and a hierarchy of complementary metric families. The framework distinguishes stochastic uncertainty from robustness-induced distortion, carries both explicitly through the comparison chain, and uses the resulting metric-level uncertainty and distortion information to support layered validation at the pipeline, solver, and model levels. We also introduce actuator-aware feedback logic aimed at improving agreement without obscuring the physical origin of any remaining mismatch. We close by outlining future extensions of this methodology, including upstream uncertainty and distortion modeling, adaptive feedback, asymmetric validation beyond full classical benchmarking, fault-tolerant workflows, and community infrastructure for reproducible validation.

quant-ph↗

arXiv2026

VQE as Initial State Preparation for QPE on Heisenberg Spin-Glass Hamiltonians

Quantum Phase Estimation (QPE) is the quantum algorithmic workhorse for computing ground state energies of quantum Hamiltonians with quantum computers. Ground state energy calculation of physical systems is perhaps the most promising use case for quantum computing in terms of scientific and commercial value with a plausible path to outperformance of classical alternatives. This path, however, hinges on the availability of initial states for QPE with significant overlap with the true ground state. Using extensive (classical) numerical computations, we study whether the NISQ-era algorithm VQE (Variational Quantum Eigensolver) could be used to efficiently prepare high-overlap states of disordered fully-connected anisotropic Heisenberg spin glass quantum Hamiltonians with up to $15$ qubits. We find that (i) -- consistent with widely held, but rarely numerically illustrated beliefs -- VQE is generally unable to efficiently converge to the ground state for our Hamiltonians, which is a well-known issue with VQE due to a variety of factors including vanishing gradients and local minima; (ii) low energy states do not necessarily have large ground-state overlap, but there is typically a correlation between the two measures; (iii) adding more than three layers to the VQE ansatz neither improves overlap nor the energies found; and (iv) the best-found overlap scaling as a function of the Hamiltonian system size is not strongly exponentially decreasing, suggesting potential for VQE to be a heuristic state preparation algorithm for QPE.

quant-ph↗

arXiv2026

Cybersecurity Threat Hunting and Vulnerability Analysis Using a Neo4j Graph Database of Open Source Intelligence

Open source intelligence is a powerful tool for cybersecurity analysts to gather information both for analysis of discovered vulnerabilities and for detecting novel cybersecurity threats and exploits. Here, we present a Neo4j graph database formed by shared connections (shared sub-string matches) between open source intelligence text including blogs, cybersecurity bulletins, news sites, antivirus scans, social media posts (such as Reddit and Twitter), and threat reports. These connections are comprised of possible indicators of compromise (IP addresses, domains, hashes, email addresses, phone numbers), information on known exploits and techniques (CVEs and MITRE ATT\&CK Technique IDs), and potential sources of information on cybersecurity exploits such as twitter usernames. The construction of the database of potential IOCs is detailed. Examples of utilizing the graph database for querying connections between known malicious IOCs and open source intelligence documents, including threat reports, are shown. We show that this type of relationship querying can allow for more effective use of open source intelligence for threat hunting, malware family clustering, and vulnerability analysis. We show four specific examples of interesting connections found in the graph database; the connections to a known exploited CVE, a known malicious IP address, a malware hash signature, and a portable executable shared resource file.

cs.CR↗

arXiv2026

Snapshot-QAOA: Extending QAOA to Quantum Hamiltonian Simulation

We present Snapshot-QAOA, a variation of the Quantum Approximate Optimization Algorithm (QAOA) that finds approximate minimum energy eigenstates of a large set of quantum Hamiltonians (i.e. Hamiltonians with non-diagonal terms). Traditionally, QAOA targets the task of approximately solving combinatorial optimization problems; Snapshot-QAOA enables a significant expansion of the use case space for QAOA to more general quantum Hamiltonians, where the goal is to approximate the ground-state. Such ground-state finding is a common challenge in quantum chemistry and material science applications. Snapshot-QAOA retains desirable variational-algorithm qualities of QAOA, in particular small parameter count and relatively shallow circuit depth. Snapshot-QAOA is thus a better trainable alternative to the NISQ-era Variational Quantum Eigensolver (VQE) algorithm, while retaining a significant circuit-depth advantage over the QEC-era Quantum Phase Estimation (QPE) algorithm. Our fundamental approach is inspired by the idea of Trotterization of a continuous-time linear adiabatic anneal schedule, which for sufficiently large QAOA depth gives very good performance. Snapshot-QAOA restricts the QAOA evolution to not phasing out the mixing Hamiltonian completely at the end of the evolution, instead evolving only a partial typical linear QAOA schedule, thus creating a type of snapshot of the typical QAOA evolution. As a test case, we simulate Snapshot-QAOA on a 16 qubit J1-J2 frustrated square transverse field Ising model with periodic boundary conditions.

