arXiv subjects

Xiansong Xu

Publications and source records attributed to Xiansong Xu.

At least 19 recordsLinked to original sources

arXiv2026

Time-evolving matrix product operators for off-diagonal system-bath coupling

The time-evolving matrix product operator (TEMPO) method has proven to be a powerful method to study the long-time dynamics of bosonic impurity problems where a small system is linearly coupled to a noninteracting bosonic bath. However, current developments of TEMPO have mostly focused on the case of diagonal system-bath coupling, i.e., $\sum_k \Aop(V_k \bdop_k + \hc)$, with $\Aop$ a Hermitian operator of the system. Based on the process tensor framework, we extend TEMPO to the more general case of off-diagonal system-bath coupling in the form $\sum_k (V_k\Aop\bdop_k + \hc)$, where $\Aop$ could be non-Hermitian. As applications, we study the real-time dynamics of a spin that is coupled to a sub-ohmic bath via the Jaynes-Cummings-type system-bath coupling and compare it against the standard spin-boson model, where we show that the commonly used rotating-wave approximation could be very poor for this bath. We also study the imaginary-time evolution of a bosonic impurity with nonzero on-site interaction that is coupled to a sub-ohmic bath, to illustrate the flexibility of our method. Our method provides a unified framework to understand different variants of TEMPO, and is a promising building block for an impurity solver in the bosonic dynamical mean field theory for the normal phase with a scalar hybridization function.

cond-mat.mes-hall↗

arXiv2026

Polaron Transformed Canonically Consistent Quantum Master Equation

A central challenge in the theory of open quantum systems is the development of theoretical frameworks capable of accurately describing large, strongly interacting quantum many-body systems in the regime of strong system-bath interactions. In this work, we take a step toward this goal by formulating a polaron-transformed version of the canonically consistent quantum master equation (CCQME) [T. Becker \emph{et~al.}, Phys. Rev. Lett. \textbf{129}, 200403 (2022)]. The CCQME extends beyond standard weak coupling approaches while retaining the same numerical complexity as conventional quantum master equations, thereby enabling the treatment of large quantum systems. The polaron transformation further enhances the accessible system-bath interaction strengths, allowing us to move from moderate to ultra-strong interaction regimes. We present a unified and transparent derivation of these two approaches and combine them to obtain the polar-transformed CCQME (PT-CCQME). Applying our method to the paradigmatic spin boson model, we find excellent agreement with numerically exact time-evolving matrix product operator (TEMPO) simulations. Finally, we predict an initial-state-independent \emph{slowing} down of thermalization in the strong-coupling regime of the spin-boson model.

quant-ph↗

arXiv2026

Grassmann time-evolving matrix product operators for fermionic impurities coupled to a superconducting bath

The Grassmann time-evolving matrix product operator (GTEMPO) method, which represents the Feynman-Vernon influence functional as a temporal matrix product state, has been shown to be a flexible and potentially scalable solution for fermionic quantum impurity problems. In this work, we extend GTEMPO to solve fermionic impurity problems in the Nambu formalism, in which the impurity is coupled to a superconducting bath. A key insight is that by employing the Bogoliubov transformation for the superconducting bath, one could obtain the analytic expression of the Feynman-Vernon influence functional in a similar form to the case of a normal bath, after which the core algorithms of GTEMPO can be straightforwardly adapted. We demonstrate the accuracy of our method by benchmarking it against exact diagonalization in several exactly solvable cases, and against the continuous-time quantum Monte Carlo method using converged dynamical mean field theory (DMFT) iterations on the imaginary contour in the non-integrable case. In all cases, we perform both imaginary- and real-time calculations to illustrate the flexibility of our method. These results illustrate that our method could be potentially useful as an impurity solver in DMFT as well as its non-equilibrium extension for fermionic impurity problems in the Nambu formalism.

cond-mat.str-el↗

arXiv2026

Continuous-time parametrization of neural quantum states for quantum dynamics

Neural quantum states are a promising framework for simulating many-body quantum dynamics, as they can represent states with volume-law entanglement. As time evolves, the neural network parameters are typically optimized at discrete time steps to approximate the wave function at each point in time. Given the differentiability of the wave function stemming from the Schrödinger equation, here we impose a time-continuous and differentiable parameterization of the neural network by expressing its parameters as linear combinations of temporal basis functions with trainable, time-independent coefficients. We test this ansatz, referred to as the smooth neural quantum state (\textit{s}-NQS) with a loss function defined over an extended time interval, under a sudden quench of a non-integrable many-body quantum spin chain. We demonstrate accurate time evolution using a restricted Boltzmann machine as the instantaneous neural network architecture. We show that the parameterization enables accurate simulations with fewer variational parameters, independent of time-step resolution. Furthermore, the smooth neural quantum state also allows us to initialize and evaluate the wave function at times not included in the training set, both within and beyond the training interval.

