Tobias Rohe, Federico Harjes Ruiloba, Markus Baumann, Gerhard Stenzel, Leo Sünkel, Thomas Gabor, Claudia Linnhoff-Popien
In the Quantum Approximate Optimization Algorithm (QAOA), the entanglement topology, where qubit pairs are connected by two-qubit gates, is conventionally set equal to the edge set of the problem graph. This coupling ties circuit design to explicit problem knowledge and may not yield the most trainable circuit under limited optimization budgets. We investigate whether a reinforcement learning (RL) agent can discover more effective entanglement topologies for QAOA-based MaxCut optimization without direct access to the problem graph. A Masked Proximal Policy Optimization agent sequentially places IsingZZ gates to construct a circuit topology, while a variational inner loop optimizes the resulting QAOA parameters and returns the approximation ratio as a sparse terminal reward. The agent’s observation contains only the edges placed so far and the current approximation ratio; graph structure can only be inferred indirectly through the optimization reward. On Erdős–Rényi instances with up to 10 qubits, the agent consistently converges to topologies that are strict subsets of the problem graph, achieving overlap ratios approaching 1.0, despite receiving no explicit information about the graph structure in its observations. These sparse, problem-aligned topologies outperform the full graph topology and several structural baselines when the optimization budget is limited (50 gradient steps), but are overtaken by denser topologies given sufficient optimization budget. Our results reveal a trainability–expressibility trade-off governed by topology density and are consistent with the hypothesis that, in the small-scale setting studied, the variational optimization landscape implicitly encodes structural information about the problem Hamiltonian.
Quantum key distribution (QKD) enables information-theoretically secure communication by exploiting the quantum properties of single photons. Real-world deployment of QKD, however, requires reliable operation under uncontrolled environmental conditions where background illumination, atmospheric loss, coupling fluctuations, and polarization drift can significantly degrade performance. In this work, we experimentally demonstrate entanglement-based free-space QKD over an atmospheric channel with a passive, low-bandwidth polarization-correction strategy that avoids high-bandwidth real-time polarization tracking during the QKD acquisition. Using a 50-m free-space optical link implementing the BBM92 protocol, we compensate polarization scrambling arising from fiber birefringence and reference-frame misalignment by optimizing Bob’s measurement bases through quantum state tomography. QKD performance is evaluated across three 24-h acquisition campaigns spanning daylight and nighttime conditions, where high background noise, atmospheric fluctuations, and polarization drift pose significant challenges for secure key generation. By combining spectral, temporal, and spatial filtering with optimized coincidence-window selection, threshold-compatible average QKD performance is maintained across these acquisition campaigns. The optimized daylight key rate and QBER are (6.39 ± 0.81 k H z, 8.05 ± 1.48 %), while nighttime operation yields (6.98 ± 0.81 k H z, 8.25 ± 0.85 %). Under representative operating conditions with 8.3 % QBER, we obtain a final secure key rate of 351 H z after reconciliation and privacy amplification. To assess loss tolerance, we further emulate attenuation equivalent to a 1 k m free-space link using controlled attenuation, demonstrating approximately 6 k H z raw key rate under 30 % additional link loss. This attenuation study reproduces the additional loss budget only and does not constitute a physical kilometer-scale free-space demonstration. These results demonstrate that tomography-assisted measurement-basis correction can enable stable free-space entanglement-based QKD without high-bandwidth polarization tracking during key acquisition, providing a basis for future studies of more dynamic terrestrial and satellite-relevant quantum communication links.
The migration from quantum-vulnerable public-key cryptography to post-quantum cryptography (PQC) is now governed by formal standards and binding deadlines; yet, when an organization should migrate remains contested. Published treatments diverge, and the disagreement traces less to data than to modeling choices. This article synthesizes the decision-analytic and economic models used for migration timing, extracting from each its objective, parameters, threat-arrival assumption, cost treatment, and discount rate. Four model families are compared: the Mosca risk inequality; expected-value and net-present-value cost models; real-options models adapted from the information-security investment literature; and risk-prioritization or portfolio models, with decision-making under deep uncertainty as a cross-cutting criterion. A qualitative comparison indicates that recommendations depend most on three contestable inputs: the assumed distribution over the arrival of a cryptographically relevant quantum computer (CRQC), the discount rate applied to deferred costs and harms, and whether the harm from the “harvest now, decrypt later” interception is modeled at all. Early migration is the robust choice whenever confidentiality requirements outlast the plausible CRQC horizon, when interception harm is included, or when a robustness criterion replaces expected-value optimization. The case for deferral strengthens only under short data lifetimes, high discount rates, and no adversary collecting ciphertext today, a narrow set of conditions. We conclude that migration timing is better treated as a decision under Knightian uncertainty than an expected-value optimization, and that the discount rate and arrival distribution should be stated openly as the value judgments they are.
