Dissipative Quantum Systems

This paper introduces the Theorem of Topological Dissipation, a novel theoretical framework that demonstrates how topological invariants can direct dissipative processes in hybrid quantum systems. We present a master equation formalism for chiral polaritons formed by the coupling of edge magnetoplasmons (EMPs) in quantum Hall systems with cavity photons. Our central finding is that topological protection can be extended beyond coherent dynamics to actively shape decoherence processes, creating asymmetric dissipation that preserves quantum information along specific directions. The theory predicts exponential suppression of decoherence for anti-chiral modes, with protection scaling as e^(-α|ν|B), where ν is the filling factor and B is the magnetic field strength. We derive experimentally testable predictions, including a Topological Asymmetry Ratio and modified input-output relations for cavity systems. This work establishes the Principle of Topologically Directed Dissipation, opening pathways for dissipation-engineered quantum devices with built-in topological protection.

By analyzing a paradigmatic example of the theory of dissipative systems -the classical and quantum dissipative standard map -we are able to explain the main features of the decay to the quantum equilibrium state. The classical isoperiodic stable structures typically present in the parameter space of these kind of systems play a fundamental role. In fact, we have found that the period of stable structures that are near in this space determines the phase of the leading eigenstates of the corresponding quantum superoperator. Moreover, the eigenvectors show a strong localization on the corresponding periodic orbits (limit cycles). We show that this sort of scarring phenomenon (an established property of Hamiltonian and projectively open systems) is present in the dissipative case and it is of extreme simplicity.

This paper presents an approach to developing computer-aided music composition (CAMC) systemswith quantum computing. CAMC systems are aimed at supporting musicians in creating music ratherthan generating complete pieces of music autonomously. For instance, they may generate ideas orprompts to be further developed during the creative process. We developed a CAMC system using amachine-learning method called Quantum Reservoir Computing (QRC) that learns to create tunes inthe style of given examples. The system proved to run satisfactorily on the Noisy Intermediate-ScaleQuantum (NISQ) machines available today. It does not require large amounts of qubits to outperformequivalent classical Deep Learning methods. Furthermore, it can serve the purposes of a CAMCsystem without the need for big data for training. The paper provides a general introduction to reservoircomputing fundamentals and explains how quantum mechanics can harness its performance. Then, itwalks the reader through the development of our system and presents demonstrations. A comparativeexperiment against a classic Recurrent Neural Network (RNN) model is also discussed.

Reservoir computing is a form of machine learning that utilizes nonlinear
dynamical systems to perform complex tasks in a cost-effective manner when compared to typical neural networks. Recent advancements in reservoir computing, in particular quantum reservoir computing, use reservoirs that are inherently stochastic. In this paper, we investigate the universality of stochastic reservoir computers which use the probabilities of each stochastic reservoir state as the readout instead of the states themselves. This allows the number of readouts to scale exponentially with the size of the reservoir hardware, offering the advantage of compact device size. We prove that classes of stochastic echo state networks form universal approximating classes. We also investigate the performance of two practical examples in classification and chaotic time series prediction. While shot noise is a limiting factor, we show significantly improved performance compared to a deterministic reservoir computer with similar hardware when noise effects are small.

We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential equations in phase space determining the Wigner function of an energy eigenstate of the inverted oscillator. The reflection or transmission coefficients R or T are then given by the total weight of all classical phase space trajectories corresponding to energies below, or above the top of the barrier given by the Wigner function.

Reconstruction of equations of motion from incomplete or noisy data and dimension reduction are two fundamental problems in the study of dynamical systems with many degrees of freedom. For the latter extensive efforts have been made but with limited success to generalize the Zwanzig-Mori projection formalism, originally developed for Hamiltonian systems close to thermodynamic equilibrium, to general non-Hamiltonian systems lacking detailed-balance. One difficulty introduced by such systems is the lack of an invariant measure, needed to define a statistical distribution. Based on a recent discovery that a non-Hamiltonian system defined by a set of stochastic differential equations can be mapped to a Hamiltonian system, we develop such general projection formalism. In the resulting generalized Langevin equations, a set of generalized fluctuation-dissipation relations connect the memory kernel and the random noise terms, analogous to Hamiltonian systems obeying detailed balance. Lacking of these relations restricts previous application of the generalized Langevin formalism. Result of this work may serve as the theoretical basis for further technical developments on model reconstruction with reduced degrees of freedom. We first use an analytically solvable example to illustrate the formalism and the fluctuation-dissipation relation. Our numerical test on a chemical network with end-product inhibition further demonstrates the validity of the formalism. We suggest that the formalism can find wide applications in scientific modeling. Specifically, we discuss potential applications to biological networks. In particular, the method provides a suitable framework for gaining insights into network properties such as robustness and parameter transferability.

