Operational scale detection in quantum magnetism via susceptibility analysis: Critical-like behavior at the quantum–classical crossover on NISQ hardware
What defines the operational boundary between quantum information and classical magnetism? We present a model-independent methodology for detecting characteristic scales in quantum systems through generalized susceptibility analysis χ(σ)=|d〈O〉/dσ|, where σ represents observation scales across spatial, temporal, and decoherence dimensions. Through comprehensive experiments on a Rigetti Ankaa-3 quantum processor, we identify an operational threshold at γc=0.6737±0.036 under tested noise profiles, exhibiting exceptional peak clarity κ=8.58—the sharpest signal observed across all phenomena. This pronounced transition, validated through bootstrap analysis and multiple susceptibility metrics, suggests critical-like behavior in the quantum-to-classical crossover, though we carefully refrain from claiming a thermodynamic phase transition. The framework successfully extracts characteristic scales without prior theoretical knowledge: correlation length ξ=8.00 qubits, distinct ordering timescales for ferromagnetic (tc=0.36) versus antiferromagnetic (tc=0.91) systems, and the quantum critical field hc=1.821 in the transverse-field Ising model. Robustness analysis confirms stability across smoothing parameters, methods, and metric definitions. Beyond providing actionable guidance for noisy intermediate-scale quantum-era quantum computing, our findings suggest that magnetic correlations exhibit characteristic transitions at specific decoherence scales—an operational perspective connecting quantum information theory and condensed matter physics. While framing this as methodological advance rather than fundamental physics, the identification of critical-like information-to-physics transitions provides practical diagnostics for quantum device characterization and optimization.
What defines the operational boundary between quantum information and classical magnetism? We present a model-independent methodology for detecting characteristic scales in quantum systems through generalized susceptibility analysis χ(σ)=|d〈O〉/dσ|, where σ represents observation scales across spatial, temporal, and decoherence dimensions. Through comprehensive experiments on a Rigetti Ankaa-3 quantum processor, we identify an operational threshold at γc=0.6737±0.036 under tested noise profiles, exhibiting exceptional peak clarity κ=8.58—the sharpest signal observed across all phenomena. This pronounced transition, validated through bootstrap analysis and multiple susceptibility metrics, suggests critical-like behavior in the quantum-to-classical crossover, though we carefully refrain from claiming a thermodynamic phase transition. The framework successfully extracts characteristic scales without prior theoretical knowledge: correlation length ξ=8.00 qubits, distinct ordering timescales for ferromagnetic (tc=0.36) versus antiferromagnetic (tc=0.91) systems, and the quantum critical field hc=1.821 in the transverse-field Ising model. Robustness analysis confirms stability across smoothing parameters, methods, and metric definitions. Beyond providing actionable guidance for noisy intermediate-scale quantum-era quantum computing, our findings suggest that magnetic correlations exhibit characteristic transitions at specific decoherence scales—an operational perspective connecting quantum information theory and condensed matter physics. While framing this as methodological advance rather than fundamental physics, the identification of critical-like information-to-physics transitions provides practical diagnostics for quantum device characterization and optimization.
The quantum phase transitions provide a paradigm for studying collective quantum phenomena that are a result of competing non-commuting interactions. This paper will study the ground state properties and quantum critical dynamics of the one-dimensional transverse field Ising model through a combined perspective that includes exact diagonalisation, variational quantum eigensolver (VQE) simulations, and simulations on realistic physical quantum devices. We focus on a lattice of four spins, where we calculate the ground-state energies, magnetic order parameters and correlation functions at uniformly applied conditions, which is repeated by all systems. Precise diagonalisation provides both a benchmark, which is symmetry-conserving, and a depth-two, physics inspired variational approximation, which provides simulations accessible to hardware. The circuits that have been optimised identically are then placed on the IQM Garnet quantum processor, using a resource-efficient batched protocol. We find that the ground-state energies of shallow variational circuits are reliably captured by the circuit over the entire parameter space; the magnetic arrangement parameters and observables sensitive to correlation signal significantly more noise. The error analysis of quantitative analysis reveals a strong broadening of critical crossover on hardware, which is consistent with the noise attenuation of long-range correlations. These findings highlight the current capabilities as well as the fundamental limitations of noisy intermediate-scale quantum systems in modelling quantum critical phenomena as a benchmark to future enhancements in obtaining quantum hardware and quantum algorithms development.
This paper presents a formal framework framing quantum decoherence as an information-theoretic phase transition at the quantum-to-classical boundary. We demonstrate that environment-induced superselection (einselection) can be characterized as a true dynamical phase transition where the system-environment coupling strength acts as a thermodynamic control parameter, and the suppression of off-diagonal density matrix elements functions as an order parameter analogous to magnetization in the Ising model. Using quantum mutual information, von Neumann entropy, and entanglement entropy, we track the operational flow of information from a quantum system into environmental degrees of freedom, demonstrating how a singular classical reality emerges via the redundant copying of pointer states into environmental fragments—a process governed by Quantum Darwinism. We analyze a simulated spin-boson model and random unitary circuits with tunable dissipation, extracting clear signatures of criticality including power-law scaling and diverging correlation times at a critical threshold . Crucially, we connect this behavior to recent advancements (2023–2025) in mixed-state topological order, establishing that decoherence-induced transitions map onto anyon condensation transitions within an errorfield double formulation. Finally, we explore the foundational implications of this framework: it sharpens the measurement problem via informational symmetry breaking, reframes observation as a high-decoherence thermodynamic limit, and introduces a Gödelian perspective by demonstrating that determining the critical threshold for arbitrary many-body environments is formally undecidable due to the non-computability of the spectral gap in the thermodynamic limit.