quant-ph↗

arXiv2025

Hydrodynamics and the eigenstate thermalization hypothesis

The eigenstate thermalization hypothesis (ETH) describes the properties of diagonal and off-diagonal matrix elements of local operators in the eigenenergy basis. In this work, we propose a relation between (i) the singular behaviour of the off-diagonal part of ETH at small energy differences, and (ii) the smooth profile of the diagonal part of ETH as a function of the energy density. We establish this connection from the decay of the autocorrelation functions of local operators, which is constrained by the presence of local conserved quantities whose evolution is described by hydrodynamics. We corroborate our predictions with numerical simulations of two non-integrable spin-1 Ising models, one diffusive and one super-diffusive, which we perform using dynamical quantum typicality up to 18 spins.

quant-ph↗

arXiv2024

Emergence of steady quantum transport in a superconducting processor

Non-equilibrium quantum transport is crucial to technological advances ranging from nanoelectronics to thermal management. In essence, it deals with the coherent transfer of energy and (quasi-)particles through quantum channels between thermodynamic baths. A complete understanding of quantum transport thus requires the ability to simulate and probe macroscopic and microscopic physics on equal footing. Using a superconducting quantum processor, we demonstrate the emergence of non-equilibrium steady quantum transport by emulating the baths with qubit ladders and realising steady particle currents between the baths. We experimentally show that the currents are independent of the microscopic details of bath initialisation, and their temporal fluctuations decrease rapidly with the size of the baths, emulating those predicted by thermodynamic baths. The above characteristics are experimental evidence of pure-state statistical mechanics and prethermalisation in non-equilibrium many-body quantum systems. Furthermore, by utilising precise controls and measurements with single-site resolution, we demonstrate the capability to tune steady currents by manipulating the macroscopic properties of the baths, including filling and spectral properties. Our investigation paves the way for a new generation of experimental exploration of non-equilibrium quantum transport in strongly correlated quantum matter.

quant-ph↗

arXiv2024

Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations

Developing numerical exact solvers for open quantum systems is a challenging task due to the non-perturbative and non-Markovian nature when coupling to structured environments. The Feynman-Vernon influence functional approach is a powerful analytical tool to study the dynamics of open quantum systems. Numerical treatments of the influence functional including the quasi-adiabatic propagator technique and the tensor-network-based time-evolving matrix product operator method, have proven to be efficient in studying open quantum systems with bosonic environments. However, the numerical implementation of the fermionic path integral suffers from the Grassmann algebra involved. In this work, we present a detailed introduction of the Grassmann time-evolving matrix product operator method for fermionic open quantum systems. In particular, we introduce the concepts of Grassmann tensor, signed matrix product operator, and Grassmann matrix product state to handle the Grassmann path integral. Using the single-orbital Anderson impurity model as an example, we review the numerical benchmarks for structured fermionic environments for real-time nonequilibrium dynamics, real-time and imaginary-time equilibration dynamics, and its application as an impurity solver. These benchmarks show that our method is a robust and promising numerical approach to study strong coupling physics and non-Markovian dynamics. It can also serve as an alternative impurity solver to study strongly-correlated quantum matter with dynamical mean-field theory.

cond-mat.str-el↗

arXiv2024

Paths towards time evolution with larger neural-network quantum states

In recent years, the neural-network quantum states method has been investigated to study the ground state and the time evolution of many-body quantum systems. Here we expand on the investigation and consider a quantum quench from the paramagnetic to the anti-ferromagnetic phase in the tilted Ising model. We use two types of neural networks, a restricted Boltzmann machine and a feed-forward neural network. We show that for both types of networks, the projected time-dependent variational Monte Carlo (p-tVMC) method performs better than the non-projected approach. We further demonstrate that one can use K-FAC or minSR in conjunction with p-tVMC to reduce the computational complexity of the stochastic reconfiguration approach, thus allowing the use of these techniques for neural networks with more parameters.