We address the problem of spin dynamics in the presence of a thermal bath, by solving exactly the appropriate quantum master equations with continued-fraction methods. The crossover region between the quantum and classical domains is studied by increasing the spin value S, and the asymptote for the classical absorption spectra is eventually recovered. Along with the recognized relevance of the coupling strength, we show the critical role played by the structure of the system-environment interaction in the emergence of classical phenomenology.

Due to the linearity of quantum operations, it is not straightforward to implement nonlinear transformations on a quantum computer, making some practical tasks like a neural network hard to achieve. In this paper, we define a task called nonlinear transformation of complex amplitudes and provide an algorithm to achieve this task. Specifically, we construct a block encoding of complex amplitudes from a state preparation unitary. This allows us to transform the complex amplitudes by using quantum singular value transformation. We evaluate the required overhead in terms of input dimension and precision, which reveals that the algorithm depends on the roughly square root of input dimension and achieves an exponential speedup on precision compared with previous work. We also discuss its possible applications to quantum machine learning, where complex amplitudes encoding classical or quantum data are processed by the proposed method. In this paper, we provide a promising way to introduce the highly complex nonlinearity of the quantum states, which is essentially missing in quantum mechanics.

It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand how quantum mechanics works. I refer to this method as a guided numerical approximation scheme and it is based upon a new look at what the path integral tells us about states in Hilbert space. I begin with simple exactly solvable models and show how to handle problems which cannot be dealt with analytically, this includes the treatment of the evolution of a Gaussian wave-packet in an anharmonic potential as well tunneling problems (i.e., instanton effects)

Based on laboratory based growth of plant-like structures from inorganic materials, we present new theory for the emergence of plant structure at a range of scales dictated by levels of ionization, which can be traced directly back to proteins transcribed from genetic code and their interaction with external sources of charge in real plants. Beyond a critical percolation threshold, individual charge induced quantum potentials merge to form a complex, interconnected geometric web, creating macroscopic quantum potentials, which lead to the emergence of macroscopic quantum processes. The assembly of molecules into larger, ordered structures operates within these charge-induced coherent bosonic fields, acting as a structuring force in competition with exterior potentials. Within these processes many of the phenomena associated with standard quantum theory are recovered, including quantization, non-dissipation, self-organization, confinement, structuration conditioned by the environment,...

If we consider the nucleus as a relativistic composite, then we are able to derive from a many-particle Dirac model a coupling between the center of mass motion and internal nuclear degrees of freedom. This interaction can be rotated out in free space, but has the potential to give rise to new physics when two or more nuclei exchange phonons with a common vibrational mode. The simplest example of such a system is a homonuclear diatomic molecule in a frozen matrix, for which we are able to develop an expression for the second-order phonon–nuclear interaction that can result in a splitting of the nuclear energy levels as a result of excitation transfer between the nuclei. The phonon-nuclear coupling is an E1 interaction, so the low energy 6.237 keV E1 transition in Ta is special; this motivates an interest in molecular Ta2 as a candidate for a Mössbauer experiment where the splitting might be observable. We also consider excitation transfer in the case of a macroscopic a Ta plate. c ©...

We will give an introduction into the quantum search algorithms on the Markov chains introduced by Szegedy and recent modifications based on partially absorbing Markov chains due to Krovi et al. Algorithmica 74, 851 (2016) It has been shown that a quantum search can find a set of marked vertices quadratically faster (in units of the hitting time) for any reversible Markov chain. The proofs are based on certain properties of the stationary state of the partially absorbing walk and rely on quantum phase estimation techniques. We will offer an alternative view of the underlying mechanism of the quantum search based on spectral properties of the quantum walk operator. By considering the complete graph as an example, we identify the relevant two-level quantum subspace leading to a Grover-like rotation in the underlying vector space.

We study out-of-equilibrium energy transport in a quantum critical fluid with Lifshitz scaling symmetry following a local quench between two semi-infinite fluid reservoirs. The late time energy flow is universal and is accommodated via a steady state occupying an expanding central region between outgoing shock and rarefaction waves. We consider the admissibility and entropy conditions for the formation of such a non-equilibrium steady state for a general dynamical critical exponent z in arbitrary dimensions and solve the associated Riemann problem. The Lifshitz fluid with z = 2 can be obtained from a Galilean boost invariant field theory and the non-equilibrium steady state is identified as a boosted thermal state. A Lifshitz fluid with generic z is scale invariant but without boost symmetry and in this case the non-equilibrium steady state is genuinely non-thermal.