quant-ph↗

arXiv2026

Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms

The emergent practical applicability of the Quantum Approximate Optimization Algorithm (QAOA) for approximate combinatorial optimization is a subject of considerable interest. One of the primary limitations of QAOA is the task of finding a set of good parameters. Parameter transfer is a phenomenon where QAOA angles trained on problem instances that are self-similar tend to perform well for other problem instances from that similar class. This suggests a potentially highly efficient and scalable non-variational learning method for QAOA angle finding. We systematically study QAOA parameter transferability from small problems (16, 27 qubits) onto large problem instances (up to 156 qubits) for heavy-hex graph Ising models with geometrically local higher order terms using the Julia based QAOA simulation tool JuliQAOA to perform classical angle finding for up to 49 QAOA layers. Parameter transfer of the fixed angles is validated using a combination of full statevector, Projected Entangled Pair States, Matrix Product State, and LOWESA numerical simulations. We find that the QAOA parameter transfer from single instances applied to unseen problem instances does not in general provide monotonically improving performance as a function of p - there are many cases where the performance temporarily decreases as a function of p - but despite this the transferred angles have a general trend of improved expectation value as the QAOA depth increases, in many cases converging close to the true ground-state energy of the 100+ qubit instances. We also sample the hardware-compatible Ising models using the ensemble of fixed QAOA angles on several superconducting qubit IBM Quantum processors with 127, 133, and 156 qubits. We find continuous solution quality improvement of the hardware-compatible QAOA circuits run on the IBM NISQ processors up to p=5 on ibm_fez, p=9 on ibm_torino, and p=10 on ibm_pittsburgh.

quant-ph↗

arXiv2025

Partition Function Estimation Using Analog Quantum Processors

We evaluate using programmable superconducting flux qubit D-Wave quantum annealers to approximate the partition function of Ising models. We propose the use of two distinct quantum annealer sampling methods: chains of Monte Carlo-like reverse quantum anneals, and standard linear-ramp quantum annealing. The control parameters used to attenuate the quality of the simulations are the effective analog energy scale of the J coupling, the total annealing time, and for the case of reverse annealing the anneal-pause. The core estimation technique is to sample across the energy spectrum of the classical Hamiltonian of interest, and therefore obtain a density of states estimate for each energy level, which in turn can be used to compute an estimate of the partition function with some sampling error. This estimation technique is powerful because once the distribution is sampled it allows thermodynamic quantity computation at arbitrary temperatures. On a $25$ spin $\pm J$ hardware graph native Ising model we find parameter regimes of the D-Wave processors that provide comparable result quality to two standard classical Monte Carlo methods, Multiple Histogram Reweighting and Wang-Landau. Remarkably, we find that fast quench-like anneals can quickly generate ensemble distributions that are very good estimates of the true partition function of the classical Ising model; on a Pegasus graph-structured QPU we report a logarithmic relative error of $7.6 \times 10^{-6}$, from $171,000$ samples generated using $0.2$ seconds of QPU time with an anneal time of $8$ nanoseconds per sample which is interestingly within the closed system dynamics timescale of the superconducting qubits.

quant-ph↗

arXiv2025

Depth One Quantum Alternating Operator Ansatz as an Approximate Gibbs Distribution Sampler

This study numerically investigates the thermal sampling properties of QAOA, the Quantum Alternating Operator Ansatz which was generalized from the original Quantum Approximate Optimization Algorithm. Specifically, the ability of QAOA to sample from the Gibbs distribution, equivalently the Boltzmann distribution, defined by a classical Ising model, specifically a fully connected disordered spin glass (Sherrington-Kirkpatrick) model. We focus on two different QAOA mixers; the standard transverse field X mixer, and the Grover mixer. At a QAOA depth of one we examine, for a single full QAOA parameter search space period, the energy landscape, the Shannon entropy landscape of the QAOA probability distribution, and the tradeoff between Boltzmann distribution sampling temperature and error rate (how close to the true Boltzmann distribution is the QAOA distribution). We find that at very high temperatures one-round Grover mixer QAOA can sample from the Boltzmann distribution more accurately than the standard X mixer QAOA at one round. Both X mixer and Grover mixer depth one QAOA can serve as approximate Boltzmann distribution samplers, and how good this approximation is depends heavily on the QAOA angle choice.

quant-ph↗

arXiv2025

Erasing Classical Memory with Quantum Fluctuations: Shannon Information Entropy of Reverse Quantum Annealing

Quantum annealers can provide non-local optimization by tunneling between states in a process that ideally eliminates memory of the initial configuration. We study the crossover between memory loss and retention due to quantum fluctuations, in a transverse Ising model on odd numbered antiferromagnetic rings of thousands of spins with periodic boundary conditions, by performing reverse quantum annealing experiments on three programmable superconducting flux qubit quantum annealers. After initializing the spins to contain a single domain wall, we then expose it to quantum fluctuations by turning on the transverse Zeeman energy. We characterize the crossover between memory retention at low transverse field, and memory loss at high transverse field by extracting the Shannon information entropy of magnetic domain wall distributions. We demonstrate a clear crossover in memory retention, and its dependence on hardware platform and simulation time. Our approach establishes a general probe of the interplay between quantum fluctuations and memory.

quant-ph↗

arXiv2025

Magnetic Memory and Hysteresis from Quantum Transitions: Theory and Experiments on Quantum Annealers