Abstract We extend the Prometheus framework from classical to quantum phase transitions, demonstrat- ing unsupervised discovery of quantum critical phenomena in the disordered transverse field Ising model (DTFIM). Building upon our previous work on classical spin systems [1, 2], we develop a quantum-aware variational autoencoder (Q-VAE) architecture that operates directly on quantum ground state wavefunctions obtained via exact diagonalization. The Q-VAE learns latent represen- tations that capture the essential physics of the quantum phase transition between paramagnetic and ferromagnetic phases, achieving detection of the quantum critical point hc = 1.00 ± 0.02 in the clean limit, consistent with the theoretical value hc/J = 1. We introduce disorder through random transverse fields h i ∼ Uniform[h−W, h+W ] and investigate the disorder-driven infinite-randomness fixed point characteristic of the random TFIM. Our framework successfully identifies the shift in critical behavior with increasing disorder strength and extracts effective critical exponents through finite-size scaling analysis. We formulate and test the hypothesis that the Q-VAE latent space structure reflects the activated dynamical scaling ln ξ ∼ |h − hc| −ψ with ψ ≈ 0.5 expected at the infinite-randomness fixed point. The Prometheus quantum discovery pipeline provides a systematic approach to exploring quantum phase diagrams in systems where analytical solutions are unavail- able, with potential applications to quantum materials, cold atom systems, and quantum computing platforms.
Understanding how noise influences nonequilibrium quantum critical dynamics is essential for both fundamental physics and the development of practical quantum technologies. While the quantum Kibble-Zurek (QKZ) mechanism predicts universal scaling during quenches across a critical point, real quantum systems exhibit complex decoherence that can substantially modify these behaviors, ranging from altering critical scaling to completely suppressing it. By considering a specific case of nondemolishing noise, we first show how decoherence can reshape universal scaling and verify these theoretical predictions using numerical simulations of spin chains across a wide range of noise strengths. Then, we study linear quenches in the transverse-field Ising model on IBM superconducting processors where the noise model is unknown. Using large system sizes of 80-120 qubits, we measure equal-time connected correlations, defect densities, and excess energies across various quench times. Surprisingly, unlike earlier observations where noise-induced defect production masked universal behavior at long times, we observe clear scaling relations, pointing towards persistent universal structure shaped by decoherence. The extracted scaling exponents differ from both ideal QKZ predictions and analytic results for simplified noise models, suggesting the emergence of a distinct noise-influenced universality regime. Our results, therefore, point toward the possibility of using universal dynamical scaling as a high-level descriptor of quantum hardware, complementary to conventional gate-level performance metrics.
Quantum computing represents a foundational paradigm shift from traditional classical computational models, leveraging the intrinsic mechanics of quantum physics—specifically superposition, entanglement, and unitary interference—to execute parallel processing frameworks at an exponential operational scale. This state-of-the-art review systematically deconstructs the mathematical framework of quantum bit (qubit) state vectors within complex Hilbert spaces and details pioneering algorithms like Shor's and Grover's operations. Furthermore, we evaluate dominant contemporary hardware frameworks, specifically contrasting superconducting circuits against trapped-ion architectures across critical indices of coherence metrics, operational speeds, and thermal constraints. Finally, this review highlights systemic algorithmic barriers including phase-flip/bit-flip noise profiles, decoherence phenomena, and real-world deployment challenges across cryptographic infrastructure and biochemical modeling matrices, charting the roadmap from Noisy Intermediate-Scale Quantum (NISQ) systems toward scalable, fault-tolerant ecosystems.
We extend the Prometheus framework for unsupervised phase transition discovery from two-dimensional classical systems to three-dimensional classical systems and quantum many-body systems. Building upon preliminary observations from a 2D Ising model student abstract [Yee et al., 2026], we address two fundamental questions: (1) Does the framework scale to higher dimensions where exact solutions are unavailable? (2) Can it generalize to quantum phase transitions driven by quantum fluctuations rather than thermal fluctuations? For the 3D Ising model on lattices up to L=32, we achieve critical temperature detection within 0.01\% of literature values ($\Tc/J = 4.511 \pm 0.005$) and extract critical exponents with ≥70% accuracy, with statistical analysis correctly identifying the 3D Ising universality class (p=0.72). For quantum systems, we develop quantum-aware VAE (Q-VAE) architectures operating on complex-valued wavefunctions with fidelity-based loss functions, achieving 2\% accuracy in quantum critical point detection for the transverse field Ising model. For the disordered TFIM, we perform a consistency check of activated dynamical scaling $\ln ξ\sim |h - \hc|^{-ψ}$, extracting tunneling exponent ψ=0.48±0.08 consistent with theoretical predictions (ψ=0.5, Δχ2=12.3, p<0.001). This demonstrates that unsupervised learning can identify qualitatively different \emph{types} of critical behavior, serving as a consistency check on known IRFP physics.