Complex microscopic many-body processes are often interpreted in terms of so-called "reaction coordinates", i.e. in terms of the evolution of a small set of coarse-grained observables. A rigorous method to produce the equation of motion of such observables is to use projection operator techniques, which split the dynamics of the observables into a main contribution and a marginal one. The basis of any derivation in this framework is the classical (or quantum) Heisenberg equation for an observable. If the Hamiltonian of the underlying microscopic dynamics and the observable under study do not explicitly depend on time, this equation is obtained by a straightforward derivation. However, the problem is more complicated if one considers Hamiltonians which depend on time explicitly as e.g. in systems under external driving, or if the observable of interest has an explicit dependence on time. We use an analogy to fluid dynamics to derive the classical Heisenberg picture and then apply a projection operator formalism to derive the non-stationary generalized Langevin equation for a coarse-grained variable. We show, in particular, that the results presented for timeindependent Hamiltonians and observables in J. Chem. Phys. 147, 214110 (2017) can be generalized to the time-dependent case.

Reservoir computing is a form of machine learning that utilizes nonlinear dynamical systems to perform complex tasks in a cost-effective manner when compared to typical neural networks. Many recent advancements in reservoir computing, in particular quantum reservoir computing, make use of reservoirs that are inherently stochastic. However, the theoretical justification for using these systems has not yet been well established. In this paper, we investigate the universality of stochastic reservoir computers, in which we use a stochastic system for reservoir computing using the probabilities of each reservoir state as the readout instead of the states themselves. In stochastic reservoir computing, the number of distinct states of the entire reservoir computer can potentially scale exponentially with the size of the reservoir hardware, offering the advantage of compact device size. We prove that classes of stochastic echo state networks, and therefore the class of all stochastic reservoir computers, are universal approximating classes. We also investigate the performance of two practical examples of stochastic reservoir computers in classification and chaotic time series prediction. While shot noise is a limiting factor in the performance of stochastic reservoir computing, we show significantly improved performance compared to a deterministic reservoir computer with similar hardware in cases where the effects of noise are small.

Vibrational energy transfer driven by anharmonicity is the major mechanism of energy dissipation in polyatomic molecules and in molecules embedded in condensed phase environment. Energy transfer pathways are sensitive to the particular intra-molecular structure as well as to specific interactions between the molecule and its environment, and their identification is a challenging many-body problem. This work introduces a theoretical approach which enables to identify the dominant pathways for specified initial excitations, by screening the different possible relaxation channels. For each channel, the many-body Hamiltonian is mapped onto a respective all-vibrational Spin-Boson Hamiltonian, expressed in terms of the harmonic frequencies and the anharmonic coupling parameters obtained from the electronic structure of the molecule in its environment. A focus is given on the formulation of the relaxation rates when different limits of perturbation theory apply. In these cases the proposed Spin-Boson Screening approach becomes especially powerful.

We derive explicit expressions for the first and second moments as well as the correlation function for a planar (one-dimensional) quantum Brownian rotator placed in the external harmonic potential. Our results directly provide the standard deviations for the azimuthal angle and the canonically conjugate angular momentum for the rotator. We find that there are some significant physical differences between this model and the free rotator model, which is well investigated in the literature.

We generalize the effective field theory of single clock inflation to include dissipative effects. Working in unitary gauge we couple a set of composite operators, $$ {\mathcal{O}_{{\mu \nu }}}_{ \ldots } $$ , in the effective action which is constrained solely by invariance under time-dependent spatial diffeomorphisms. We restrict ourselves to situations where the degrees of freedom responsible for dissipation do not contribute to the density perturbations at late time. The dynamics of the perturbations is then modified by the appearance of ‘friction’ and noise terms, and assuming certain locality properties for the Green’s functions of these composite operators, we show that there is a regime characterized by a large friction term γ ≫ H in which the ζ-correlators are dominated by the noise and the power spectrum can be significantly enhanced. We also compute the three point function 〈ζζζ〉 for a wide class of models and discuss under which circumstances large friction leads to an i...

Commonly, nanosystems are characterized by their response to timedependent external fields in the presence of inevitable environmental fluctuations. The direct impact of the external driving on the environment is generally neglected. While this approach is satisfactory for macroscopic systems, on the nanoscale, an interaction of external fields with the environment is often unavoidable on principle. We extend the standard linear response theory of quantum dissipative systems to strongly driven baths. Significant modifications are found for two paradigm examples. First, we evaluate the polarizability of a molecule immersed in a strongly polarizable medium that responds to terahertz radiation. We find an increase of the molecular polarizability by about 30%. Second, we determine the response of a semiconductor quantum dot in close proximity to a metallic nanoparticle. Both are placed in a polarizable medium and exposed to electromagnetic irradiation. We show that the response of the quantum dot is qualitatively modified by the driven nanoparticle, including the generation of an additional channel of stimulated emission.