Quantum annealing leverages quantum tunneling for non-local searches, thereby minimizing memory effects that typically arise from metastabilities. Nonetheless, recent work has demonstrated robust hysteresis in large-scale transverse-field Ising systems implemented on D-Wave's analog quantum hardware. The quantum nature of these intriguing results remains to be understood at a deeper level. Here, we present a conceptual framework that explains the observed behavior by combining two-level Landau-Zener transitions via a first-order piecewise-constant propagator with semiclassical domain-wall kinetics. We test this approach experimentally on a quantum annealer, where we observe clear coercivity even in one-dimensional rings with periodic boundary conditions comprising up to 4,906 qubits-regimes where classical hysteresis is forbidden, but quantum hysteresis is not. Our framework reproduces the measured kink densities, hysteresis loop shapes, and longitudinal sweep-rate scaling trends observed in data from three different D-Wave quantum annealers. In particular, it captures striking non-monotonic features and transiently negative susceptibilities, identifying them as genuine quantum memory effects. These results establish programmable quantum annealers as powerful testbeds for exploring memory-endowed non-equilibrium dynamics in quantum many-body systems.

quant-ph↗

arXiv2025

Magnetic Hysteresis Experiments Performed on Quantum Annealers

While quantum annealers have emerged as versatile and controllable platforms for experimenting on correlated spin systems, the important phenomenology of magnetic memory and hysteresis remain unexplored on hardware designed to escape metastable states via quantum tunneling. Here, we present the first general protocol to experiment on magnetic hysteresis on programmable quantum annealers, and implement it on three D-Wave superconducting qubit quantum annealers, using up to thousands of spins, for both ferromagnetic and disordered Ising models, and across different graph topologies. We observe hysteresis loops whose area depends non-monotonically on quantum fluctuations, exhibiting both expected and unexpected features, such as disorder-induced steps and non-monotonicities. Our work establishes quantum annealers as a platform for probing non-equilibrium emergent magnetic phenomena, thereby broadening the role of analog quantum computers into foundational questions in condensed matter physics.

quant-ph↗

arXiv2025

Variational Quantum Simulations of a Two-Dimensional Frustrated Transverse-Field Ising Model on a Trapped-Ion Quantum Computer

Quantum computers are an ideal platform to study the ground state properties of strongly correlated systems due to the limitation of classical computing techniques particularly for systems exhibiting quantum phase transitions. While the error rates of Noisy Intermediate-Scale Quantum (NISQ) computers are still high, simulating strongly correlated systems on such devices and extracting information of possible phases may be within reach. The frustrated transverse-field Ising model (TFIM) is such a system with multiple ordered magnetic phases. In this study, we simulate a two-dimensional frustrated TFIM with next-nearest-neighbor spin-exchange interactions at zero temperature. The competition between the nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic coupling gives rise to frustration in the system. Moreover, the presence of quantum fluctuations makes the ground-state phase profile even richer. We use the Variational Quantum Eigensolver (VQE) to compute the phases on a square lattice with periodic boundary conditions for a system of 16 sites (qubits). The trained VQE circuits are compared to exact diagonalization, allowing us to extract error measures of VQE. We focus on the ground-state phase transitions of this model, where VQE succeeds in finding the dominant magnetic phases. The optimized VQE circuits are then executed on the Quantinuum H1-1 trapped-ion quantum computer without using any error mitigation techniques. Our experiments show near perfect recovery of the magnetic phases of the frustrated model through ground-state energy, the energy derivative, and the spin correlation functions. Thus, we show that the trapped-ion quantum processor is able to achieve reliable simulations of a strongly correlated system within the limitations of the VQE approach.

quant-ph↗

arXiv2025

Digital Zero-Noise Extrapolation with Quantum Circuit Unoptimization

Quantum circuit unoptimization is an algorithm that transforms a quantum circuit into a different circuit that uses more gate operations while maintaining the same unitary transformation. We demonstrate that this method can implement digital zero-noise extrapolation (ZNE), a quantum error mitigation technique. By employing quantum circuit unoptimization as a form of circuit folding, noise can be systematically amplified. The key advantages of this approach are twofold. First, its ability to generate an exponentially increasing number of distinct circuit variants as the noise level is amplified, which allows noise averaging over many circuit variants with slightly different circuit structure. Averaging over these variants can mitigate the effect of biased error propagation due to the significantly altered circuit structure from quantum circuit unoptimization, or biased noise sources on a quantum processor. Second, quantum circuit unoptimization by design resists circuit simplification back to the original unmodified circuit, making it plausible to use ZNE in contexts where circuit compiler optimization is applied server-side. We evaluate the effectiveness of quantum circuit unoptimization as a noise-scaling method for ZNE in two test cases using depolarizing noise numerical simulations: random quantum volume circuits, where the observable is the heavy output probability, and QAOA circuits for the (unweighted) maximum cut problem on random 3-regular graphs, where the observable is the cut value. We show that using quantum circuit unoptimization to perform ZNE can approximately recover signal from noisy quantum simulations.

quant-ph↗