arXiv subjects

Ilya Sinayskiy

Publications and source records attributed to Ilya Sinayskiy.

At least 19 recordsLinked to original sources

arXiv2026

Adiabatic elimination and Wigner function approach in microscopic derivation of Open Quantum Brownian Motion

Open Quantum Brownian Motion (OQBM) is a new class of quantum Brownian motion in which the dynamics of the Brownian particle depend not only on interactions with a thermal environment but also on the state of its internal degrees of freedom. For an Ohmic bath spectral density with a Lorentz--Drude cutoff frequency at a high-temperature limit, we derive the Born--Markov master equation for the reduced density matrix of an open Brownian particle in a harmonic potential. The resulting master equation is written in phase-space representation using the Wigner function, and due to the separation of associated timescales in the high-damping limit, we perform adiabatic elimination of the momentum variable to obtain OQBM. We numerically solve the derived master equation for the reduced density matrix of the OQBM, using both Gaussian and non-Gaussian initial distributions. In each case, the OQBM dynamics converge to several Gaussian distributions. To gain physical insight into the studied system, we also plotted the dynamics of the off-diagonal element of the open quantum Brownian particle and found damped coherent oscillations. Finally, we investigated the time-dependent variance in the position of the OQBM walker and observed initial diffusive spreading, followed by a crossover to a finite steady-state value.

quant-ph↗

arXiv2026

The Cross-Kernel Margin: A Robustness Measure for Quantum Kernel Methods

Quantum devices in the current Noisy Intermediate-Scale Quantum (NISQ) era are inherently affected by noise, which can degrade the predictive performance of quantum machine learning models. In this work, we introduce a new margin-based robustness measure for Quantum Kernel-Assisted Support Vector Machines (QSVMs), termed the cross-kernel margin. This measure quantifies the stability of a classifier learned under a perturbed kernel relative to the ideal feature space. We derive a posteriori stability bounds for the corresponding cross-kernel inverse squared-margin under kernel perturbations using the Tikhonov-stabilised SVM dual formulation. The local depolarising noise model is then applied to this framework to induce perturbations in the kernel. The resulting bounds are numerically checked using simulations across multiple datasets and further tested using kernel matrices obtained from real quantum hardware and a noisy backend simulator. Furthermore, we empirically compare the degradation of test accuracy under local depolarising noise with the commonly used global depolarising noise model in order to motivate its use in our study. Finally, we present empirical results linking margin-based quantities with the generalisation performance of QSVMs, providing additional motivation for our margin-based robustness analysis.

quant-ph↗

arXiv2026

Microscopic derivation of a completely positive master equation for the description of Open Quantum Brownian Motion of a particle in a potential

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.

quant-ph↗

arXiv2025

Generating Generalised Ground-State Ansatzes from Few-Body Examples

We introduce a method that generates ground-state ansatzes for quantum many-body systems which are both analytically tractable and accurate over wide parameter regimes. Our approach leverages a custom symbolic language to construct tensor network states (TNS) via an evolutionary algorithm. This language provides operations that allow the generated TNS to automatically scale with system size. Consequently, we can evaluate ansatz fitness for small systems, which is computationally efficient, while favouring structures that continue to perform well with increasing system size. This ensures that the ansatz captures robust features of the ground state structure. Remarkably, we find analytically tractable ansatzes with a degree of universality, which encode correlations, capture finite-size effects, accurately predict ground-state energies, and offer a good description of critical phenomena. We demonstrate this method on the Lipkin-Meshkov-Glick model (LMG) and the quantum transverse-field Ising model (TFIM), where the same ansatz was independently generated for both. The simple structure of the ansatz allows us to obtain exact expressions for the expectation values of local observables as well as for correlation functions. In addition, it permits symmetries that are broken in the ansatz to be restored, which provides a systematic means of improving the accuracy of the ansatz.

