arXiv subjects

Cristian Zanoci

Publications and source records attributed to Cristian Zanoci.

10 recordsLinked to original sources

arXiv2023

Thermalization at Low Temperatures via Weakly-Damped Multi-Site Baths

We study the thermalization properties of one-dimensional open quantum systems coupled to baths at their boundary. The baths are driven to their thermal states via Lindblad operators, while the system undergoes Hamiltonian dynamics. We specifically consider multi-site baths and investigate the extent to which the late-time steady state resembles a Gibbs state at some controllable temperature set by the baths. We study three models: a non-interacting fermion model accessible via free-fermion technology, and two interacting models, the XZ model and the chiral clock model, which are accessible via tensor network methods. We show that, by tuning towards the weak coupling and slow relaxation limits, one can engineer low temperatures in the bulk of the system provided the bath size is big enough. We use this capability to study energy transport in the XZ model at lower temperatures than previously reported. Our work paves the way for future studies of interacting open quantum systems at low temperatures.

cond-mat.str-el↗

arXiv2022

Near-Equilibrium Approach to Transport in Complex Sachdev-Ye-Kitaev Models

We study the non-equilibrium dynamics of a one-dimensional complex Sachdev-Ye-Kitaev chain by directly solving for the steady state Green's functions in terms of small perturbations around their equilibrium values. The model exhibits strange metal behavior without quasiparticles and features diffusive propagation of both energy and charge. We explore the thermoelectric transport properties of this system by imposing uniform temperature and chemical potential gradients. We then expand the conserved charges and their associated currents to leading order in these gradients, which we can compute numerically and analytically for different parameter regimes. This allows us to extract the full temperature and chemical potential dependence of the transport coefficients. In particular, we uncover that the diffusivity matrix takes on a simple form in various limits and leads to simplified Einstein relations. At low temperatures, we also recover a previously known result for the Wiedemann-Franz ratio. Furthermore, we establish a relationship between diffusion and quantum chaos by showing that the diffusivity eigenvalues are upper bounded by the chaos propagation rate at all temperatures. Our work showcases an important example of an analytically tractable calculation of transport properties in a strongly interacting quantum system and reveals a more general purpose method for addressing strongly coupled transport.

cond-mat.str-el↗

arXiv2021

Energy Transport in Sachdev-Ye-Kitaev Networks Coupled to Thermal Baths

We develop a general framework for studying the equilibrium and non-equilibrium properties of arbitrary networks of Sachdev-Ye-Kitaev clusters coupled to thermal baths. We proceed to apply this technique to the problem of energy transport, which is known to be diffusive due to the strange metal behavior of these models. We use the external baths to impose a temperature gradient in the system and study the emerging non-equilibrium steady state using the Schwinger-Keldysh formalism. We consider two different configurations for the baths, implementing either a boundary or bulk driving, and show that the latter leads to a significantly faster convergence to the steady state. This setup allows us to compute both the temperature and frequency dependence of the diffusion constant. At low temperatures, our results agree perfectly with the previously known values for diffusivity in the conformal limit. We also establish a relationship between energy transport and quantum chaos by showing that the diffusion constant is upper bounded by the chaos propagation rate at all temperatures. Moreover, we find a simple analytical form for the non-equilibrium Green's functions in the linear response regime and use it to derive exact closed-form expressions for the diffusion constant in various limits. We mostly focus on uniform one-dimensional chains, but we also discuss higher-dimensional generalizations.

cond-mat.str-el↗

arXiv2021

Quantum Sampling Algorithms, Phase Transitions, and Computational Complexity

Drawing independent samples from a probability distribution is an important computational problem with applications in Monte Carlo algorithms, machine learning, and statistical physics. The problem can in principle be solved on a quantum computer by preparing a quantum state that encodes the entire probability distribution followed by a projective measurement. We investigate the complexity of adiabatically preparing such quantum states for the Gibbs distributions of various classical models including the Ising chain, hard-sphere models on different graphs, and a model encoding the unstructured search problem. By constructing a parent Hamiltonian, whose ground state is the desired quantum state, we relate the asymptotic scaling of the state preparation time to the nature of transitions between distinct quantum phases. These insights enable us to identify adiabatic paths that achieve a quantum speedup over classical Markov chain algorithms. In addition, we show that parent Hamiltonians for the problem of sampling from independent sets on certain graphs can be naturally realized with neutral atoms interacting via highly excited Rydberg states.

quant-ph↗

arXiv2021

Quantum Sampling Algorithms for Near-Term Devices

Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of quantum algorithms that provide unbiased samples by preparing a state encoding the entire Gibbs distribution. We show that this approach leads to a speedup over a classical Markov chain algorithm for several examples including the Ising model and sampling from weighted independent sets of two different graphs. Our approach connects computational complexity with phase transitions, providing a physical interpretation of quantum speedup. Moreover, it opens the door to exploring potentially useful sampling algorithms on near-term quantum devices as the algorithm for sampling from independent sets on certain graphs can be naturally implemented using Rydberg atom arrays.

