Geometry and non-adiabatic responses in non-equilibrium systems

The existence of periodicity in a finite time for a time-dependent classically chaotic Hamiltonian implies the absence of chaos. The question that we ask is can a spin system, having claically chaotic limit, shows periodicity in time? An intuitive answer to this question is positive at least for small Hilbert space. Here, we study the periodicity of the kicked top model using techniques from abstract algebra, particularly the theory of algebraic extensions of the field of rational numbers. We used the tool of Cyclotomic polynomials and studied the characteristics polynomial for the QKT unitary. For the given Hamiltonian parameters, we were able to construct the set of possible $n$ such that $F^n = \tau I,$ where $F$ be a unitary matrix and $\tau = e^{-i\theta} \in S^1$. We then check the periodicity for all such $n$. Given that the set of all possible $n$ is small and finite, it can be computationally checked. As an example, we generates the list of possible periodicity for $j=3$ (and $j=4$) and show that that even though Hilbert space is just 3 (and 4) -dimensional, for many sets of parameters state never repeats. This means for these cases the system is at least non-periodic. This techniques can be use for other system as well and it will help to understand the difference is classical and quantum dynamics.

In recent years, the presence of control phase transitions emerged while numerically surveying the quantum control landscape associated with population-transfer problems in few-qubit systems [10.1103/PhysRevX.8.031086]. Despite all efforts, an analytical understanding of quantum optimal control landscapes is largely missing. In this work, we present a set of perturbative methods that allow for the analytical characterization of various control phase transitions. These methods provide an explicit mapping between quantum control problems and classical many-body systems at thermal equilibrium (exhibiting long-range, multi-body interactions). We demonstrate the effectiveness of these approaches by explicitly considering the single- and two- qubit state-preparation problems, previously extensively studied via numerical optimization algorithms [10.1103/PhysRevA.97.052114]. Through this approach, control phase transitions are connected to dramatic changes in the topological and geometrical properties of the near-optimal part of the control landscape. The methods developed are largely independent from the quantum systems underlying the control problem and can be easily adapted to more complicated settings. Our work shed new light on the close connection between optimal quantum control and (spin) glassy systems.

Many robust physical phenomena in quantum physics are based on topological invariants arising due to intriguing geometrical properties of quantum states. Prime examples are the integer and fractional quantum Hall effects that demonstrate quantized Hall conductances, associated with topology both in the single particle and the strongly correlated many-body limit. Interestingly, the topology of the integer effect can be realized in superconducting multiterminal systems, but a proposal for the more complex fractional counterpart is lacking. In this work, we theoretically demonstrate how to achieve fractional quantized transconductance in an engineered chain of Josephson junctions. Crucially, similar to the stabilization of the conductance plateaus in Hall systems by disorder, we obtain stable transconductance plateaus as a result of nonadiabatic Landau-Zener transitions. We furthermore show that the fractional plateaus are robust to disorder and study the optimal operation regime to observe these effects. Our proposal paves the way for quantum simulation of exotic many-body out-of-equilibrium states in Josephson junction systems. Reference: Hannes Weisbrich, Raffael L. Klees, Oded Zilberberg, and Wolfgang Belzig Fractional transconductance via non-adiabatic topological Cooper pair pumping Phys. Rev. Res. 5, 043045 (2023)

Superconductivity is the basis of manymodern quantum coherent phenomena in many-body solid state systems. Due to the activation of quantum mechanical phases as degrees of freedom in superconducting multi-terminal structures, effects lie topological quantum bits, Weyl physics and macroscopically quantized phenomena become possible. In my talk, I will discuss novel possibilities to realize complex, topological nontrivial states of matter in superconducting complex structures. Examples are Berry spectroscopy of Weyl-Andreev nodes in synthetic dimensions [1] high-dimensional topology such as the Second Chern number accompanied by a non-Abelian Berry phase [2] or tensor monopoles [3]. First experimental steps towards realizing such highly non-trivial quantum effects will be discussed [4]and accompanied by concrete theoretical predictions for experimentally observables like tunnel spectroscopy, supercurrent and quantized responses. [1] R. L. Klees, G. Rastelli, J. C. Cuevas, and W. Belzig Microwave spectroscopy reveals the quantum geometric tensor of topological Josephson matter Phys. Rev. Lett. 124, 197002 (2020) [2] H. Weisbrich, R.L. Klees, G. Rastelli and W. Belzig Second Chern Number and Non-Abelian Berry Phase in Superconducting Systems PRX Quantum 2, 010310 (2021) [3] Hannes Weisbrich, Markus Bestler, and Wolfgang Belzig Tensor Monopoles in superconducting systems Quantum 5, 601 (2021) [4]M. Coraiola, D. Z. Haxell, D. Sabonis, H. Weisbrich, A. E. Svetogorov, M. Hinderling, S. C. ten Kate, E. Cheah, F. Krizek, R. Schott, W. Wegscheider, J. C. Cuevas, W. Belzig, and F. Nichele Phase-engineering the Andreev band structure of a three-terminal Josephson junction Nat. Commun. 14, 6784 (2023)

Coherent control of complex many-body systems is critical to the development of useful quantum devices. Fast perfect state transfer can be exactly achieved through additional counterdiabatic fields. We show that the additional energetic overhead associated with implementing counterdiabatic driving can be reduced while still maintaining high target state fidelities. This is achieved by implementing control fields only during the impulse regime, as identified by the Kibble-Zurek mechanism. We demonstrate that this strategy successfully suppresses most of the defects that would be generated due to the finite driving time for two paradigmatic settings: the Landau-Zener model and the Ising model. For the latter case, we also investigate the performance of our impulse control scheme when restricted to more experimentally realistic local control fields.

We investigate the sensitivity of a quantum chaotic system to changes of a parameter by exploring the quantum Fisher information. Our analysis is based on a description of non-integrable quantum systems in terms of a random matrix Hamiltonian. Based on this we derive analytical expression for the time evolution of the quantum Fisher information. We test the prediction of the random matrix model with the exact diagonalization of a non-integrable spin system. We find that the information for the parameter describing a single spin is distributed throughout the quantum system. The initial information spread is quadratic in time which quickly passes into linear increase with slope determine by the decay rate of the spin observable. When the information is fully spread among all degrees of freedom a second quadratic time scale determines the long time behaviour of the quantum Fisher information.