quant-ph↗

arXiv2024

Quantum evolution: terrestrial fine-tuning of magnetic parameters

For the first time in history, humankind might conceivably begin to imagine itself as a multi-planetary species. This goal will entail technical innovation in a number of contexts, including that of healthcare. All life on Earth shares an evolution that is coupled to specific environmental conditions, including gravitational and magnetic fields. While the human body may be able to adjust to short term disruption of these fields during space flights, any long term settlement would have to take into consideration the effects that different fields will have on biological systems, within the space of one lifetime, but also across generations. Magnetic fields, for example, influence the growth of stem cells in regenerative processes. Circadian rhythms are profoundly influenced by magnetic fields, a fact that will likely have an effect on mental as well as physical health. Even the brain responds to small perturbations of this field. One possible mechanism for the effects of weak magnetic fields on biological systems has been suggested to be the radical pair mechanism. The radical pair mechanism originated in the context of spin chemistry to describe how magnetic fields influence the yields of chemical reactions. This mechanism was subsequently incorporated into the field of quantum biology. Quantum biology, most generally, is the study of whether non-trivial quantum effects play any meaningful role in biological systems. The radical pair mechanism has been used most consistently in this context to describe the avian compass. Recently, however, a number of studies have investigated other biological contexts in which the radical pair might play a role, from the action of anaesthetics and antidepressants, to microtubule development and the proper function of the circadian clock... (full abstract in the manuscript)

physics.bio-ph↗

arXiv2024

QAOA Performance in Noisy Devices: The Effect of Classical Optimizers and Ansatz Depth

The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum algorithm for Near-term Intermediate-Scale Quantum computers (NISQ) providing approximate solutions for combinatorial optimiz\-ation problems. The QAOA utilizes a quantum-classical loop, consisting of a quantum ansatz and a classical optimizer, to minimize some cost function, computed on the quantum device. This paper presents an investigation into the impact of realistic noise on the classical optimizer and the determination of optimal circuit depth for the Quantum Approximate Optimization Algorithm (QAOA) in the presence of noise. We find that, while there is no significant difference in the performance of classical optimizers in a state vector simulation, the Adam and AMSGrad optimizers perform best in the presence of shot noise. Under the conditions of real noise, the SPSA optimizer, along with ADAM and AMSGrad, emerge as the top performers. The study also reveals that the quality of solutions to some 5 qubit minimum vertex cover problems increases for up to around six layers in the QAOA circuit, after which it begins to decline. This analysis shows that increasing the number of layers in the QAOA in an attempt to increase accuracy may not work well in a noisy device.

quant-ph↗

arXiv2024

Markovian Noise Modelling and Parameter Extraction Framework for Quantum Devices

In recent years, Noisy Intermediate Scale Quantum (NISQ) computers have been widely used as a test bed for quantum dynamics. This work provides a new hardware-agnostic framework for modelling the Markovian noise and dynamics of quantum systems in benchmark procedures used to evaluate device performance. As an accessible example, the application and performance of this framework is demonstrated on IBM Quantum computers. This framework serves to extract multiple calibration parameters simultaneously through a simplified process which is more reliable than previously studied calibration experiments and tomographic procedures. Additionally, this method allows for real-time calibration of several hardware parameters of a quantum computer within a comprehensive procedure, providing quantitative insight into the performance of each device to be accounted for in future quantum circuits. The framework proposed here has the additional benefit of highlighting the consistency among qubit pairs when extracting parameters, which leads to a less computationally expensive calibration process than evaluating the entire device at once.

