Dmitry Bagrets

The Dicke-Ising model, one of the few paradigmatic models of matter-light interaction, exhibits a superradiant quantum phase transition above a critical coupling strength. However, in natural optical systems, its experimental validation is hindered by a “no-go theorem.” Here, we propose a digital-analog quantum simulator for this model based on an ensemble of interacting qubits coupled to a single-mode photonic resonator. We analyze the system's free-energy landscape using field-theoretical methods and develop a digital-analog quantum algorithm that disentangles qubit and photon degrees of freedom through a parity-measurement protocol. This disentangling enables the emulation of a photonic Schrödinger cat state, which is a hallmark of the superradiant ground state in finite-size systems and can be unambiguously probed through the Wigner tomography of the resonator's field.

Quantum computing has the potential to revolutionize quantum chemistry and material science by offering solutions to complex problems unattainable with classical computers. However, the development of efficient quantum algorithms that are efficient under noisy conditions remains a major challenge. This paper introduces the truncated Variational Hamiltonian Ansatz (tVHA), a novel circuit design for conducting quantum calculations on Noisy Intermediate-Scale Quantum (NISQ) devices. tVHA provides a promising approach for a broad range of applications by utilizing principles from the adiabatic theorem in solid state physics. Our proposed ansatz significantly reduces the parameter count and can decrease circuit size substantially, with a trade-off in accuracy. Thus, tVHA facilitates easier convergence within the variational quantum eigensolver framework compared to state-of-the-art ansätze such as Unitary Coupled Cluster (UCC) and Hardware-Efficient Ansatz (HEA). While this paper concentrates on the practical applications of tVHA in quantum chemistry, demonstrating its suitability for both weakly and strongly correlated systems and its compatibility with active space calculations, its underlying principles suggest a wider applicability extending to the broader field of material science computations on quantum computing platforms.

The quantum approximate optimization algorithm (QAOA) is suggested as a promising application on early quantum computers. Here a quantum-inspired classical algorithm, the mean-field approximate optimization algorithm (mean-field AOA), is developed by replacement of the quantum evolution of the QAOA with classical spin dynamics through the mean-field approximation. Because of the alternating structure of the QAOA, this classical dynamics can be found exactly for any number of QAOA layers. We benchmark its performance against the QAOA on the Sherrington-Kirkpatrick model and the partition problem, and find that the mean-field AOA outperforms the QAOA in both cases for most instances. Our algorithm can thus serve as a tool to delineate optimization problems that can be solved classically from those that cannot, i.e., we believe that it will help to identify instances where a true quantum advantage can be expected from the QAOA. To quantify quantum fluctuations around the mean-field trajectories, we solve an effective scattering problem in time, which is characterized by a spectrum of time-dependent Lyapunov exponents. These provide an indicator for the hardness of a given optimization problem relative to the mean-field AOA.

For a generic quantum many-body system, the quantum ergodic regime is defined as the limit in which the spectrum of the system resembles that of a random matrix theory (RMT) in the corresponding symmetry class. In this paper, we analyze the time dependence of correlation functions of operators. We study them in the ergodic limit as well as their approach to the ergodic limit, which is controlled by nonuniversal massive modes. An effective field theory (EFT) corresponding to the causal symmetry and its breaking describes the ergodic phase. We demonstrate that the resulting Goldstone-mode theory has a topological expansion, analogous to the one described by Altland and Sonner [ SciPost Phys. 11, 034 (2021)] with added operator sources, whose leading nontrivial topologies give rise to the universal ramp seen in correlation functions. The ergodic behavior of operators in our EFT is seen to result from a combination of RMT-like spectral statistics and Haar averaging over wave functions. Furthermore, we capture analytically the plateau behavior by taking into account the contribution of a second saddle point. Our main interest is quantum many-body systems with holographic duals, and we explicitly establish the validity of the EFT description in the Sachdev-Ye-Kitaev class of models, starting from their microscopic description. By studying the tower of massive modes above the Goldstone sector, we get a detailed understanding of how the ergodic EFT phase is approached, and we derive the relevant Thouless timescales. We point out that the topological expansion can be reinterpreted in terms of contributions of bulk wormholes and baby universes.

We consider one-dimensional quantum walks in optical linear networks with synthetically introduced disorder and tunable system parameters allowing for the engineered realization of distinct topological phases. The option to directly monitor the walker's probability distribution makes this optical platform ideally suited for the experimental observation of the unique signatures of the one-dimensional topological Anderson transition. We analytically calculate the probability distribution describing the quantum critical walk in terms of a (time-staggered) spin polarization signal and propose a concrete experimental protocol for its measurement. Numerical simulations back the realizability of our blueprint with current date experimental hardware.

The anomalous Floquet Anderson insulator (AFAI) is a two-dimensional periodically driven system in which static disorder stabilizes two topologically distinct phases in the thermodynamic limit. The presence of a unit-conducting chiral edge mode and the essential role of disorder induced localization are reminiscent of the integer quantum Hall (IQH) effect. At the same time, chirality in the AFAI is introduced via an orchestrated driving protocol, there is no magnetic field, no energy conservation, and no (Landau level) band structure. In this paper, we show that in spite of these differences the AFAI topological phase transition is in the IQH universality class. We do so by mapping the system onto an effective theory describing phase coherent transport in the system at large length scales. Unlike with other disordered systems, the form of this theory is almost fully determined by symmetry and topological consistency criteria, and can even be guessed without calculation. (However, we back this expectation by a first-principles derivation.) Its equivalence to the Pruisken theory of the IQH demonstrates the above equivalence. At the same time, it makes predictions on the emergent quantization of transport coefficients, and the delocalization of bulk states at quantum criticality which we test against numerical simulations.

We investigate existence of replica off-diagonal solutions in the field-theoretical description of Sachdev-Ye-Kitaev model. To this end we evaluate a set of local and non-local dynamic correlation functions in the long time limit. We argue that the structure of the soft-mode Schwarzian action is qualitatively different in replica-diagonal vs. replica-off-diagonal scenarios, leading to distinct long-time predictions for the correlation functions. We then evaluate the corresponding correlation functions numerically and compare the simulations with analytical predictions of replica-diagonal and replica-off-diagonal calculations. We conclude that all our numerical results are in a quantitative agreement with the theory based on the replica-diagonal saddle point plus Schwarzian and massive Gaussian fluctuations (the latter do contain replica off-diagonal components). This seems to exclude any contributions from replica-off-diagonal saddle points, at least on the time scales shorter than the inverse many-body level spacing.