Post-selection for quantum control

Adiabatic driving provides a robust method to engineer ground states of many-body quantum systems. However, achieving adiabaticity can require impractically long timescales, leading to unwanted excitations when driving at finite speeds. Counterdiabatic driving provides a general solution to the problem, at the cost of introducing further (non-local and multiple-body) operators, collectively called adiabatic gauge potential. Nonetheless, even counterdiabatic driving fails at quantum phase transition: the adiabatic gauge potential blows up at the transition point. Here, we show that combining counterdiabatic driving with a time reparametrization of the driving schedule enables crossing certain second-order quantum phase transitions with a finite (yet still non-local) gauge potential. We relate this capability to the critical properties of the transition, particularly hyperscaling, and further provide a geometrical interpretation in terms of the ground-state manifold. We illustrate our theoretical findings with the exactly-soluble transverse-field Ising and Lipkin-Meshkov-Glick models, and further confirm them in a non-integrable case.

We investigate the classical limit of quantum master equations featuring double-bracket dissipators. We consider dissipators defined by double commutators, which describe dephasing dynamics, as well as dissipators involving double anticommutators, associated with fluctuating anti-Hermitian Hamiltonians (by systematic \hbar expansion). We begin with the well-known model of energy dephasing, associated with energy diffusion. We then turn to master equations containing a double anticommutator with the system Hamiltonian, recently derived in the context of noisy non-Hermitian systems. We provide a gradient-flow representation of the dynamics. We analyze the classical limit of the resulting evolutions for harmonic and driven anharmonic quantum oscillators, considering both classical and nonclassical initial states. The dynamics is characterized through the evolution of several observables as well as the Wigner logarithmic negativity. We conclude by extending our analysis to generalized master equations involving higher-order nested brackets, which provide a time-continuous description of spectral filtering techniques commonly used in the numerical analysis of quantum systems. Authors: Ankit W. Shrestha, Budhaditya Bhattacharjee and Adolfo del Campo Link: https://arxiv.org/abs/2601.20925

Measurement-induced phase transitions (MIPTs) are inherently properties of individual quantum trajectories, making their observation challenging when measurement outcomes cannot be perfectly distinguished. Using an exactly solvable Liouvillian model, we show that limited trajectory resolution effectively averages over many realizations, introducing a finite lengthscale that suppresses long-range correlations and washes out the critical features associated with MIPTs. Exact results for correlations, the Liouvillian gap, and entanglement negativity illustrate how partial averaging progressively obscures the underlying trajectory-level physics. We then examine how the detailed structure of individual trajectories shapes entanglement dynamics in a free fermionic chain monitored on a single site. Here, strongly super-Poissonian jump statistics—bunched events separated by long “dark” intervals—drive a surprising volume-law growth of entanglement, unlike both unitary quenches and fully post-selected no-click evolution. Increasing the number of monitored sites ultimately induces a Zeno-like crossover to area-law behavior. Together, these results show how the visibility of measurement-induced phases and entanglement structure hinges on the interplay between trajectory statistics and the observer’s ability to resolve measurement outcomes.

We propose a new theoretical method to describe the monitored dynamics of bosonic many-body systems based on the concept of the most likely trajectory. We show how such trajectory can be identified from the probability distribution of quantum trajectories, i.e. measurement readouts, and how it successfully captures the monitored dynamics beyond the average state. We prove the method to be exact in the case of Gaussian theories and then extend it to the interacting Sine-Gordon model. Although no longer exact in this framework, the method captures the dynamics through a self-consistent time-dependent harmonic approximation and reveals an entanglement phase transition in the steady state from an area-law to a logarithmic-law scaling.

Recently, there has been interest in the dynamics of monitored quantum systems using linear jump operators related to the creation or annihilation of particles. Here, we study the dynamics of the entanglement entropy under quantum jumps that induce local particle losses in a model of free fermions with hopping and $\mathbb{Z}_2$ pairing. We solve the nonunitary dynamics using the recently developed Faber polynomial method and explore the different steady-state entanglement regimes by tuning the pairing strength, thus interpolating between monitored free fermions coherently driven by a particle-number-conserving Hamiltonian and a parity-conserving one. In the absence of pairing, all quantum trajectories approach the vacuum at long times, with the entanglement entropy showing nonmonotonic behavior over time that we capture with a phenomenological quasiparticle ansatz. In this regime, quantum jumps play a key role, and we highlight this by exactly computing their waiting-time distribution. On the other hand, the interplay between losses and pairing gives rise to quantum trajectories with entangled steady states. We show that by tuning the system parameters, a measurement-induced entanglement transition occurs, where the entanglement entropy scaling changes from logarithmic to area law. We compare this transition with the one derived in the no-click limit and observe qualitative agreement in most of the phase diagram. Furthermore, the statistics of entanglement gain and loss are analyzed to better understand the impact of the linear jump operators.