We develop and exploit an out-of-equilibrium theory, valid in arbitrary dimensions, which does not require initial thermalization. It is perturbative with respect to a weak time-dependent (TD) Hamiltonian term, but is non-perturbative with respect to strong coupling to an electromagnetic environment, or to Coulomb or superconducting correlations. We derive unifying relations between the current generated by coherent radiation or statistical mixture of radiations, superimposed on a dc voltage V dc , and the out-of-equilibrium dc current which encodes the effects of interactions. Thus we extend fully the lateral band-transmission picture, thus quantum superposition, to coherent many-body correlated states. This provides methods for a determination of the carrier's charge q free from unknown parameters through the robustness of the Josephson-like frequency. Similar relations we have derived for noise have allowed, recently, to determine the fractional charge in the Fractional Quantum Hall Effect (FQHE) within the Jain series. 1 The present theory allows for breakdown of inversion symmetry and for asymmetric rates for emission and absorption of radiations. This generates a photo-ratchet effect we exploit to propose a novel method to measure the charge q, as well as spectroscopical analysis of the out-of-equilibrium dc current and the third cumulant of non-gaussian statistical radiations. We apply the theory to the Tomonaga-Luttinger Liquid (TLL), showing a counterintuitive feature: a lorentzian pulse superimposed on V dc can reduce the current compared to its dc value, at the same V dc , questioning the terminology "photo-assisted". Beyond a charge current, the theory applies to operators such as spin current in the spin Hall effect, or voltage drop across a phase-slip Josephson junction.

I want to sincerely thank my advisor, Professor Misha Ovchinnikov, for his considerate support, guidance and encouragement. I have also benefitted immensely from numerous interesting and stimulating discussions with Professors Miguel Alonso and Harry Stern. I will always remain indebted to them for their guidance. My sincerest gratitude also to Debra Haring for her patient help and expert advice in the preparation of manuscripts and other material that have contributed to the completion of this thesis. I will always value Debra's help and guidance. I have been privileged to have as my teachers, Professors Ashok Das, C. R. Hagen, Avijit Lahiri, Arnab Laha, Akhilesh Pandey and Yonathan Shapir, without them my training in Physics would have remained incomplete. This work would not be possible without the blessings of my parents and the prayers of my sister and my wife. Their happiness will always be my best reward. My wife, Sarmistha, came into my life at a very crictical juncture. Her love, encouragement and belief in my abilities will always be my guiding force and inspiration. I also wanted to express my whole hearted gratitude to my extended family. They have welcomed me in to their fold, time spent with them have been among the most happiest in my life. I will always cherish the company of my friends in Rochester, especially

We analyze the propagation of excitons in a d-dimensional lattice with power-law hopping ∝ 1/r α in the presence of dephasing, described by a generalized Haken-Strobl-Reineker model. We show that in the strong dephasing (quantum Zeno) regime the dynamics is described by a classical master equation for an exclusion process with long jumps. In this limit, we analytically compute the spatial distribution, whose shape changes at a critical value of the decay exponent αcr = (d + 2)/2. The exciton always diffuses anomalously: a superdiffusive motion is associated to a Lévy stable distribution with long-range algebraic tails for α ≤ αcr, while for α > αcr the distribution corresponds to a surprising mixed Gaussian profile with long-range algebraic tails, leading to the coexistence of shortrange diffusion and long-range Lévy-flights. In the many-exciton case, we demonstrate that, starting from a domain-wall exciton profile, algebraic tails appear in the distributions for any α, which affects thermalization: the longer the hopping range, the faster equilibrium is reached. Our results are directly relevant to experiments with cold trapped ions, Rydberg atoms and supramolecular dye aggregates. They provide a way to realize an exclusion process with long jumps experimentally.

The time-dependent transmission coefficient for the generalized Kramers problem with exponential memory friction has recently been calculated by Kohen and Tannor [D. Kohen and D. J. Tannor, J. Chem. Phys. 103, 6013 (1995)] using a procedure based on the method of reactive flux and the phase space distribution function. Their analysis is restricted to the high friction regime or diffusion-limited regime. We recently developed a complementary theory for the low-friction energy-diffusion-limited regime in the Markovian limit [Sancho et al., to appear in J. Chem. Phys.; cond-mat/9806001]. Here we generalize our method to the case of an exponential dissipative memory kernel. We test our results, as well as those of Kohen and Tannor, against numerical simulations.

The destruction of quantum coherence can pump energy into a system. For our examples this is paradoxical since the destroyed correlations are ordinarily considered negligible. Mathematically the explanation is straightforward and physically one can identify the degrees of freedom supplying this energy. Nevertheless, the energy input can be calculated without specific reference to those degrees of freedom.

The adiabatic theorem of quantum mechanics states that the error between an instantaneous eigenstate of a time-dependent Hamiltonian and the state given by quantum evolution of duration τ is upper bounded by C/τ for some positive constant C. It has been known for decades that this error can be reduced to C k /τ k+1 if the Hamiltonian has vanishing derivatives up to order k at the beginning and end of the evolution. Here we extend this result to open systems described by a time-dependent Liouvillian superoperator. We find that the same results holds provided the Liouvillian has vanishing derivatives up to order k only at the end of the evolution. This asymmetry is ascribable to the arrow of time inherent in open system evolution. We further investigate whether it is possible to satisfy the required assumptions by controlling only the system, as required for realistic implementations. Surprisingly, we find the answer to be affirmative. We establish this rigorously in the setting of the Davies-Lindblad adiabatic master equation, and numerically in the setting of two different time-dependent Redfield-type master equations we derive. The results are shown to be stable with respect to imperfections in the preparation. Finally, we prove that the results hold also in a fully Hamiltonian model.