quant-ph↗

arXiv2024

Real-time Impurity Solver Using Grassmann Time-Evolving Matrix Product Operators

An emergent and promising tensor-network-based impurity solver is to represent the path integral as a matrix product state, where the bath is analytically integrated out using Feynman-Vernon influence functional. Here we present an approach to calculate the equilibrium impurity spectral function based on the recently proposed Grassmann time-evolving matrix product operators method. The central idea is to perform a quench from a separable impurity-bath initial state as in the non-equilibrium scenario. The retarded Green's function $G(t+t_0, t'+t_0)$ is then calculated after an equilibration time $t_0$ such that the impurity and bath are approximately in thermal equilibrium. There are two major advantages of this method. First, since we focus on real-time dynamics, we do not need to perform the numerically ill-posed analytic continuation in the continuous-time quantum Monte Carlo case that relies on imaginary-time evolution. Second, the entanglement growth of the matrix product states in real-time calculations is observed to be much slower than that in imaginary-time calculations, leading to a significant improvement in numerical efficiency. The accuracy of this method is demonstrated in the single-orbital Anderson impurity model and benchmarked against the continuous-time quantum Monte Carlo method.

cond-mat.str-el↗

arXiv2024

Grassmann Time-Evolving Matrix Product Operators for Equilibrium Quantum Impurity Problems

Tensor-network-based methods are promising candidates to solve quantum impurity problems. They are free of sampling noises and the sign problem compared to state-of-the-art continuous-time quantum Monte Carlo methods. Recent progress made in tensor-network-based impurity solvers is to use the Feynman-Vernon influence functional to integrate out the bath analytically, retaining only the impurity dynamics and representing it compactly as a matrix product state. The recently proposed Grassmann time-evolving matrix product operator (GTEMPO) method is one of the representative methods in this direction. In this work, we systematically study the performance of GTEMPO in solving equilibrium quantum impurity problems at a finite temperature with a semicircular spectrum density of the bath. Our results show that its computational cost would generally increase as the temperature goes down and scale exponentially with the number of orbitals. In particular, the single-orbital Anderson impurity model can be efficiently solved with this method, for two orbitals we estimate that one could possibly reach inverse temperature $β\approx 20$ if high-performance computing techniques are utilized, while beyond that only very high-temperature regimes can be reached in the current formalism. Our work paves the way to apply GTEMPO as an imaginary-time impurity solver.

cond-mat.str-el↗

arXiv2024

Grassmann Time-Evolving Matrix Product Operators for Quantum Impurity Models

The time-evolving matrix product operators (TEMPO) method, which makes full use of the Feynman-Vernon influence functional, is the state-of-the-art tensor network method for bosonic impurity problems. However, for fermionic impurity problems the Grassmann path integral prohibits application of this method. We develop Grassmann time-evolving matrix product operators, a full fermionic analog of TEMPO, that can directly manipulates Grassmann path integrals with similar numerical cost as the bosonic counterpart. We further propose a zipup algorithm to compute expectation values on the fly without explicitly building a single large augmented density tensor, which boosts our efficiency on top of the vanilla TEMPO. Our method has a favorable complexity scaling over existing tensor network methods, and we demonstrate its performance on the non-equilibrium dynamics of the single impurity Anderson models. Our method solves the long standing problem of turning Grassmann path integrals into efficient numerical algorithms, which could significantly change the application landscape of tensor network based impurity solvers, and could also be applied for broader problems in open quantum physics and condensed matter physics.

cond-mat.str-el↗

arXiv2023

Simulating quantum transport via collisional models on a digital quantum computer

Digital quantum computers have the potential to study the dynamics of complex quantum systems. Nonequilibrium open quantum systems are, however, less straightforward to be implemented. Here we consider a collisional model representation of the nonequilibrium open dynamics for a boundary-driven XXZ spin chain, with a particular focus on its steady states. More specifically, we study the interplay between the accuracy of the result versus the depth of the circuit by comparing the results generated by the corresponding master equations. We study the simulation of a boundary-driven spin chain in regimes of weak and strong interactions, which would lead in large systems to diffusive and ballistic dynamics, considering also possible errors in the implementation of the protocol. Last, we analyze the effectiveness of digital simulation via the collisional model of current rectification when the XXZ spin chains are subject to non-uniform magnetic fields.