quant-ph↗

arXiv2023

Entanglement and coherence in pure and doped Posner molecules

The potential role of spin in biological systems is a primary topic in quantum biology. However, much of this research focuses on electron spin. A recent hypothesis suggests that nuclear spin may be better suited to biological processes, being less sensitive to decoherence. The hypothesis details how phosphorus nuclei might be prepared in a spin-entangled state, how this entanglement is protected by assembly into calcium phosphate (Posner) molecules, and how this entanglement might modulate calcium ion production and concomitant neural activation. In this paper, we investigate the robustness of quantum effects such as coherence and entanglement in Posner molecules. We investigate how these effects are directly dependent on specific parameters such as spin-spin coupling strengths and Posner molecule symmetry. We also investigate how lithium isotope-doped Posner molecules differentially modulate quantum resources such as coherence and entanglement and whether this is a viable explanation for lithium's mechanism of action in bipolar disease. Finally, we illustrate how entanglement might possibly be preserved through the exploitation of the biological environment.

quant-ph↗

arXiv2023

Quantitative Comparison of Nearest Neighbor Search Algorithms

We compare the performance of three nearest neighbor search algorithms: the Orchard, ball tree, and VP-tree algorithms. These algorithms are commonly used for nearest-neighbor searches and are known for their efficiency in large datasets. We analyze the fraction of distances computed in relation to the size of the dataset and its dimension. For each algorithm we derive a fitting function for the efficiency as a function to set size and dimension. The article aims to provide a comprehensive analysis of the performance of these algorithms and help researchers and practitioners choose the best algorithm for their specific application.

cs.DS↗

arXiv2023

Hierarchical quantum circuit representations for neural architecture search

Machine learning with hierarchical quantum circuits, usually referred to as Quantum Convolutional Neural Networks (QCNNs), is a promising prospect for near-term quantum computing. The QCNN is a circuit model inspired by the architecture of Convolutional Neural Networks (CNNs). CNNs are successful because they do not need manual feature design and can learn high-level features from raw data. Neural Architecture Search (NAS) builds on this success by learning network architecture and achieves state-of-the-art performance. However, applying NAS to QCNNs presents unique challenges due to the lack of a well-defined search space. In this work, we propose a novel framework for representing QCNN architectures using techniques from NAS, which enables search space design and architecture search. Using this framework, we generate a family of popular QCNNs, those resembling reverse binary trees. We then evaluate this family of models on a music genre classification dataset, GTZAN, to justify the importance of circuit architecture. Furthermore, we employ a genetic algorithm to perform Quantum Phase Recognition (QPR) as an example of architecture search with our representation. This work provides a way to improve model performance without increasing complexity and to jump around the cost landscape to avoid barren plateaus. Finally, we implement the framework as an open-source Python package to enable dynamic QCNN creation and facilitate QCNN search space design for NAS.

quant-ph↗

arXiv2023

Hybrid Genetic Optimisation for Quantum Feature Map Design

Kernel methods are an important class of techniques in machine learning. To be effective, good feature maps are crucial for mapping non-linearly separable input data into a higher dimensional (feature) space, thus allowing the data to be linearly separable in feature space. Previous work has shown that quantum feature map design can be automated for a given dataset using NSGA-II, a genetic algorithm, while both minimizing circuit size and maximizing classification accuracy. However, the evaluation of the accuracy achieved by a candidate feature map is costly. In this work, we demonstrate the suitability of kernel-target alignment as a substitute for accuracy in genetic algorithm-based quantum feature map design. Kernel-target alignment is faster to evaluate than accuracy and doesn't require some data points to be reserved for its evaluation. To further accelerate the evaluation of genetic fitness, we provide a method to approximate kernel-target alignment. To improve kernel-target alignment and root mean squared error, the final trainable parameters of the generated circuits are further trained using COBYLA to determine whether a hybrid approach applying conventional circuit parameter training can easily complement the genetic structure optimization approach. A total of eight new approaches are compared to the original across nine varied binary classification problems from the UCI machine learning repository, showing that kernel-target alignment and its approximation produce feature map circuits enabling comparable accuracy to the previous work but with larger margins on training data (in excess of 20\% larger) that improve further with circuit parameter training.

quant-ph↗

arXiv2023

Classical Ensembles of Single-Qubit Quantum Variational Circuits for Classification