We discuss an efficient Hierarchical Effective Mode (HEM) representation of a high-dimensional harmonic oscillator bath, which describes phonon-driven vibrational relaxation of an adsorbate-surface system, namely, deuterium adsorbed on Si(100). Starting from the original Hamiltonian of the adsorbate-surface system, the HEM representation is constructed via iterative orthogonal transformations, which are efficiently implemented with Householder matrices. The detailed description of the HEM representation and its construction are given in the second quantization representation. The hierarchical nature of this representation allows access to the exact quantum dynamics of the adsorbate-surface system over finite time intervals, controllable via the truncation order of the hierarchy. To study the convergence properties of the effective mode representation, we solve the time-dependent Schrödinger equation of the truncated system-bath HEM Hamiltonian, with the help of the multilayer extension of the Multiconfigurational Time-Dependent Hartree (ML-MCTDH) method. The results of the HEM representation are compared with those obtained with a quantum-mechanical tiermodel. The convergence of the HEM representation with respect to the truncation order of the hierarchy is discussed for different initial conditions of the adsorbate-surface system. The combination of the HEM representation with the ML-MCTDH method provides information on the time evolution of the system (adsorbate) and multiple effective modes of the bath (surface). This permits insight into mechanisms of vibration-phonon coupling of the adsorbate-surface system, as well as inter-mode couplings of the effective bath.

The fallacy of the often postulated connection between the passage of time and the process of increasing entropy is shown. An obvious counterexample to this popular hypothesis is the existence and functioning of living organisms living in time with almost unchanged thermodynamic parameters. It is also shown that the application of the second law of thermodynamics to macroscopic subsystems of the Universe as a whole encounters difficulty, since the existence of a hierarchy of nonequilibrium systems determines the growth or decrease of entropy depends on the scale of isolation and consideration of such systems. In particular, the ordering of such a subsystem as the biosphere of the Earth is constant, or increases in time. Therefore, in addition to the well-known laws of thermodynamics, on the basis of the works of I. Prigogine, Yu. Klimontovich, G. Haken, A. Bukalov and others, a new law of nonequilibrium thermodynamics is proposed as a generalization: in highly nonequilibrium open, synergetic systems, their average ordering it is either constant or increases, provided that the incoming flow of energy, information and substance, and the ability of the system elements to function and interact, are maintained.

This paper presents an application of white noise functional approach to derive the quantum propagator and the evolution of the reduced density matrix for an open quantum system consisting of coupled harmonic oscillators which are coupled to a bath consisting of a multimode harmonic oscillator. It is shown that the full quantum propagator is a product of three individual propagators. These propagators were obtained after two successive transformations of the coordinates for the system, and the coordinates for the coupling between the bath and one of the two harmonic oscillators in the system. The obtained propagator is then used to derive the time evolution equation for the density matrix describing the system. The method used to derive the propagator of the open quantum system considered in this paper shows promise for analyzing open quantum systems, due to its ease of use and mathematical rigor.

We develop a Hamiltonian-based microscopic description of laser pump induced displacive coherent phonons. The theory captures the feedback of the phonon excitation upon the electronic fluid, which is missing in the state-of-the-art phenomenological formulation. We show that this feedback leads to chirping at short time scales, even if the phonon motion is harmonic. At long times this feedback appears as a finite phase in the oscillatory signal. We apply the theory to BaFe2As2, explain the origin of the phase in the oscillatory signal reported in recent experiments, and we predict that the system will exhibit red-shifted chirping at larger fluence. Our theory also opens the possibility to extract equilibrium information from coherent phonon dynamics.

High-quality nanomechanical oscillators can sensitively probe force, mass, or displacement in experiments bridging the gap between the classical and quantum domain. Dynamics of these stochastic systems is inherently determined by the interplay between acting external forces, viscous dissipation, and random driving by the thermal environment. The importance of inertia then dictates that both position and momentum must, in principle, be known to fully describe the system, which makes its quantitative experimental characterization rather challenging. We introduce a general method of Bayesian inference of the force field and environmental parameters in stochastic inertial systems that operates solely on the time series of recorded noisy positions of the system. The method is first validated on simulated trajectories of model stochastic harmonic and anharmonic oscillators with damping. Subsequently, the method is applied to experimental trajectories of particles levitating in tailored optical fields and used to characterize the dynamics of particle motion in a nonlinear Duffing potential, a static or time-dependent double-well potential, and a non-conservative force field. The presented inference procedure does not make any simplifying assumptions about the nature or symmetry of the acting force field and provides robust results with trajectories two orders of magnitude shorter than those typically required by alternative inference schemes. In addition to being a powerful tool for quantitative data analysis, it can also guide experimentalists in choosing appropriate sampling frequency (at least 20 measured points per single characteristic period) and length of the measured trajectories (at least 10 periods) to estimate the force field and environmental characteristics with a desired accuracy and precision.