We theoretically investigate quantum control protocols for the creation of NOON states using ultracold bosonic atoms on two modes, corresponding to the coherent superposition $|N,0\rangle + |0,N\rangle$, for a small number N of bosons. One possible method to create this state is to consider a third mode where all bosons are initially placed, which is symmetrically coupled to the two other modes. Tuning the energy of this third mode across the energy level of the other two modes allows the adiabatic creation of the NOON state. The main issue with this method is that it requires a large amount of time to reach the NOON state. However, this problem can be addressed by the application of a counterdiabatic Hamiltonian, which allows one to significantly reduce the time required to achieve these entangled states. We demonstrate that such a counterdiabatic protocol is feasible and effective for a single particle, and then discuss how to extend its application to a larger number of bosons.

While limitations on quantum computation by Markovian environmental noise are well-understood in generality, their behavior for different quantum circuits and noise realizations can be less universal. Here we consider a canonical quantum algorithm - Grover’s algorithm for unordered search - in the presence of systematic noise. This allows us to write the behavior as a random Floquet unitary, which we show is well-characterized by random matrix theory (RMT). The RMT analysis enables analytical predictions for gap-closing phase transitions which are directly relevant to computing power in the presence of noise. We comment on relevance to non-systematic noise in realistic quantum computers, including cold atom, trapped ion, and superconducting platforms.

An intriguing regime of universal charge transport at high entropy density has been proposed for periodically driven interacting one-dimensional systems with Bloch bands separated by a large single-particle band gap. For weak interactions, a simple picture based on well-defined Floquet quasiparticles suggests that the system should host a quasisteady state current that depends only on the populations of the system's Floquet-Bloch bands and their associated quasienergy winding numbers. Here we show that such topological transport persists into the strongly interacting regime where the single-particle lifetime becomes shorter than the drive period. Analytically, we show that the value of the current is insensitive to interaction-induced band renormalizations and lifetime broadening when certain conditions are met by the system's nonequilibrium distribution function. We show that these conditions correspond to a quasisteady state. We support these predictions through numerical simulation of a system of strongly interacting fermions in a periodically modulated chain of Sachdev-Ye-Kitaev dots. Our paper establishes universal transport at high entropy density as a robust far from equilibrium topological phenomenon, which can be readily realized with cold atoms in optical lattices.

The topological properties of the flat band states of a one-electron Hamiltonian that describes a chain of atoms with s − p orbitals are explored. This model is mapped onto a Kitaev–Creutz type model, providing a useful framework to understand the topology through a nontrivial winding number and the geometry introduced by the Fubini–Study (FS) metric. This metric allows us to distinguish between pure states of systems with the same topology and thus provides a suitable tool for obtaining the fingerprint of flat bands. Moreover, it provides an appealing geometrical picture for describing flat bands as it can be associated with a local conformal transformation over circles in a complex plane. In addition, the presented model allows us to relate the topology with the formation of compact localized states and pseudo-Bogoliubov modes. Also, the properties of the squared Hamiltonian are investigated in order to provide a better understanding of the localization properties and the spectrum. The presented model is equivalent to two coupled SSH chains under a change of basis [1]. [1] Abdiel de Jes ́us Espinosa-Champo and Gerardo G Naumis, J. Phys.: Condens. Matter 36, 015502 (2024).

The study of topological superconductors has been one of the central topics in physics in recent decades due to the possible realisation of Majorana zero energy modes which are non-Abelian particles with potential applications in fault-tolerant quantum computation. While the existence of Majorana modes is known to be protected by nontrivial topology and symmetry of the Bogoliubov-de-Gennes Hamiltonian, the role of quantum metric still remains unrevealed. In this work, we extend the Kitaev chain to a multiband version which supports Majorana zero modes in a nearly flat band with tunable quantum metric and investigate the quantum geometric effects on these Majorana bound states. We point out that both the long-range decay length and the quadratic spread of Majorana wavefunctions are determined by the Brillioun Zone averaged quantum metric. Importantly, with a large quantum metric, the dramatic long-distance decay property helps to sustain the crossed Andreev reflection signal in a much longer device than that of conventional Kitaev chain. Our study explores the role of quantum metric in topological superconductivity bound states and suggests the possibility for detecting Majorana through crossed Andreev reflection measurements in a significantly long two-terminal device.

Chiral multifold fermions are quasiparticles that appear only in chiral crystals, such as the CoSi family. Here we present the injection and shift photoconductivities and the related geometrical quantities for several types of chiral fermions, including spin-1/2, pseudospin-1 and -3/2 fermions, dubbed as Kramer Weyl, triple-point fermion (TPF), and Rarita-Schwinger-Weyl (RSW) fermion, respectively. We found that in the TPF model, the linear shift conductivities, responsible for the shift current generation by linearly polarized light, are proportional to the quadratic pseudo spin-orbit coupling and independent of photon frequency. In contrast, for the RSW and Kramer Weyl fermions, the linear shift conductivity is linearly proportional to photon frequency. The numerical results agree with the power-counting analysis for quadratic Hamiltonians. The frequency independence of the linear shift conductivity could be attributed to the strong resonant symplectic Christoffel symbols of the flat bands. Moreover, the calculated symplectic Christoffel symbols show significant peaks at the nodes, suggesting that the shift currents are due to the strong geometrical response near the topological nodes.

Controlling material properties using optical cavities is now a reality. In a recent experiment, the metal-to-insulator transition (charge-density-wave transition) in 1T-TaS2 was controlled by tuning cavity geometry. It was shown that the critical temperature varies non-monotonically with the cavity fundamental frequency. We investigate similar phenomenology in a simple model of electrons coupled to cavity photons. We also find qualitatively similar non-monotonic dependence of the critical temperature on the cavity fundamental frequency. We investigated the effect of the non-thermal nature of the steady state on the critical temperature.

