Francesco Petruccione

Simulating an open quantum system on a digital quantum computer often involves the use of Trotter-Suzuki (TS) Product Formulas (PF) to approximate the system’s time evolution. Precise estimates for the required number of Trotter steps (and hence the overall gate count) can be crucial for minimising the computational cost of these methods. Building on established theoretical guarantees, we derive analytic bounds for the first- and second-order deterministic and randomised TS-PF, directly relating the number of Trotter steps to the model parameters, evolution time and precision. These bounds enable concrete resource estimation for each method. We then present a computationally efficient classical algorithm that uses diamond norm estimates of individual Liouvillian terms and a binary search to significantly reduce the Trotter steps required for a target precision. Our numerical results on two prototypical models—an XX-Spin Chain with boundary driving and local dephasing, and a Transverse Field Ising Model—show that the theoretical (analytic) bounds are often overly conservative, whereas the empirical (optimised) bounds yield a significantly smaller number of Trotter steps for the same precision. Among the methods investigated, the second-order randomised TS-PF typically achieves the lowest resource demands, especially for larger systems. These findings emphasise the significance of empirical bounding strategies in achieving more resource-efficient simulations of Markovian open quantum systems.

We present a general open-quantum-system framework to model decoherence induced by stochastic Planck-scale fluctuations of spacetime, focusing on the κ -Minkowski noncommutative geometry as a representative quantum gravity scenario. Treating the deformation parameter as Gaussian white noise, we derive a Lindblad-type master equation applicable to arbitrary quantum systems and obtain a distinctive inverse-energy scaling of the decoherence rate, Γ ∝ E − 4 . As an illustrative example, we analyze a three-level system motivated by neutrino flavor oscillations and derive closed-form expressions for survival and transition probabilities with spacetime-induced damping. The E − 4 scaling contrasts sharply with the positive power laws often invoked in quantum gravity phenomenology and predicts negligible decoherence for high-energy neutrinos—consistent with IceCube observations—while implying that the strongest effects arise in the extreme low-energy regime. In this context, the sub-eV-scale energies characteristic of the cosmic neutrino background provide a natural infrared benchmark for illustrating the enhanced sensitivity to quantum spacetime fluctuations. Our results establish a unified formalism connecting quantum information methods, open-system dynamics, and quantum spacetime phenomenology, thereby offering a framework for exploring potential signatures of Planck-scale physics in future low-energy neutrino studies.

We compare a parameterized quantum kernel (pQK) with a quantum leaky integrate-and-fire (QLIF) neuromorphic computing approach that employs either the Victor–Purpura or van Rossum kernel in a spectral clustering task, as well as the classical radial basis function kernel. To our knowledge, this is the first study to employ quantum neuromorphic leaky integrate-and-fire neurons as kernel generators within a spectral clustering framework and to directly compare them against gate-based quantum fidelity kernels under identical conditions. Performance evaluation includes label-based classification and clustering metrics, as well as optimal number of clusters predictions for each dataset based on an elbow-like curve, as is typically used in K-means clustering. The pQK encodes feature vectors through angle encoding, with rotation angles scaled parametrically. Parameters are optimized through grid search to maximize kernel-target alignment, producing a kernel that reflects distances in the feature space. The quantum neuromorphic approach uses population coding to transform data into spike trains, which are then processed using temporal distance metrics. Kernel matrices are used as input into a classical spectral clustering pipeline prior to performance evaluation. For the synthetic datasets and Iris, the QLIF kernel typically achieves better classification and clustering performance than pQK. However, on higher-dimensional datasets, such as a preprocessed version of the Sloan Digital Sky Survey, pQK performed better, indicating better relative performance compared to QLIF in higher-dimensional regimes.

We compare two quantum approaches that use support vector machines for multi-class classification on a reduced Sloan Digital Sky Survey () dataset: the quantum kernel-based QSVM and the Harrow-Hassidim-Lloyd least-squares SVM (HHL LS-SVM). Both one-vs-rest and two-step hierarchical classification schemes were implemented. The QSVM involves angle encoding of ten features, two unitary operator blocks consisting of rotational operator gates, and a projective measurement that projects the final state to the zero state. The HHL-based method involves solving a system of linear equations using the HHL algorithm and using the solution in a support vector machine approach. The results indicate that the QSVM outperforms HHL LS-SVM in most cases. HHL LS-SVM performs somewhat competitively in selected cases, particularly when isolating galaxies (majority), however, it also performs poorly in others, especially when isolating QSOs (minority). Comparisons with classical SVMs confirm that quantum and classical methods achieve broadly similar performance, with classical models performing slightly ahead overall. Scaling analysis reveals a trade-off: QSVM performance suffers from quadratic scaling with the number of samples and features, but benefits from explicit feature representation during training, while HHL LS-SVM scales essentially constantly, with moderate fluctuations, but suffers from limited representative elements. The HHL-based method is also highly noise-sensitive. These results suggest that QSVM performs better overall under the experimental conditions considered here and is likely to be more amenable to near-term hardware execution in terms of circuit depth and structure, while the more efficient scaling of HHL LS-SVM makes it a useful option for larger datasets beyond the NISQ era.