In the era of noisy intermediate scale quantum devices, variational quantum circuits (VQCs) are currently one of the main strategies for building quantum machine learning models. These models are made up of a quantum part and a classical part. The quantum part is given by a parametrization U , which, in general, is obtained from the product of different quantum gates. By its turn, the classical part corresponds to an optimizer that updates the parameters of U in order to minimize a cost function C. However, despite the many applications of VQCs, there are still questions to be answered, such as for example: What is the best sequence of gates to be used? How to optimize their parameters? Which cost function to use? How the architecture of the quantum chips influences the final results? In this article, we focus on answering the last question. We will show that, in general, the cost function will tend to a typical average value the closer the parameterization used is from a 2-design. Therefore, the closer this parameterization is to a 2-design, the less the result of the quantum neural network model will depend on its parametrization. As a consequence, we can use the own architecture of the quantum chips to defined the VQC parametrization, avoiding the use of additional swap gates and thus diminishing the VQC depth and the associated errors.

Interactions by mutual excitation in neural populations in human and animal brains create a mesoscopic order parameter that is recorded in brain waves (electroencephalogram, EEG). Spatially and spectrally distributed oscillations are imposed on the background activity by inhibitory feedback in the gamma range (30-80 Hz). Beats recur at theta rates (3-7 Hz), at which the order parameter transiently approaches zero and microscopic activity becomes disordered. After these null spikes, the order parameter resurges and initiates a frame bearing a mesoscopic spatial pattern of gamma amplitude modulation that governs the microscopic activity, and that is correlated with behavior. The brain waves also reveal a spatial pattern of phase modulation in the form of a cone. Using the formalism of the dissipative many-body model of brain, we describe the null spikes and the accompanying phase cones as vortices.

Open quantum systems evolving according to discrete-time dynamics are capable, unlike continuous-time counterparts, to converge to a stable equilibrium in finite time with zero error. We consider dissipative quantum circuits consisting of sequences of quantum channels subject to specified quasi-locality constraints, and determine conditions under which stabilization of a pure multipartite entangled state of interest may be exactly achieved in finite time. Special emphasis is devoted to characterizing scenarios where finite-time stabilization may be achieved robustly with respect to the order of the applied quantum maps, as suitable for unsupervised control architectures. We show that if a decomposition of the physical Hilbert space into virtual subsystems is found, which is compatible with the locality constraint and relative to which the target state factorizes, then robust stabilization may be achieved by independently cooling each component. We further show that if the same condition holds for a scalable class of pure states, a continuous-time quasilocal Markov semigroup ensuring rapid mixing can be obtained. Somewhat surprisingly, we find that the commutativity of the canonical parent Hamiltonian one may associate to the target state does not directly relate to its finite-time stabilizability properties, although in all cases where we can guarantee robust stabilization, a (possibly non-canonical) commuting parent Hamiltonian may be found. Beside graph states, quantum states amenable to finite-time robust stabilization include a class of universal resource states displaying two-dimensional symmetry-protected topological order, along with tensor network states obtained by generalizing a construction due to Bravyi and Vyalyi. Extensions to representative classes of mixed graph-product and thermal states are also discussed.

Quantum computing has become a promising computing approach because of its capability to solve certain problems, exponentially faster than classical computers. A n -qubit quantum system is capable of providing 2 n computational space to a quantum algorithm. However, quantum computers are prone to errors. Quantum circuits that can reliably run on today’s Noisy Intermediate-Scale Quantum (NISQ) devices are not only limited by their qubit counts but also by their noisy gate operations. In this article, we have introduced i -QER, a scalable machine learning-based approach to evaluate errors in a quantum circuit and reduce these without using any additional quantum resources. The i -QER predicts possible errors in a given quantum circuit using supervised learning models. If the predicted error is above a pre-specified threshold, it cuts the large quantum circuit into two smaller sub-circuits using an error-influenced fragmentation strategy for the first time to the best of our knowledge....

Dissipation can be used as a resource to control and simulate quantum systems. We discuss a modular model based on fast dissipation capable of performing universal quantum computation, and simulating arbitrary Lindbladian dynamics. The model consists of a network of elementary dissipation-generated modules and it is in principle scalable. In particular, we demonstrate the ability to dissipatively prepare all single qubit gates, and the CNOT gate; prerequisites for universal quantum computing. We also show a way to implement a type of quantum memory in a dissipative environment, whereby we can arbitrarily control the loss in both coherence, and concurrence, over the evolution. Moreover, our dissipation-assisted modular construction exhibits a degree of inbuilt robustness to Hamiltonian, and indeed Lindbladian errors, and as such is of potential practical relevance.