Understanding and predicting the temporal evolution of quantum systems is essential for the development of theoretical physics and modern quantum technologies. A significant group of models that have been intensively researched in recent years are non-ergodic systems of interacting particles. They open the way to future technological solutions such as quantum memories. In the relaxation process, these systems do not strive for thermal states, which means that the initial quantum information encoded in the initial conditions is not lost. Attempts to understand the physical mechanisms responsible for the above-mentioned anomalous quantum dynamics constitute an important research goal in the theory of non-equilibrium processes. They are extensively studied in condensed matter and high energy physics. Such systems have an experimental implementation on the so-called cold atoms on optical lattices [1-2]. Their great advantage is that they can be easily applied to various geometries. For this purpose, a semiclassical description of time evolution within the Wigner-Weyl representation will be used [3]. My poster will present spinless fermion model with disorder and interactions. I will show that semiclassical dynamics relaxes faster than the full quantum dynamics. Then I will present that strongly disordered one-dimensional and two-dimensional systems exhibit logarithmic-in-time relaxation, which was established for one-dimensional chains [4-6]. [1] J. Choi, S. Hild, J. Zeiher, P. Schauß, A. Rubio-Abadal, T. Yefsah, V. Khemani, D. A. Huse, I. Bloch, and C. Gross, Science, 352, 1547 (2016) [2] P. Bordia, H. Luschen, S. Scherg, S. Gopalakrishnan nad M. Knap, U. Schneider, and I. Bloch, Physical Review X,7 (2017) [3] A. Polkovnikov, Annals of Physics 325, 1790 (2010) [4] M. Žnidarič, T. Prosen, and P. Prelovšek, Phys. Rev. B 77, 064426 (2008). [5] M. Mierzejewski, J. Herbrych, and P. Prelovšek, Phys. Rev. B 94, 224207 (2016). [6] M. Schecter, T. Iadecola, and S. Das Sarma, Phys. Rev. B 98, 174201 (2018).

Quantum geometry of non-Abelian multi-band systems was recently formulated in terms of generalized Plücker embeddings, which capture homotopy-classified band topologies associated with multiple gaps [1]. Further to this, the resultant quantum-geometric bounds were recast in terms of observables such as AC conductivities, optical transition rates, optical weights, higher order photoconductivities, and even gap energies in multi-gap systems hosting a novel non-Abelian multi-gap topological invariant, the Euler class [2]. While these observables can be naturally linked to Riemannian geometry [3], an unprecedented topological, rather than solely geometric, response encoded in second-order circular shift photoconductivities was furthermore identified in multi-gap phases [4]. Namely, a quantized shift effect was found in three-dimensional PT-symmetric topological insulators hosting Pontryagin indices, isoclinic winding numbers [5], or real Hopf indices [6], as non-Abelian multi-gap topological invariants imposing the quantization. As demonstrated analytically, the effect can be understood in terms of the real Chern-Simons forms associated with the torsion tensor, which captures the amplitudes of virtual optical transitions. [1] A. Bouhon, et al., arXiv:2303.02180 [2] W.J. Jankowski, et al., arXiv:2311.07545 [3] J. Ahn, et. al., Nat. Phys. 18, 290-295 (2022) [4] W.J. Jankowski, and R.-J. Slager, arXiv:2402.13245 [5] Z. Davoyan, W.J. Jankowski, A. Bouhon, R.-J. Slager, arXiv:2308.15555 [6] H. Lim, et al., Phys. Rev. B 108, 125101 (2023)

Krylov complexity has recently gained attention where the growth of operator complexity in time is measured in terms of the off-diagonal operator Lanczos coefficients. The operator Lanczos algorithm reduces the problem of complexity growth to a single-particle semi-infinite tight-binding chain (known as the Krylov chain). Employing the phenomenon of Anderson localization, we propose the inverse localization length on the Krylov chain as a probe to detect weak ergodicity-breaking. On the Krylov chain we find delocalization in an ergodic regime, as we show for the SYK model, and localization in case of a weakly ergodicity-broken regime. Considering the dynamics beyond scrambling, we find a collapse across different system sizes at the point of weak ergodicity-breaking leading to a quantitative prediction. We further show universal traits of different operators in the ergodic regime beyond the scrambling dynamics. We test for two settings: (1) the coupled SYK model, and (2) the quantum East model. Our findings open avenues for mapping ergodicity/weak ergodicity-breaking transitions to delocalization/localization phenomenology on the Krylov chain.

The interplay between quantum chaos and integrability has been extensively studied in the past decades. We approach this topic from the point of view of geometry encoded in the quantum geometric tensor, which describes the complexity of adiabatic transformations. In particular, we consider two generic models of spin chains that are parameterized by two independent couplings. In one, the integrability breaking perturbation is global while, in the other, integrability is broken only at the boundary. In both cases, the shortest paths in the coupling space lead towards integrable regions and we argue that this behavior is generic. These regions thus act as attractors of adiabatic flows similar to river basins in nature. Physically, the directions towards integrable regions are characterized by faster relaxation dynamics than those parallel to integrability, and the anisotropy between them diverges in the thermodynamic limit as the system approaches the integrable point. We also provide evidence that the transition from integrable to chaotic behavior is characterized by anomalously slow relaxation dynamics for numerous spin chain models, similar to critical slowing down in continuous phase transitions.