The quantum asymptotically universal multi-feature (QAUM) encoding architecture was recently introduced and showed improved expressivity and performance in classifying pulsar stars. The circuit uses generalized trainable layers of parameterized single-qubit rotation gates and single-qubit feature encoding gates. Although the improvement in classification accuracy is promising, the single-qubit nature of this architecture, combined with the circuit depth required for accuracy, limits its applications on NISQ devices due to their low coherence times. This work reports on the design, implementation, and evaluation of ensembles of single-qubit QAUM classifiers using classical bagging and boosting techniques. We demonstrate an improvement in validation accuracy for pulsar star classification. We find that this improvement is not problem-specific as we observe consistent improvements for the MNIST Digits and Wisconsin Cancer datasets. We also observe that the boosting ensemble achieves an acceptable level of accuracy with only a small amount of training, while the bagging ensemble achieves higher overall accuracy with ample training time. This shows that classical ensembles of single-qubit circuits present a new approach for certain classification problems.

quant-ph↗

arXiv2022

Statistical and machine learning approaches for prediction of long-time excitation energy transfer dynamics

One of the approaches used to solve for the dynamics of open quantum systems is the hierarchical equations of motion (HEOM). Although it is numerically exact, this method requires immense computational resources to solve. The objective here is to demonstrate whether models such as SARIMA, CatBoost, Prophet, convolutional and recurrent neural networks are able to bypass this requirement. We are able to show this successfully by first solving the HEOM to generate a data set of time series that depict the dissipative dynamics of excitation energy transfer in photosynthetic systems then, we use this data to test the models ability to predict the long-time dynamics when only the initial short-time dynamics is given. Our results suggest that the SARIMA model can serve as a computationally inexpensive yet accurate way to predict long-time dynamics.

quant-ph↗

arXiv2021

Machine learning for excitation energy transfer dynamics

A well-known approach to describe the dynamics of an open quantum system is to compute the master equation evolving the reduced density matrix of the system. This approach plays an important role in describing excitation transfer through photosynthetic light harvesting complexes (LHCs). The hierarchical equations of motion (HEOM) was adapted by Ishizaki and Fleming (J. Chem. Phys., 2009) to simulate open quantum dynamics in the biological regime. We generate a set of time dependent observables that depict the coherent propagation of electronic excitations through the LHCs by solving the HEOM. We solve the inverse problem using classical machine learning (ML) models as this is a computationally intractable problem. The objective here is to determine whether a trained ML model can perform Hamiltonian tomography by using the time dependence of the observables as inputs. We demonstrate the capability of convolutional neural networks to tackle this research problem. The models developed here can predict Hamiltonian parameters such as excited state energies and inter-site couplings of a system up to 99.28\% accuracy and mean-squared error as low as 0.65.

quant-ph↗

arXiv2021

Bad vibrations: Quantum tunnelling in the context of SARS-CoV-2 infection

The SARS-CoV-2 pandemic has added new urgency to the study of viral mechanisms of infection. But while vaccines offer a measure of protection against this specific outbreak, a new era of pandemics has been predicted. In addition to this, COVID-19 has drawn attention to post-viral syndromes and the healthcare burden they entail. It seems integral that knowledge of viral mechanisms is increased through as wide a research field as possible. To this end we propose that quantum biology might offer essential new insights into the problem, especially with regards to the important first step of virus-host invasion. Research in quantum biology often centres around energy or charge transfer. While this is predominantly in the context of photosynthesis there has also been some suggestion that cellular receptors such as olfactory or neural receptors might employ vibration assisted electron tunnelling to augment the lock-and-key mechanism. Quantum tunnelling has also been observed in enzyme function. Enzymes are implicated in the invasion of host cells by the SARS-CoV-2 virus. Receptors such as olfactory receptors also appear to be disrupted by COVID-19. Building on these observations we investigate the evidence that quantum tunnelling might be important in the context of infection with SARS-CoV-2. We illustrate this with a simple model relating the vibronic mode of, for example, a viral spike protein to the likelihood of charge transfer in an idealised receptor. Our results show a distinct parameter regime in which the vibronic mode of the spike protein enhances electron transfer. With this in mind, novel therapeutics to prevent SARS-CoV-2 transmission could potentially be identified by their vibrational spectra.