B Akoramurthy, B Surendiran, Xiaochun Cheng, Mohanty SN
Quantum phase estimation (QPE) is a foundational subroutine in quantum algorithms that ranges from Shor’s factoring scheme to variational quantum eigensolvers and quantum metrology protocols. Classical post-processing replacements for the inverse quantum Fourier transform (iQFT) —specifically Kitaev-style iterative estimation and Bayesian update schemes—substantially reduce circuit depth, making them practical for noisy intermediate-scale quantum (NISQ) hardware. Despite this promise, the statistical performance of these methods under the conditions that actually arise in practice—non-eigenstate inputs characterised by eigenstate overlap p ≡ O = | ψ | ϕ | 2 < 1 and mixed-state purity γ ≡ P = Tr (ρ 2) < 1 —remains uncharacterised in the literature. We develop a rigorous information-theoretic framework for Bayesian QPE (BQPE) beyond the eigenstate assumption. Starting from the binary measurement likelihood attenuated by the joint factor O P, we derive exact classical Fisher information expressions and apply the Cramér–Rao inequality to obtain tight variance lower bounds. We then construct an adaptive measurement protocol based on von Mises posterior updates, prove its asymptotic efficiency in the frequentist sense, and establish matching upper and lower bounds on sample complexity. All theoretical results are validated against 2,000 -trial Monte Carlo simulations and cross-checked against published nitrogen-vacancy (NV) centre and photonic experimental data. We prove that the fundamental variance floor for any unbiased frequentist estimator is (1 − p γ) / (N p γ n ̄ 2) 1 / (N (p γ) 2 n ̄ 2), where N is the number of measurement shots and n ̄ 2 is the mean squared measurement exponent evaluated at the optimal basis ϕ * = n θ * − π / 2. The Bayesian MAP estimator achieves this bound asymptotically. The adaptive protocol attains sample complexity Θ log (1 / δ) / (ε 2 p γ) Θ log (1 / δ) / (ε 2 (p γ) 2) to reach precision ε with probability ≥ 1 − δ, representing a 2– 4 × 2– 6 × improvement over semiclassical QPE in the practically relevant regime p < 0.8 (at matched γ = 1). We additionally characterise estimation regimes in the (p, γ) plane; the minimum relative sample overhead of the adaptive protocol compared to the corrected CRLB occurs in the limit p γ → 1, while the absolute sample count is minimised at fixed ε by maximising (p γ) 2. Abstract CRLB and sample-complexity formulas are corrected to use (p γ) 2 throughout, consistent with Theorem 1. We derive a corrected frequentist Cramér–Rao lower bound V a r (θ ̂) ≥ 1 / (N (p γ) 2 n ̄ 2) for BQPE under non-eigenstate and mixed-state inputs, prove that the MAP estimator is asymptotically efficient, establish matching sample complexity bounds Θ (log (1 / δ) / (ε 2 (p γ) 2)) with explicit constants C 1 = 1 / 8 and C 2 = 12, and validate the protocol via 2,000 -trial Monte Carlo simulation. A numerical cross-check against digitised data from three published hardware experiments shows agreement within 7.7– 13.4 %. hardware-specific quantum advantage claims, direct comparison of shot counts across baselines under non-matched definitions, and the claim that performance is optimal at p γ = 0.5 are not supported by the current analysis and are reserved for future research with full experimental access and matched comparisons. Confirmed results separated from speculative claims.
Tolga Yarman, Alexander L. Kholmetskii, Ozan Yarman, Christian B. Marchal
This study develops the two-entity formalism of the Quantal Theory of Gravity (QTG) to model the coexistence of the diffractively expanding wavefront constituent of a particle and its localized mass (core or kernel) constituent that couples to the wavefront. These two constituents together co-dependently form the entire particle. Starting from a single root integral energy conservation law, we arrive at a quasi-Newtonian equation of motion for each entity, both of which converge to the classical equation of Newton in the weak-field and low-velocity limit. The said root conservation law can also lead to a Schrödinger-type wave equation that is yet fully relativistic, through a modified momentum operator corresponding to the wave-like description of the interaction. In the corpuscular regime, the same equation reduces to a projectile-like or ballistic equation of motion. Such a unified treatment provides the mechanical explanation for the reciprocity of wave and corpuscule manifestations, as observed in the gradual transition from the former to the latter in recent single-particle diffraction experiments (including single-photon realizations). In particular, QTG posits that interference patterns and localized detection events arise from two distinct physical entities that exist simultaneously, rather than positing mutually exclusive and philosophically puzzling measurement outcomes. Our findings thus suggest that wave equations and classical trajectories emerge from a common energy conservation principle, offering a singularity-free framework aimed at bridging quantum mechanics (QM) and gravitational physics. QTG makes empirically testable predictions, where we propose diffraction experiments be performed i) in the single-particle regime at a vertical incline or ii) via the application of an electrical field (in the case where one deals with diffracting charged particles). The rest-mass dynamics (RMD) approach at hand is applicable to all bound fields, and, in addition, anticipated the practical absence of gravitational deflection, as lately corroborated for ultra-high-energy γ -rays near Earth’s surface.