Recently, topological physics in the space of superconducting phases has attracted a lot of research and it was predicted that the transconductance $G_{\alpha\beta} \propto C_{\alpha\beta} V_\beta$ between two superconductors $\alpha$ and $\beta$ is quantized in terms of the Chern number $C_{\alpha\beta}$ when a voltage bias $V_\beta$ is applied [1]. We present superconducting model systems, derived from a microscopic approach, that exhibit nontrivial topological invariants in the space of superconducting phases [2], and show how to combine these with measurement protocols to gain access to the elements of the quantum geometric tensor [3]. In fact, some of these systems present strong similarities to the hybrid semiconductor-superconductor devices which are currently under investigation for the implementation of the Kitaev model [4], which host topologically protected Majorana zero modes by default, and more complex qubits based on Kitaev-Josephson junctions [5]. Our overarching goal is to engineer protocols for qubit operations and readout in these devices and combine them with the promise of additional topological protection via the control of the superconducting phases of the terminals. [1] R. P. Riwar, M. Houzet, J. Meyer, and Y. V. Nazarov, Nat. Commun. 7, 11167 (2016); E. Eriksson et al., Phys. Rev. B 95, 075417 (2017); J. S. Meyer and M. Houzet, Phys. Rev. Lett. 119, 136807 (2017). [2] R. L. Klees et al., Phys. Rev. Lett. 124, 197002 (2020); R. L. Klees et al., Phys. Rev. B 103, 014516 (2021); H. Weisbrich et al., PRX Quantum 2, 010310 (2021); H. Weisbrich et al., Phys. Rev. Research 5, 043045 (2023); H. Weisbrich et al., Quantum 5, 601 (2021). [3] M. Kolodrubetz et al., Phys. Rep. 697, 1 (2017); M. Kolodrubetz et al., Phys. Rev. B 88, 064304 (2013); T. Ozawa and N. Goldman, Phys. Rev. B 97, 201117 (2018); M. Kolodrubetz, Phys. Rev. Lett. 117, 015301 (2016). [4] A. Y. Kitaev, Phys.-Usp. 44, 131 (2001). [5] M. Leijnse and K. Flensberg, Phys. Rev. B 86, 134528 (2012); D. M. Pino, R. Seoane Souto, and R. Aguado, arXiv:2309.12313 (2023); A. Bargerbos et al., Phys. Rev. Lett. 131, 097001 (2023); M. Geier et al., arXiv:2307.05678 (2023).

We investigate the loss of adiabaticity when cooling a many-body quantum system from an initial thermal state towards a quantum critical point. The excitation density, which quantifies the degree of adiabaticity of the dynamics, is found to obey scaling laws in the cooling velocity as well as in the initial and final temperatures of the cooling protocol. The scaling laws are universal, governed by the critical exponents of the quantum phase transition. The validity of these statements is shown analytically for a Kitaev quantum wire coupled to Markovian baths, and subsequently argued to be valid under rather general conditions. Our results establish that quantum critical properties can be probed dynamically at finite temperature, without even varying the control parameter of the quantum phase transition.

We formulate a renormalization-group approach to a general nonlinear oscillator problem. The approach is based on the exact group law obeyed by solutions of the corresponding ordinary differential equation. We consider both the autonomous models with time-independent parameters, as well as nonautonomous models with slowly varying parameters. We show that the renormalization-group equations for the nonautonomous case can be used to determine the geometric phase acquired by the oscillator during the change of its parameters. We illustrate the obtained results by applying them to the Van der Pol and Van der Pol-Duffing models.

The dynamics of dissipative many-body quantum systems is typically governed by non-Hermitian operators. As a result, their eigenvalues cannot be systematically ordered, hindering the use of spectral statistics. Moreover, while quantum simulators could offer valuable insights, they provide limited access to spectral information. In contrast, dynamical measures such as correlation functions and fidelities can be feasibly traced in experimental settings. We focus on generalizing the Spectral Form Factor as the survival probability of an initial Coherent Gibbs State, examining its behavior and properties in various scenarios of open dynamics. We study a series of dissipative models, including Lindbladian dynamics, non-Hermitian systems, and quantum channels. We further introduce Parametric Quantum Channels, a discrete-time model of unitary evolution periodically interrupted by the effects of measurements or transient interactions with an environment.

We introduce the concept of the almost-companion matrix (ACM) by relaxing the non-derogatory property of the standard companion matrix (CM). That is, we define an ACM as a matrix whose characteristic polynomial coincides with a given monic and generally complex polynomial. The greater flexibility inherent in the ACM concept, compared to CM, allows the construction of ACMs that have convenient matrix structures satisfying desired additional conditions, compatibly with specific properties of the polynomial coefficients. We demonstrate the construction of Hermitian and unitary ACMs starting from appropriate third-degree polynomials, with implications for their use in physical-mathematical problems, such as the parameterization of the Hamiltonian, density, or evolution matrix of a qutrit. We show that the ACM provides a means of identifying the properties of a given polynomial and finding its roots. For example, we describe the ACM-based solution of cubic complex algebraic equations without resorting to the use of the Cardano-Dal Ferro formulas. We also show the necessary and sufficient conditions on the coefficients of a polynomial for it to represent the characteristic polynomial of a unitary ACM. The presented approach can be generalized to complex polynomials of higher degrees.

Quantum many-body scars(QMBS) are the mid-spectrum states of a non-integrable model that violate the Eigentstate thermalization hypothesis(ETH). Though integrable models also violate ETH, it has been shown that they satisfy a weaker version of ETH known as generalized ETH. Generalized ETH suggests following a global quench starting from an initial state, the steady state is reached which can be explained by a generalized Gibbs ensemble(GGE). Here we show that there exist many such low entangled states for which the quench dynamics can't be predicted by GGE, i.e. they are analogous to scar states of non-integrable models.

Local counterdiabatic driving (CD) provides a feasible approach for realizing approximate reversible/adiabatic processes like quantum state preparation using only local controls and without demanding excessively long protocol times. However, in many instances getting high accuracy of such CD protocols requires engineering very complicated new controls or pulse sequences. In this work, we describe a systematic method for altering the adiabatic path by adding extra local controls along which performance of local CD protocols is enhanced. We then show that this method provides dramatic improvement in the preparation of non-trivial GHZ ground states of several different spin systems with both short-range and long-range interactions.

We theoretically predict a working principle for optical amplification, based on Weyl semimetals: When a Weyl semimetal is suitably irradiated at two frequencies, electrons close to the Weyl points convert energy between the frequencies through the mechanism of topological frequency conversion from [Martin et al., Phys. Rev. X 7, 041008 (2017)]. Each electron converts energy at a quantized rate given by an integer multiple of Planck's constant multiplied by the product of the two frequencies. In simulations, we show that optimal, but feasible band structures, can support topological frequency conversion in the “THz gap” at intensities down to 2W/mm^2; the gain from the effect can exceed the dissipative loss when the frequencies are larger than the relaxation time of the system. Topological frequency conversion forms a paradigm for optical amplification, which further extends Weyl semimetals' promise for technological applications.