quant-ph↗

arXiv2020

Temperature Dependent Energy Diffusion in Chaotic Spin Chains

We study the temperature dependence of energy diffusion in two chaotic gapped quantum spin chains, a tilted-field Ising model and an XZ model, using an open system approach. We introduce an energy imbalance by coupling the chain to thermal baths at its boundary and study the non-equilibrium steady states of the resulting Lindblad dynamics using a matrix product operator ansatz for the density matrix. We define an effective local temperature profile by comparing local reduced density matrices in the steady state to those of a uniform thermal state. We then measure the energy current for a variety of driving temperatures and extract the temperature dependence of the energy diffusion constant. For the Ising model, we are able to study temperatures well below the energy gap and find a regime of dilute excitations where rare three-body collisions control energy diffusion. A kinetic model correctly predicts the observed exponential increase of the energy diffusion constant at low temperatures. For the XZ model, we are only able to access intermediate to high temperatures relative to the energy gap and we show that the data is well described by an expansion around the infinite temperature limit. We also discuss the limitations of the particular driving scheme and suggest that lower temperatures can be accessed using larger baths.

cond-mat.str-el↗

arXiv2020

Entanglement and thermalization in open fermion systems

We numerically study two non-interacting fermion models, a quantum wire model and a Chern insulator model, governed by open system Lindblad dynamics. The physical setup consists of a unitarily evolving "bulk" coupled via its boundaries to two dissipative "leads". The open system dynamics is chosen to drive the leads to thermal equilibrium, and by choosing different temperatures and chemical potentials for the two leads we may drive the bulk into a non-equilibrium current carrying steady state. We report two main results in this context. First, we show that for an appropriate choice of dynamics of the leads, the bulk state is also driven to thermal equilibrium even though the open system dynamics does not act directly on it. Second, we show that the steady state which emerges at late time, even in the presence of currents, is lightly entangled in the sense of having small mutual information and conditional mutual information for appropriate regions. We also report some results for the rate of approach to the steady state. These results have bearing on recent attempts to formulate a numerically tractable method to compute currents in strongly interacting models; specifically, they are relevant for the problem of designing simple leads that can drive a target system into thermal equilibrium at low temperature.

cond-mat.mes-hall↗

arXiv2019

Heuristic Recurrent Algorithms for Photonic Ising Machines

The inability of conventional electronic architectures to efficiently solve large combinatorial problems motivates the development of novel computational hardware. There has been much effort recently toward developing novel, application-specific hardware, across many different fields of engineering, such as integrated circuits, memristors, and photonics. However, unleashing the true potential of such novel architectures requires the development of featured algorithms which optimally exploit their fundamental properties. We here present the Photonic Recurrent Ising Sampler (PRIS), a heuristic method tailored for parallel architectures that allows for fast and efficient sampling from distributions of combinatorially hard Ising problems. Since the PRIS relies essentially on vector-to-fixed matrix multiplications, we suggest the implementation of the PRIS in photonic parallel networks, which realize these operations at an unprecedented speed. The PRIS provides sample solutions to the ground state of arbitrary Ising models, by converging in probability to their associated Gibbs distribution. By running the PRIS at various noise levels, we probe the critical behavior of universality classes and their critical exponents. In addition to the attractive features of photonic networks, the PRIS relies on intrinsic dynamic noise and eigenvalue dropout to find ground states more efficiently. Our work suggests speedups in heuristic methods via photonic implementations of the PRIS. We also hint at a broader class of (meta)heuristic algorithms derived from the PRIS, such as combined simulated annealing on the noise and eigenvalue dropout levels. Our algorithm can also be implemented in a competitive manner on fast parallel electronic hardware, such as FPGAs and ASICs.

physics.app-ph↗

arXiv2019

Near-Term Quantum-Classical Associative Adversarial Networks

We introduce a new hybrid quantum-classical adversarial machine learning architecture called a quantum-classical associative adversarial network (QAAN). This architecture consists of a classical generative adversarial network with a small auxiliary quantum Boltzmann machine that is simultaneously trained on an intermediate layer of the discriminator of the generative network. We numerically study the performance of QAANs compared to their classical counterparts on the MNIST and CIFAR-10 data sets, and show that QAANs attain a higher quality of learning when evaluated using the Inception score and the Fréchet Inception distance. As the QAAN architecture only relies on sampling simple local observables of a small quantum Boltzmann machine, this model is particularly amenable for implementation on the current and next generations of quantum devices.

cs.LG↗

arXiv2018

Ensemble Inhibition and Excitation in the Human Cortex: an Ising Model Analysis with Uncertainties

The pairwise maximum entropy model, also known as the Ising model, has been widely used to analyze the collective activity of neurons. However, controversy persists in the literature about seemingly inconsistent findings, whose significance is unclear due to lack of reliable error estimates. We therefore develop a method for accurately estimating parameter uncertainty based on random walks in parameter space using adaptive Markov Chain Monte Carlo after the convergence of the main optimization algorithm. We apply our method to the spiking patterns of excitatory and inhibitory neurons recorded with multielectrode arrays in the human temporal cortex during the wake-sleep cycle. Our analysis shows that the Ising model captures neuronal collective behavior much better than the independent model during wakefulness, light sleep, and deep sleep when both excitatory (E) and inhibitory (I) neurons are modeled; ignoring the inhibitory effects of I-neurons dramatically overestimates synchrony among E-neurons. Furthermore, information-theoretic measures reveal that the Ising model explains about 80%-95% of the correlations, depending on sleep state and neuron type. Thermodynamic measures show signatures of criticality, although we take this with a grain of salt as it may be merely a reflection of long-range neural correlations.

cond-mat.dis-nn↗