quant-ph↗

arXiv2023

Efficacy of noisy dynamical decoupling

Dynamical decoupling (DD) refers to a well-established family of methods for error mitigation, comprising pulse sequences aimed at averaging away slowly evolving noise in quantum systems. Here, we revisit the question of its efficacy in the presence of noisy pulses in scenarios important for quantum devices today: pulses with gate control errors, and the computational setting where DD is used to reduce noise in every computational gate. We focus on the well-known schemes of periodic (or universal) DD, and its extension, concatenated DD, for scaling up its power. The qualitative conclusions from our analysis of these two schemes nevertheless apply to other DD approaches. In the presence of noisy pulses, DD does not always mitigate errors. It does so only when the added noise from the imperfect DD pulses do not outweigh the increased ability in averaging away the original background noise. We present breakeven conditions that delineate when DD is useful, and further find that there is a limit in the performance of concatenated DD, specifically in how far one can concatenate the DD pulse sequences before the added noise no longer offers any further benefit in error mitigation.

quant-ph↗

arXiv2023

A real neural network state for quantum chemistry

The restricted Boltzmann machine (RBM) has been successfully applied to solve the many-electron Schr$\ddot{\text{o}}$dinger equation. In this work we propose a single-layer fully connected neural network adapted from RBM and apply it to study ab initio quantum chemistry problems. Our contribution is two-fold: 1) our neural network only uses real numbers to represent the real electronic wave function, while we obtain comparable precision to RBM for various prototypical molecules; 2) we show that the knowledge of the Hartree-Fock reference state can be used to systematically accelerate the convergence of the variational Monte Carlo algorithm as well as to increase the precision of the final energy.

quant-ph↗

arXiv2022

Ground state search by local and sequential updates of neural network quantum states

Neural network quantum states are a promising tool to analyze complex quantum systems given their representative power. It can however be difficult to optimize efficiently and effectively the parameters of this type of ansatz. Here we propose a local optimization procedure which, when integrated with stochastic reconfiguration, outperforms previously used global optimization approaches. Specifically, we analyze both the ground state energy and the correlations for the non-integrable tilted Ising model with restricted Boltzmann machines. We find that sequential local updates can lead to faster convergence to states which have energy and correlations closer to those of the ground state, depending on the size of the portion of the neural network which is locally updated. To show the generality of the approach we apply it to both 1D and 2D non-integrable spin systems.

quant-ph↗

arXiv2022

Non-Markovian effects in stochastic resonance in a two level system

Stochastic resonance is a phenomenon where the response signal to external driving is enhanced by environment noise. In quantum regime, the effect of environment is often intrinsically non-Markovian. Due to the combination of such non-Markovian quantum noise and external driving force, it is difficult to evaluate the correlation function and hence the power spectrum. Nevertheless, a recently developed algorithm, which is called time-evolving matrix product operators (TEMPO), and its extensions provide an efficient and numerically exact approach for this task. Using TEMPO we investigate non-Markovian effects in quantum stochastic resonance in a two level system. The periodic signal and the time-averaged asymptotic correlation function, along with the power spectrum, are calculated. From the power spectrum the signal-to-noise ratio is evaluated. It is shown that both signal strength and signal-to-noise ratio are enhanced by non-Markovian effects, which indicates the importance of non-Markovian effects in quantum stochastic resonance. In addition, we show that the non-Markovian effects can shift the peak position of the background noise power spectrum.

cond-mat.mes-hall↗

arXiv2022

Emergence of steady currents due to strong prethermalization

A steady current between baths is a manifestation of the prethermalization phenomenon, a quasi-equilibrium dynamical process with weak conserved quantity breaking. We consider two finite nonintegrable many-body baths each following the eigenstate thermalization hypothesis, and each prepared in a random product state with fixed and different energy constraints, i.e., within the mean energy ensemble. Such an initialization, not being constrained to superpositions or mixtures of many-body eigenstates, opens the door to experimental realization and also significantly simplifies numerical simulations. We show that such dynamical process is typical as the current variance decreases exponentially with respect to the size of baths. We also demonstrate that the emerging current is prethermalized in a strong sense, analogously to strong thermalization, meaning that the current values stay close to the microcanonical one for most of the time.

cond-mat.stat-mech↗

arXiv2022

Thermopower in a boundary driven bosonic ladder in the presence of a gauge field

We consider a bosonic two-legged ladder whose two-band energy spectrum can be tuned in the presence of a uniform gauge field, to four distinct scenarios: degenerate or non-degenerate ground states with gapped or gapless energy bands. We couple the ladder to two baths at different temperatures and chemical potentials and analyze the efficiency and power generated in the linear as well as nonlinear response regime. Our results, obtained with the Green's function method, show that the maximum performance efficiency and generated power are strongly dependent on the type of the underlying energy spectrum. We also show that the ideal scenario for efficient energy conversion, as well as power generation, corresponds to the case in which the spectrum has a gap between the bands, and the ground state is degenerate.

cond-mat.mes-hall↗