We propose a type of phase transition in quantum many-body systems, which occurs in highly excited quantum many-body scar states, while the rest of the spectrum is largely unaffected. Such scar state phase transitions can be realized by embedding a matrix product state, known to undergo a phase transition, as a scar state into the thermal spectrum of a parent Hamiltonian. We find numerically that the mechanism for the scar state phase transition involves the formation or presence of low-entropy states at energies similar to the scar state in the vicinity of the phase transition point. Reference: arXiv:2405.20113.

We investigate an implementation of collisional thermometry based on Gaussian quantum systems. Contrary to the qubit-based implementation, this continuous variable analogue allows for an efficient computation of the Quantum Fisher Information (QFI) even for a large number of ancillae. For that purpose, we also provide a slight modification to an existing formula for the QFI in terms of the covariance matrix. This numerical flexibility enables us, in turn, to explore the thermometric properties of the model for a wide range of configurations. We give a particular focus to how the QFI behaves with an increasing number of ancillae. Despite the infinite Markov order of the stochastic process of the model, we provide a simple phenomenological analysis for the behavior of the QFI, estimating the asymptotic Fisher information density and how the transient effects of correlations for an increasing number of ancillae depend on the physical parameters of the model.

Using the notion of the generator of adiabatic transformations, two distinct generalizations of the quantum geometric tensor [Provost and Vallee, Commun. Math. Phys. 76, 289 (1980)] for non- Hermitian systems are proposed. One of these generalizations has already emerged in the literature to characterize phase transitions in non-Hermitian Hamiltonians. However, for non-equilibrium steady-states in dissipative systems this quantity is equal to zero for kinematical reasons. Instead, we argue that our second generalization of the geometric tensor can be used as a novel approach for the investigation of phase transitions in either systems with non-Hermitian Hamiltonian or open dissipative systems. As our trial area we use the non-Hermitian Su-Schrieffer-Heeger model (NH- SSH) as a Hamiltonian system and a general fermionic model with quadratic Lindbladian as a dissipative one. We find that our method allows to identify phase transitions in all models under consideration, giving a universal tool to explore general non-Hermitian systems.

Braiding non-Abelian anyons in topologically ordered systems has been proposed as a possible route towards topologically protected quantum computing. While recent experiments based on various platforms have made significant progress towards this goal, coherent control over individual anyonic excitations has still not been achieved today. At the same time, progress in cold-atom quantum simulators resulted in the realization of a two-boson $\nu=1/2$-Laughlin state, a paradigmatic fractional quantum Hall state hosting Abelian anyonic quasi-holes. Here we show that cold atoms in quantum gas microscopes are a suitable platform to create and manipulate these quasi-holes. First, we show that a Laughlin state of eight bosons can be realized by connecting small patches accessible in experiments. Next, we demonstrate that two cross-shaped pinning potentials are sufficient to create two quasi-holes in this Laughlin state. Starting with these two quasi-holes we numerically perform an adiabatic exchange procedure, and reveal their semionic braiding statistics for various exchange paths, thus clarifying the topological nature of these excitations. Finally, we propose an experimentally feasible interferometry protocol to probe the braiding phase in quantum gas microscopes, using a two-level impurity immersed in the fractional quantum Hall fluid. We conclude that braiding experiments of Abelian anyons are now within reach in cold-atom quantum simulators, providing a crucial step towards the long-standing goal of non-Abelian anyon braiding with local coherent control.

In recent years, adiabatic quantum computing (AQC) (alternatively quantum annealing) has gained attention for tackling quadratic unconstrained binary optimization (QUBO) problems. Despite AQC’s potential equivalence to gate-based quantum computing, achieving successful AQC experimentally remains challenging due to the requirement of long interaction time which results in a long circuit depth in the NISQ devices. As a potential alternative, Counterdiabatic (CD) terms are introduced to reduce the circuit depth and realize AQC using shallow quantum circuits. However, computing exact coefficients for the CD terms for many-body system are rather challenging and even more expensive to implement. So there has been proposals in recent years to find the optimal coefficients for the CD terms using quantum optimal control [1], Variational quantum circuits [2] and various others. Here we propose a novel approach to design optimal Counterdiabatic driving for finding the ground state of quantum many body systems. This method employs nested expansion of the CD term, identifies key components via analytical calculations, and integrates them with time-dependent coefficients parameterized through piecewise cubic interpolation (PCI) and optimized by a gradient based numerical optimization while minimizing an appropriate cost function. This approach consistently exhibits strong performance across diverse instances of Ising models, consistently achieving unit fidelities in each case. Additionally, its effectiveness is further studied by computing the energy cost and respective quantum speed limit. This study is provides a timely approach for optimal CD driving and potentially become very useful in current adiabatic and variational quantum computing algorithms, determining ground states of quantum many-body systems or solving NP-hard problems more broadly. 1. Čepaitė, I., Polkovnikov, A., Daley, A. J., & Duncan, C. W. (2023). Counterdiabatic optimized local driving. PRX Quantum, 4(1), 010312. 2. Sun, D., Chandarana, P., Xin, Z. H., & Chen, X. (2022). Optimizing counterdiabaticity by variational quantum circuits. Philosophical Transactions of the Royal Society A, 380(2239), 20210282.

Leveraging the potential of current noisy intermediate-scale quantum (NISQ) computers has become a key objective within the quantum computing community. Variational quantum algorithms (VQAs) stand out as promising candidates to achieve this aim, utilizing the limited quantum resources available in existing NISQ computers. Presently, much research effort is directed towards encoding discrete optimization problems using qubit-based approaches, particularly suitable for implementation in superconducting circuits and trapped ions. Conversely, photonic quantum computing (PQC) employs the continuous variable (CV) formalism, allowing quantum information to be encoded in the quadrature amplitudes of an electromagnetic field known as qumodes. Introducing the photonic counterdiabatic quantum optimization (PCQO) algorithm [1] within the CV paradigm, we aim to address problems suited for currently available photonic devices. PCQO is a hybrid quantum-classical algorithm, incorporating a photonic circuit ansatz and a classical optimization routine. The circuit ansatz is constructed from a selection of Gaussian and non-Gaussian operations inspired by counterdiabatic (CD) protocols. Drawing from these CD protocols, our algorithm significantly reduces the required quantum operations for optimization compared to other and offers a practical and feasible experimental realization, circumventing the need for high-order operations and overcoming experimental limitations. 1. Chandarana, P., Paul, K., Garcia-de-Andoin, M., Ban, Y., Sanz, M., & Chen, X. (2023). Photonic counterdiabatic quantum optimization algorithm. arXiv preprint arXiv:2307.14853.