We develop and exploit an out-of-equilibrium theory, valid in arbitrary dimensions, which does not require initial thermalization. It is perturbative with respect to a weak time-dependent (TD) Hamiltonian term, but is non-perturbative with respect to strong coupling to an electromagnetic environment, or to Coulomb or superconducting correlations. We derive unifying relations between the current generated by coherent radiation or statistical mixture of radiations, superimposed on a dc voltage V dc , and the out-of-equilibrium dc current which encodes the effects of interactions. Thus we extend fully the lateral band-transmission picture, thus quantum superposition, to coherent many-body correlated states. This provides methods for a determination of the carrier's charge q free from unknown parameters through the robustness of the Josephson-like frequency. Similar relations we have derived for noise have allowed, recently, to determine the fractional charge in the Fractional Quantum Hall Effect (FQHE) within the Jain series. 1 The present theory allows for breakdown of inversion symmetry and for asymmetric rates for emission and absorption of radiations. This generates a photo-ratchet effect we exploit to propose a novel method to measure the charge q, as well as spectroscopical analysis of the out-of-equilibrium dc current and the third cumulant of non-gaussian statistical radiations. We apply the theory to the Tomonaga-Luttinger Liquid (TLL), showing a counterintuitive feature: a lorentzian pulse superimposed on V dc can reduce the current compared to its dc value, at the same V dc , questioning the terminology "photo-assisted". Beyond a charge current, the theory applies to operators such as spin current in the spin Hall effect, or voltage drop across a phase-slip Josephson junction.

The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its dynamical evolution, is perhaps the most elegant and universal framework developed in theoretical physics, second only to the standard model of particle physics. In this Tutorial, we retrace the steps that led to the creation of such a remarkable framework, discuss its foundations, and present some of the classical examples of problems that can be solved using the path integral formalism, as a way to introduce the readers to the topic and help them get familiar with the formalism. Then, we focus our attention on the use of path integrals in optics and photonics and discuss in detail how they have been used in the past to approach several problems, ranging from the propagation of light in inhomogeneous media to parametric amplification and quantum nonlin...

We present a rigorous method to set up a system-bath Hamiltonian for the coupling of adsorbate vibrations (the system) to surface phonons (the bath). The Hamiltonian is straightforward to derive and exact up to second order in the environment coordinates, thus capable of treating one-and two-phonon contributions to vibration-phonon coupling. The construction of the Hamiltonian uses orthogonal coordinates for system and bath modes, is based on an embedded cluster approach, and generalizes previous Hamiltonians of a similar type, but avoids several (additional) approximations. While the parametrization of the full Hamiltonian is in principle feasible by a first principles quantum mechanical treatment, here we adopt in the spirit of a QM/MM model a combination of density functional theory (''QM", for the system) and a semiempirical forcefield (''MM", for the bath). We apply the Hamiltonian to a fully H-covered Si(100)-(2 Â 1) surface, using Fermi's Golden Rule to obtain vibrational relaxation rates of various H-Si bending modes of this system. As in earlier work it is found that the relaxation is dominated by two-phonon contributions because of an energy gap between the Si-H bending modes and the Si phonon bands. We obtain vibrational lifetimes (of the first excited state) on the order of 2 ps at T ¼ 0 K. The lifetimes depend only little on the type of bending mode (symmetric vs. antisymmetric, parallel vs. perpendicular to the Si 2 H 2 dimers). They decrease by a factor of about two when heating the surface to 300 K. We also study isotope effects by replacing adsorbed H atoms by deuterium, D. The Si-D bending modes are shifted into the Si phonon band of the solid, opening up one-phonon decay channels and reducing the lifetimes to few hundred fs.

Mattias T. Johnsson, Ben Q. Baragiola, 3, 4 Thomas Volz, 4 and Gavin K. Brennen 4 Department of Physics and Astronomy, Macquarie University, North Ryde, NSW 2109, Australia Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan Centre for Quantum Computation and Communication Technology, School of Science, RMIT University, Melbourne, VIC 3001, Australia Centre for Engineered Quantum Systems, Department of Physics and Astronomy, Macquarie University, North Ryde, NSW 2109, Australia

Bayesian Networks (BN) are probabilistic graphical models that are widely used for uncertainty modeling, stochastic prediction and probabilistic inference. A Quantum Bayesian Network (QBN) is a quantum version of the Bayesian network that utilizes the principles of quantum mechanical systems to improve the computational performance of various analyses. In this paper, we experimentally evaluate the performance of QBN on various IBM QX hardware against Qiskit simulator and classical analysis. We consider a 4-node BN for stock prediction for our experimental evaluation. We construct a quantum circuit to represent the 4-node BN using Qiskit, and run the circuit on nine IBM quantum devices: Yorktown,