The origins of life is a question that continues to intrigue scientists across disciplines. The hypothesis that life began with a simple form of metabolism is constrained by the lack of necessary enzymes to catalyze reactions such as carbon fixation. Other catalytic mechanisms have been suggested, with mineral surfaces and metals offering the redox “spark” essential to prebiotic chemistry. There has also been some suggestion that the binding affinity of the ligands synthesized in this pre-enzymatic metabolism acted as an early version of natural selection: more strongly binding ligands were accumulated into further autocatalytic reactions and the aggregation of complex biological materials. Ligand–receptor binding is thus fundamental to the origins of life. In this paper, we use the origins of life theory as a lens through which to review ligand–receptor interactions as they are more commonly understood today. In particular, we focus on the electron tunneling theory of receptor activation that has emerged from research into quantum biology. We revisit criticism against this theory, particularly the lack of evidence for electron transfer in receptors, to see what insights are offered by ligand–receptor interactions mediated by iron sulfur compounds at the origins of life. What emerges from this comparison is the central importance of redox activity in receptors, in particular, with respect to the recurring presence of the disulfide bond. While the paper is a speculative exercise, we conclude that conductivity in biomolecules, particularly the selective conductivity conferred by appropriate ligand–receptor binding, may be a powerful tool for understanding diverse phenomena such as pharmacological potency and viral infection.

Open quantum walks (OQWs) constitute a class of quantum walks whose dynamics are entirely driven by interactions with the environment. It is well known that OQWs provide a general framework for implementing dissipative quantum computation. In this work, we demonstrate the feasibility of running the previously proposed quantum distance-based classifier within the open quantum walk computation model, and we show that its expected runtime remains finite even in the slower regime.

We present a theoretical framework for a quantized memristive Leaky Integrate-and-Fire (LIF) neuron, uniting principles from neuromorphic engineering and open quantum systems. Starting from a classical memristive LIF circuit, we apply canonical quantization techniques to derive a quantum model grounded in circuit quantum electrodynamics. Numerical simulations demonstrate key dynamical features of the quantized memristor and LIF neuron in the weak-coupling and adiabatic regime, including memory effects and spiking behavior. Applications of this model to a sound localization benchmark show that it outperforms a phenomenological quantum LIF model as well as a classical LIF. This work establishes a foundational model for quantum neuromorphic computing, offering a pathway toward biologically inspired quantum spiking neural networks and paradigms in quantum machine learning.

Open Quantum Brownian Motion (OQBM) was introduced as a scaling limit of discrete-time open quantum walks. This limit defines a new class of quantum Brownian motion, which incorporates both the external and internal degrees of freedom of the Brownian particle. We consider a weakly driven Brownian particle confined in a harmonic potential and dissipatively coupled to a thermal bath. Applying the rotating wave approximation (RWA) to the system-bath interaction Hamiltonian, we derive a completely positive Born-Markov master equation for the reduced dynamics. We express the resulting master equation in the coordinate representation and, utilizing the adiabatic elimination of fast variables, derive a completely positive hybrid quantum-classical master equation that defines OQBM. We illustrate the resulting dynamics using examples of initial Gaussian and non-Gaussian distributions of the OQBM walker. Both examples reveal the emergence of Gaussian distributions in the limiting behavior of the OQBM dynamics, which closely matches that of the standard OQBM. With the help of the obtained OQBM master equation, we derive the equations for the $n$-th moments and the cumulants of the position distribution of the open Brownian walker. We subsequently solve these equations numerically for Gaussian initial distributions across various parameter regimes. Notably, we find that the third-order cumulant is nonzero, indicating that the dynamics' intrinsic generator is non-Gaussian.

All life on Earth shares an evolution that is coupled to specific environmental conditions, including the geomagnetic field, which would suggest that biological materials have evolved some degree of magnetic sensitivity. Mounting evidence supports the idea that living organisms can detect and respond to weak magnetic fields, and the radical pair mechanism provides a plausible quantum-level basis for magnetic field sensitivity in biological processes. In the context of evolution, however, fundamental questions remain. How does natural selection act on quantum phenomena such as spin dynamics? What evolutionary pressures have tuned or preserved magnetic sensitivity at the quantum level? In this paper, we offer some potential answers, by closer inspection of the spin Hamiltonian central to the radical pair mechanism. We focus on the fact that hyperfine coupling constants are determined by the local protein environment, which is specified by genetic sequence. Variations in these parameters can alter reactive oxygen species (ROS) outcomes, providing a potential pathway by which quantum-level effects influence organism fitness and possible selection. As proof of principle, we employ a simple qualitative model to demonstrate how variations in nuclear spin, hyperfine coupling strength, and anisotropy might alter ROS levels under different magnetic field conditions. Although these ideas remain speculative, they suggest a framework for investigating how magnetic environments may have influenced the evolution of biological function, with implications for health, disease, and adaptation to altered magnetic environments.

Collision models (CMs) describe an open system interacting in sequence with elements of an environment, termed ancillas. They have been established as a useful tool for analyzing non-Markovian open quantum dynamics based on the ability to control the environmental memory through simple feedback mechanisms. In this work, we investigate how ancilla–ancilla (AA) entanglement can serve as a mechanism for controlling the non-Markovianity of an open system, focusing on an operational approach to generating correlations within the environment. To this end, we first demonstrate that the open dynamics of CMs with sequentially generated correlations between groups of ancillas can be mapped onto a composite CM, where the memory part of the environment is incorporated into an enlarged Markovian system. We then apply this framework to an all-qubit CM, and show that non-Markovian behavior emerges only when the next incoming pair of ancillas are entangled prior to colliding with the system. On the other hand, when system-ancilla collisions precede AA entanglement, we find the open dynamics to always be Markovian. Our findings highlight how certain qualitative features of inter-ancilla correlations can strongly influence the onset of system non-Markovianity.