We propose two critical dissipative quantum metrology schemes for single parameter estimation which are based on a quantum probe consisting of a coherently driven ensemble of N spin-1/2 particles under the effect of a collective spin decay. The collective spin system exhibits a dissipative phase transition between thermal and ferromagnetic phases, which is characterized by a nonanalytical behavior of the spin observables. We show that thanks to the dissipative phase transition the sensitivity of the parameter estimation can be significantly enhanced. Furthermore, we show that our steady state is a spin squeezed state which allows one to perform parameter estimation with sub shot-noise limited measurement uncertainty.

Relaxation rates in nearly integrable systems usually increase quadratically with the strength of the perturbation that breaks integrability. We show that the relaxation rates can be significantly smaller in systems that are integrable along two intersecting lines in the parameter space. In the vicinity of the intersection point, the relaxation rates of certain observables increase with the fourth power of the distance from this point, whereas for other observables one observes standard quadratic dependence on the perturbation. As a result, one obtains exceedingly long-living prethermalization but with a reduced number of the nearly conserved operators. We show also that such a scenario can be realized in spin ladders.

The advancement of quantum simulators motivates the development of a theoretical framework to assist with efficient state preparation in quantum many-body systems. In our work we provide an explicit construction of the operator which exactly implements the evolution of a given MPS along a specified direction in its tangent space. The construction is benchmarked on an explicit periodic trajectory in a translationally invariant MPS manifold. We demonstrate that the Floquet unitary generating the dynamics over one period of the trajectory features an approximate MPS-like eigenstate embedded among a sea of thermalizing eigenstates. These results show that our construction is useful not only for state preparation and control of many-body systems, but also provides a generic route towards Floquet scars.

In this work, we address the challenge of uncovering patterns in variational optimal protocols for taking the system to ground states of many-body Hamiltonians, using variational quantum algorithms. We develop highly optimized classical Monte Carlo (MC) algorithms to find the optimal protocols for transformations between the ground states of the square-lattice XXZ model for finite systems sizes. The MC method obtains optimal bang-bang protocols, as predicted by Pontryagin's minimum principle. We identify the minimum time needed for reaching an acceptable error for different system sizes as a function of the initial and target states and uncover correlations between the total time and the wave-function overlap. We determine a dynamical phase diagram for the optimal protocols, with different phases characterized by a topological number, namely the number of on-pulses. Bifurcation transitions as a function of initial and final states, associated with new jumps in the optimal protocols, demarcate these different phases. The number of pulses correlates with the total evolution time. In addition to identifying the topological characteristic above, i.e., the number of pulses, we introduce a correlation function to characterize bang-bang protocols' quantitative geometric similarities. We find that protocols within one phase are indeed geometrically correlated. Identifying and extrapolating patterns in these protocols may inform efficient large-scale simulations on quantum devices.

We compute the non-equilibrium differential optical conductivity of one-dimensional fermions on the lattice, in response to a light-field pulse. Using time-dependent matrix product states, we compute the differential optical conductivity, which exhibits two main features: (i) population of mid-gap energies, and (ii) an asymmetrical optical resonance due to interference of excitons and the absorption band. Our results have relevance to pump and probe spectroscopy experiments on strongly correlated materials, where quantum interference gives rise to non-equilibrium optical excitations.

Over the last decade, periodic (Floquet) drives have emerged as a useful technique to engineer the properties of quantum systems. Additionally, periodically driven systems can manifest nonequilibrium phases of matter without static counterparts, such as discrete time crystals or anomalous topological insulators. The ability to realize effective Hamiltonians with properties drastically different from those of the non-driven system, makes Floquet engineering a vital ingredient in present-day quantum simulators. However, manipulating the states dressed by strong periodic drives remains an outstanding challenge in Floquet engineering. The state-of-the-art in Floquet control is the adiabatic change of parameters. Yet, this requires long protocols conflicting with the limited coherence times in experiments. This poster presents Floquet Counterdiabatic Driving, a generalization of variational counterdiabatic driving to Floquet systems, that enables transitionless driving of Floquet eigenstates far away from the adiabatic regime. In particular, we present a nonperturbative variational principle to find local approximations to the Floquet adiabatic gauge potential. The Floquet adiabatic gauge potential is also closely related to the response functions of the Floquet system.

The quantum geometric tensor (QGT) characterises the Hilbert-space geometry of eigenstates of parameter-dependent Hamiltonian. The real symmetric part of QGT is proportional to the Riemann geometric tensor on the space of quantum states while its imaginary antisymmetric part gives rise to the Berry curvature. In recent years both parts of QGT and related quantities have found extensive theoretical and experimental utility, in particular for quantifying quantum phase transitions at and out of equilibrium. Here we consider symmetric part of the QGT for different multi-parametric matrix Hamiltonians and discuss the possible indication of ergodic or integrable behaviour via system size dependence of induced geometry on the parameter space. We found in examples with two-dimensional parameter space that while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with conical defect. Our study thus provides more support that landscape of the parameter space yields the information on ergodic-nonergodic transition in complex quantum systems. Authors: Rustem Sharipov, Anastasiia Tiutiakina, Alexander Gorsky, Vladimir Gritsev and Anatoly Polkovnikov

We demonstrate: 1) the existence of a non-equilibrium "Floquet Fermi Liquid" state in partially filled Floquet Bloch bands, weakly connected to ideal fermionic baths. This state features a series of nested "Floquet Fermi surfaces" akin to matryoshka dolls. We explore its properties, such as quantum oscillations under magnetic fields, revealing slow amplitude beatings related to the Floquet Fermi surfaces' different areas, aligning with observations in microwave-induced resistance oscillation experiments. Additionally, we demonstrate the tunability of some Floquet Fermi surfaces towards non-equilibrium van-Hove singularities by altering the drive's frequency, without affecting electron density. 2) the existence of a quantum non-equilibrium steady state in periodically driven fermions coupled to a bosonic bath, distinct from any equilibrium counterpart. This state displays multiple distinct Fermi surfaces marked by higher order cusp-like non-analyticities in momentum occupation, lacking an associated jump or quasiparticle residue, thus categorizing these as non-equilibrium non-Fermi liquids. Remarkably, these non-analyticities persist even at finite bath temperatures, a unique feature not seen in equilibrium Fermi or non-Fermi liquids, where temperature typically blurs such sharp features.