Recently a path integral formalism has been proposed by the author which gives the time evolution of moments of slow variables in a Hamiltonian statistical system. This closure relies on evaluating the informational discrepancy of a time sequence (path) of approximating densities from the Liouvillian evolution that an exact density must follow. The discrepancy is then used to weight all possible paths using a generalized Boltzmann principle. That formalism is extended here to deal with more general and realistic autonomous dynamical systems. There the divergence of the time derivative of dynamical variables need not vanish as it does in the Hamiltonian case and this property complicates the closure derivation. Many interesting and realistic applications are covered by this new formalism including those describing realistic turbulence and the relevant specifics of this situation are outlined. The practical issues associated with the implementation of the outlined formalism are also discussed.

Starting with the mixed quantum±classical Liouville equation, projection operator methods are used to derive an equation of motion for a quantum subsystem dissipatively interacting with a classical bath. The resulting generalized master equation is reduced to the Lindblad equation after making a Markovian approximation in the weak coupling limit. The bath subsystem dynamics is studied from a similar perspective. For situations where the classical subsystem consists of few degrees of freedom, or one is interested in the nature of the modi®cations of its dynamics as a result of coupling to a large, rapidly relaxing quantum bath, a classical analog of the Lindblad equation is derived and discussed.

The time evolution of transition amplitudes at Ii-t 0 7.3 Stochastic Van Vleck formula .. 7.4 A particle in a plane wave. .. . 7.5 Examples of stochastic dynamics 7.6 Relativistic quantum dynamics 8 Complex dynamics and coherent states 118 8.1 Constants of motion and action-angle variables 8.2 Coherent states and quantum dynamics in the non-classical region. .. .. .. .. .. . 8.3 Expansion of coherent states in eigenfunctions. 8.4 Correlation functions of the complex process .. 127 134 137 Contents 9 Quantum non-linear oscillations 9.1 Perturbations of the harmonic oscillator 9.2 The semi-classical expansion of oscillatory systems 9.3 Unstable oscillations in quantum mechanics ... 9.4 The transition function of the oscillatory process .

The quantum Langevin equation has been studied for dissipative system using the approach of Ford et al. Here, we have considered the inverted harmonic oscillator potential and calculated the effect of dissipation on tunneling time, group delay, and the self-interference term. A critical value of the friction coefficient has been determined for which the self-interference term vanishes. This approach sheds new light on understanding the ion transport at nanoscale.

Noisy Intermediate-Scale Quantum (NISQ) computers are enabling development and evaluation of real quantum algorithms, but due to their highly erroneous nature, careful selection of qubits to map the algorithm on to real hardware is required to minimize the error rate of the algorithm output. In this paper, we propose UREQA, a new approach that introduces quantum-operation-aware error rate prediction to minimize of output errors of quantum algorithms running on NISQ devices.

We present a microscopic approach to quantum dissipation and sketch the derivation of the kinetic equation describing the evolution of a simple quantum system in interaction with a complex quantum system. A typical quantum complex system is modeled by means of parametric banded random matrices coupled to the subsystem of interest. We do not assume the weak coupling limit and allow for an independent dynamics of the "reservoir". We discuss the reasons for having a new theoretical approach and the new elements introduced by us. The present approach incorporates known limits and previous results, but at the same time includes new cases, previously never derived on a microscopic level. We briefly discuss the kinetic equation and its solution for a particle in the absence of an external field.

The microscopic origin of dissipation of a driven quantum many body system is addressed in the framework of a parametric banded random matrix approach. We find noticeable violations of the fluctuation-dissipation theorem and we observe also that the energy diffusion has a markedly non-Gaussian character. Within the Feynman-Vernon path integral formalism and in the Markovian limit, we further consider the time evolution of a slow subsystem coupled to such a "bath" of intrinsic degrees of freedom. We show that dissipation leads to qualitative modifications of the time evolution of the density matrix of the slow subsystem. In either the spatial, momentum or energy representation the density distribution acquires very long tails and tunneling is greatly enhanced. 1 To be published in a special issue on Chaos and Quantum Transport in Mesoscopic Cosmos of the journal Chaos, Solitons & Fractals, July (tentatively) 1997, guest editor K. Nakamura.

We describe the application of the semiclassical Liouville method for simulating coherent quantum dynamics to the ultrafast dephasing of OH vibrational quantum coherence in liquid water. We simulate the decay of quantum coherence between the n = 0 and 1 vibrational states of the OH oscillator of dilute HOD in D 2 O using the approach. A novel quantum state dependent Hamiltonian based on the classical TIP3P potential of water is employed to allow quantum delocalization of the hydrogen atom in the OH bond to be treated. The vibrational dephasing time scale observed agrees qualitatively with recent experiments and molecular dynamics simulations.