physics.bio-ph↗

arXiv2021

Near Term Algorithms for Linear Systems of Equations

Finding solutions to systems of linear equations is a common prob\-lem in many areas of science and engineering, with much potential for a speedup on quantum devices. While the Harrow-Hassidim-Lloyd (HHL) quantum algorithm yields up to an exponential speed-up over classical algorithms in some cases, it requires a fault-tolerant quantum computer, which is unlikely to be available in the near term. Thus, attention has turned to the investigation of quantum algorithms for noisy intermediate-scale quantum (NISQ) devices where several near-term approaches to solving systems of linear equations have been proposed. This paper focuses on the Variational Quantum Linear Solvers (VQLS), and other closely related methods. This paper makes several contributions that include: the first application of the Evolutionary Ansatz to the VQLS (EAVQLS), the first implementation of the Logical Ansatz VQLS (LAVQLS), based on the Classical Combination of Quantum States (CQS) method, the first proof of principle demonstration of the CQS method on real quantum hardware and a method for the implementation of the Adiabatic Ansatz (AAVQLS). These approaches are implemented and contrasted.

quant-ph↗

arXiv2021

A Comparison of Various Classical Optimizers for a Variational Quantum Linear Solver

Variational Hybrid Quantum Classical Algorithms (VHQCAs) are a class of quantum algorithms intended to run on noisy intermediate-scale quantum (NISQ) devices. These algorithms employ a parameterized quantum circuit (ansatz) and a quantum-classical feedback loop. A classical device is used to optimize the parameters in order to minimize a cost function that can be computed far more efficiently on a quantum device. The cost function is constructed such that finding the ansatz parameters that minimize its value, solves some problem of interest. We focus specifically on the Variational Quantum Linear Solver (VQLS), and examine the effect of several gradient-free and gradient-based classical optimizers on performance. We focus on both the average rate of convergence of the classical optimizers studied, as well as the distribution of their average termination cost values, and how these are affected by noise. Our work demonstrates that realistic noise levels on NISQ devices present a challenge to the optimization process. All classical optimizers appear to be very negatively affected by the presence of realistic noise. If noise levels are significantly improved, there may be a good reason for preferring gradient-based methods in the future, which performed better than the gradient-free methods with the only shot-noise present. The gradient-free optimizers, Simultaneous Perturbation Stochastic Approximation (SPSA) and Powell's method, and the gradient-based optimizers, AMSGrad and BFGS performed the best in the noisy simulation, and appear to be less affected by noise than the rest of the methods. SPSA appears to be the best performing method. COBYLA, Nelder-Mead and Conjugate-Gradient methods appear to be the most heavily affected by noise, with even slight noise levels significantly impacting their performance.

quant-ph↗

arXiv2020

Negative contributions to entropy production induced by quantum coherences

The entropy production in dissipative processes is the essence of the arrow of time and the second law of thermodynamics. For dissipation of quantum systems, it was recently shown that the entropy production contains indeed two contributions: a classical one and a quantum one. Here we show that for degenerate (or near-degenerate) quantum systems there are additional quantum contributions which, remarkably, can become negative. Furthermore, such negative contributions are related to significant changes in the ongoing thermodynamics. This includes phenomena such as generation of coherences between degenerate energy levels (called horizontal coherences), alteration of energy exchanges and, last but not least, reversal of the natural convergence of the populations toward the thermal equilibrium state. Going further, we establish a complementarity relation between horizontal coherences and population convergence, particularly enlightening for understanding heat flow reversals. Conservation laws of the different types of coherences are derived. Some consequences for thermal machines and resource theory of coherence are suggested.

quant-ph↗