A fundamental quantity in non-equilibrium thermodynamics is the statistics of the work done on a quantum system by an external coherent source that varies its Hamiltonian over time. In this talk I will investigate how this quantity is affected by the presence of quantum coherences in the initial state and long-range couplings in the Hamiltonian. In the first part of the presentation I will delve into quantum corrections to work statistics arising from the non-commutativity between the initial state of the system and the time-dependent Hamiltonian. These corrections can be revealed through the Kirkwood-Dirac quasi-probability (KDQ) approach to two-times correlators. By employing this method, one can discern non-classical signatures in the KDQ distribution of work, such as negative and complex values unattainable by classical theories. Applying these concepts to a quantum Ising chain example, I will establish connections between non-classical behaviors and the critical points of the model. In the second part, I will explore the impact of long-range couplings on the universal properties of quantum work statistics as a quantum critical point is approached during the dynamics. Additionally, I will present a quantum heat engine application, illustrating how expanding the range of interactions among constituents of the working fluid yields substantial thermodynamic advantages. Notably, in finite-time cycles, the presence of long-range interactions reduces non-adiabatic energy losses, thus mitigating the trade-off between power and efficiency.

Quantization of particle transport lies at the heart of topological physics. In Thouless pumps -- dimensionally reduced versions of the integer quantum Hall effect -- quantization is dictated by the integer winding of single-band Wannier states. Here, we show that repulsive interactions can stabilize a prethermal fractional Thouless pump resulting from the fractional winding of multiband Wannier states. To this end, we consider an Aubry-André chain with five sites and one fermion per unit cell which has a pair of low lying Thouless-pumping bands. If the repulsion is sufficiently strong the favored state is a Wigner crystal that spontaneously populates one subspecies of multi-band Wannier states of the low energy bands. As these return to themselves only after two periods of the drive the state can be viewed as a time crystal, and exhibits fractional charge pumping. However, due to the single-particle energy difference between different species of multiband Wannier states, the pump cycle forces the Wigner crystal over a background of large domain excitations, the production rate of which sets the prethermal lifetime of the fractional pump. By analogy to the problem of false vacuum decay we argue that the production rate of such excitations is exponentially suppressed in the ratio of interaction strength to the combined bandwidth of the low energy bands. To arrive at these conclusions we employ exact diagonalization studies of short chains, giving a phase diagram in terms of pumped charge and quantization lifetime as a function of interaction strength and pump frequency. We extend our results to long chains through a mean field analysis augmented by an effective model for the domain excitations. Our model may be directly realized in cold atom experiments.

We analyze the ground-state manifold of systems composed of a constant number $N$ of interacting bosons in terms of the quantum metric tensor and related geometrical entities like invariant curvature and geodesic paths in the space of control parameters. We focus particularly on the geometric implications of quantum phase transitions, their finite-$N$ precursors, and on the geometric effects of diabolic points in the parameter space. We present a method for approximating the finite-$N$ ground-state geometry within the parameter region of the first-order quantum phase transition and near a diabolic point by geometry of a two-level system. We show where this approximation holds and where it fails.

Exploring the ground state properties of many-body quantum systems conventionally involves adiabatic processes, alongside exact diagonalization, in the context of quantum annealing or adiabatic quantum computation. Shortcuts to adiabaticity by counter-diabatic driving serve to accelerate these processes by suppressing energy excitations. Motivated by this, we develop variational quantum algorithms incorporating the auxiliary counterdiabatic interactions, comparing them with digitized adiabatic algorithms. These algorithms are then implemented on gate-based quantum circuits to explore the ground states of the Fermi-Hubbard model on honeycomb lattices, utilizing systems with up to 26 qubits. The comparison reveals that the counter-diabatic inspired ansatz is superior to traditional Hamiltonian variational ansatz. Furthermore, the number and duration of Trotter steps are analyzed to understand and mitigate errors. Given the model's relevance to materials in condensed matter, our study paves the way for using variational quantum algorithms with counterdiabaticity to explore quantum materials in the noisy intermediate-scale quantum era.

Topological and geometrical features arising in bosonic Bogoliubov-de Gennes (BdG) systems have mainly been studied by utilizing a generalized symplectic version of the Berry curvature and the Chern number. Interestingly, in these systems topological features may even solely arise due to the anomalous (non-particle-number-conserving) terms in the Hamiltonian, making these systems inherently distinct from their non-interacting counterparts. Here, we propose the notion of the symplectic quantum geometric tensor (SQGT), whose imaginary part leads to the previously studied symplectic Berry curvature, while the real part gives rise to a symplectic quantum metric, providing a natural distance measure in the space of bosonic Bogoliubov modes. We propose how to measure all components of the SQGT by the use of periodic modulation of the systems’ parameters in a linear response regime and connect the symplectic Berry curvature to a generalized anomalous velocity term for Bogoliubov Bloch wave packets.

An integrable model perturbed by special "weak" perturbations thermalizes at timescales much longer than predicted by Fermi's golden rule. Recent works have proposed a systematic way of constructing families of such weak perturbations based on the so-called long-range deformations of integrable chains. The weak perturbations are obtained as truncations of the long-range deformations in some small parameter expansion and can be viewed as produced by unitary rotations of the short-range integrable models. In this study, we are primarily interested in deformations generated by boosted operators. The main aim of this work is to understand appropriate generators in systems with periodic boundary conditions since the boost is well-defined only in infinite chains. We approach this by studying the structure of the so-called adiabatic gauge potential (AGP) that was originally introduced as a very sensitive measure of quantum chaos and can serve as a proxy for such generators.

Topological classification of matter has become crucial for understanding electronic materials and wave metamaterials, with associated quantized bulk responses and robust topological boundary effects. Topological phenomena have also recently garnered significant interest in nonlinear systems. In particular, weak nonlinearities can result in parametric gain, leading to “non-Hermitian” metamaterials and the associated topological classification of open systems. Here, we venture into this expanding frontier using an approach that moves away from quasilinear approximations around the closed system classification. We harness instead the topology of structural stability of vector flows, and thus propose a new topological graph invariant to characterise nonlinear out-of-equilibrium dynamical systems via their equations of motion dynamics. We exemplify our approach on the ubiquitous model of a dissipative bosonic Kerr cavity, subject both to one-photon and two-photon drives. Using our classification, we can identify the topological origin of phase transitions in the system, as well as explain the robustness of a multi critical point in the phase diagram. We, furthermore, identify that the invariant distinguishes population inversion transitions in the system in similitude to a Z2 index. Our approach is readily extendable to coupled nonlinear cavities when considered a tensorial graph index.

We explore how interactions can facilitate cellular automata-like dynamics in quantum Floquet models with sequentially activated hopping. Specifically, we add local and short range interaction terms to classes of Floquet Hamiltonians and ask for conditions ensuring the evolution acts as a permutation on initial local number Fock states. We show that at certain values of hopping and interactions, determined by a set of Diophantine equations, such evolution can be realized. When only a subset of the Diophantine equations is satisfied the Hilbert space can be fragmented into frozen states, states obeying cellular automata like evolution, and subspaces where evolution mixes Fock states and is associated with eigenstates exhibiting high entanglement entropy and level repulsion. When disorder is added to these systems, the dynamics may be stabilized in regions of parameter space away from these special parameter values - via k-body (or many-body) localization - to create new families of interesting phases. These families of phases also include phases already of current interest such as (correlation-induced) anomalous Floquet topological insulators.

Optical box traps for cold atoms offer new possibilities for quantum-gas experiments. Building on their exquisite spatial and temporal control, we propose to engineer system-reservoir configurations using box traps, in view of preparing and manipulating topological atomic states in optical lattices. First, we consider the injection of particles from the reservoir to the system: this scenario is shown to be particularly well suited to activate energy-selective chiral edge currents, but also, to prepare fractional Chern insulating ground states. Then, we devise a practical evaporative-cooling scheme to effectively cool down atomic gases into topological ground states. Our open-system approach to optical-lattice settings provides a new path for the investigation of ultracold quantum matter, including strongly-correlated and topological phases.

We study the quantum geometry of Bloch band structure beyond the first order, namely Berry connection, and its effects on semi-classical equations of motion of wave-packet dynamics. We provide a systematical way of computing the geometric quantities in an N-band system, re-deriving for instance Berry phase, quantum geometric tensor( Fubini-Study) metric etc. We also demonstrate how to derive the dynamics from a generic coupling between Bloch momentum and an in-homogeneous external field, generalizing previous studies.

Hybrid digitized-counterdiabatic quantum computing (DCQC) is a promising approach for leveraging the capabilities of nearterm quantum computers, utilizing parameterized quantum circuits designed with counterdiabatic protocols. However, the classical aspect of this approach has received limited attention. In this study, we systematically analyze the convergence behavior and solution quality of various classical optimizers when used in conjunction with the digitized-counterdiabatic approach. We demonstrate the effectiveness of this hybrid algorithm by comparing its performance to the traditional QAOA on systems containing up to 28 qubits. Furthermore, we employ principal component analysis to investigate the cost landscape and explore the crucial influence of parametrization on the performance of the counterdiabatic ansatz. Our findings indicate that fewer iterations are required when local cost landscape minima are present, and the SPSA-based BFGS optimizer emerges as a standout choice for the hybrid DCQC paradigm.

Adiabatic time evolution of quantum systems is a widely used tool with applications ranging from state preparation and topological transformations to optimization and quantum computing. Adiabatic evolution generally works well for gapped ground states, but not for a generic thermal or (nonthermal) many-body localized state in the middle of spectrum. In this study, we show that quantum many-body scars -- a particular type of nonthermal states embedded in an otherwise thermalizing spectrum -- perform similarly to gapped ground states with respect to adiabatic dynamics despite the lack of protecting energy gap. Considering two rather different scar models, namely a one-dimensional model constructed from tensor networks and a two-dimensional fractional quantum Hall model with anyons, we identify that (i) leakage out of the scarred subspace is suppressed by the "entropy barrier" between the scar and nearby thermal states, (ii) the "spectral gap" instead of energy gap can serve to protect adiabaticity. By employing the argument of quantum speed limit in a wide class of scarring Hamiltonians, we show that the timescale for adiabaticity breakdown scales (at most) polynomially with system size. This is in contrast to the exponentially diverging timescale expected for a generic thermal or disorder-driven localized state. While manipulating a single, isolated ground state is common in quantum applications, adiabatic evolution of scar states provides the flexibility to manipulate an entire tower of ground-state-like states simultaneously in a single system.

We theoretically study the second-order direct current (dc) photocurrent phenomenon within 1T'-transition metal dichalcogenides (TMDCs). We observe a significant flip in the sign of both injection and shift current conductivities within the low-frequency regime when the 1T'-TMDCs undergo the $Z_2$ topological phase transition. We find that this flipping of conductivity tensors can be attributed to the interplay of the quantum geometric tensor, the shift vector, and the joint density of states, particularly in the vicinity of gap closing points. Such insights not only deepen our understanding of the fundamental properties of these materials but also hold promise for the development of novel electronic and optoelectronic devices based on TMDCs.

We present a general driving protocol for many-body systems to generate a sequence of prethermal regimes, each exhibiting a lower symmetry than the preceding one. We provide an explicit construction of effective Hamiltonians exhibiting these symmetries. This imprints emergent quasi-conservation laws hierarchically, enabling us to engineer the respective symmetries and concomitant orders in nonequilibrium matter. We provide explicit examples, including spatiotemporal and topological phenomena, as well as a spin chain realizing the symmetry ladder SU2-U1-Z2-E.