I consider nonstationary circuit-QED systems described by the quantum Rabi model and its generalizations, in which a few artificial multilevel atoms (with tunable transition frequencies and atom–field coupling strengths) interact with one or several resonator modes. I show analytically and numerically that, by properly modulating the system parameters, one can generate many photons from vacuum, create multimode entangled states, engineer effective multiphoton Hamiltonians, induce the dynamical Casimir effect via three- or four-photon transitions, generate quantum states of light with metrological power, optimize photon generation through optimal-control strategies, and generate nonseparable states of light capable of discriminating between different forms of the quantum jump superoperator (in the context of continuous quantum photodetection). Moreover, I numerically solve different quantum master equations in the nonstationary and many-photon regimes, showing that in the ultrastrong-coupling regime the predictions of the standard master equation of quantum optics differ substantially from those of the microscopic master equation based on the dressed-state expansion.

We analyze the role of a monitoring quantum agent in the dynamical manifestations of Hamil- tonian quantum chaos. Specifically, we analyze the generalized spectral form factor, defined as the survival probability of a coherent Gibbs state under continuous energy measurements. The effect of the measurement feedback is tantamount to stochastic temporal fluctuations of the equilibrium inverse temperature. We study these fluctuations in the monitored SYK model and reveal the statistical properties of the average and variance of energy in the monitored dynamics.

We analyze the non-equilibrium dynamics in an open system composed by a quantum gas of bosons in a lattice interacting via both contact and cavity-induced global interactions. We discuss several dynamical features stemming from the quantum nature of the cavity field and the fluctuations in the atoms-cavity coupling, using numerically exact simulations based on novel matrix product states implementations. Firstly, we characterize the interplay of light-cone dynamics and of the non-causal propagation of the globally interacting dynamics, reporting a crossover between the light-cone behavior and the supersonic spreading of correlations, where correlations can spread across the system almost simultaneously, independent of the distance. We identify the key ingredients necessary for the supersonic propagation and to pinpoint fluctuations of the global coupling which act as the carriers of the long-range correlations. Furthermore, we investigate the mechanisms necessary for the stabilization of current-current correlations by exploring dissipative couplings to nonreciprocal reservoirs. We analyze the role of locality in the coupling to the environment of the quantum system of interest, as we consider either local couplings throughout the system, or a single global coupling to a cavity mode.

Spectral degeneracies in Liouvillian generators of dissipative dynamics generically occur as exceptional points, where the corresponding non-Hermitian operator becomes non-diagonalizable. Steady states, i.e., zero-modes of Liouvillians, are considered a fundamental exception to this rule since a no-go theorem excludes non-diagonalizable degeneracies there. Here, we demonstrate that the crucial issue of diverging timescales in dissipative state preparation is largely tantamount to an asymptotic approach towards the forbidden scenario of an exceptional steady state in the thermodynamic limit. With case studies ranging from NP-complete satisfiability problems encoded in a quantum master equation to the dissipative preparation of a symmetry-protected topological phase, we reveal the close relation between the computational complexity of the problem at hand and the finite-size scaling towards the exceptional steady state, exemplifying both exponential and polynomial scaling. Formally treating the weight W of quantum jumps in the Lindblad master equation as a parameter, we show that exceptional steady states at the physical value W=1 may be understood as a critical point hallmarking the onset of dynamical instability.

We present a method of characterizing the presence of photons inside an interferometer. In particular, we can demonstrate surprising behavior when photons are not present in any one of two spacetime regions but present in both of them. Our method utilizes Mach Zehnder interferometers with Dove prisms. A recent experiment with such an interferometer demonstrated amplification of external signals. (Versmond et al., PRL, to be published)

Many important optimization tasks can be mapped to the search of ground states of effective Hamiltonians, allowing for the solution of computationally hard problems in physics, finance, logistics and other fields. In quantum annealing, an initial easy-to-prepare Hamiltonian, cooled down to its ground state, gets gradually changed towards a more complex one, whose ground state represents the solution to a specific optimization problem. Despite its evident success, quantum annealing faces the challenge of diabatic transitions that tend to excite the systems towards energetically higher states, ruining the performance of adiabatic protocols. In this work we propose a new mechanism to cool down diabatic transitions in many-body chains by coupling them to auxiliary qubits that are frequently being reset to their ground state. In contrast to previously existing protocols that rely on knowledge of the time-dependent spectrum, our protocol relies on stochastic choices of the auxiliary qubits' energy at each reset. Using our protocol, we demonstrate the ability to effectively cool static spins chains down to their ground states, independent of their initial state or size. Our results are then generalized to time-dependent Hamiltonians, showing the efficiency of our protocol in improving the performance of several quantum annealing tasks.

The dynamics of a quantum many-body system subject to measurements is naturally described by an ensemble of quantum trajectories, which can exhibit measurement-induced phase transitions. This phenomenon cannot be revealed through ensemble-averaged observables, but it requires the ability to discriminate each trajectory separately, making its experimental observation extremely challenging. In this talk, I will discuss the fate of measurement-induced transitions under an observer's reduced ability to discriminate each measurement outcome. This introduces uncertainty in the state of the system, causing observables to probe a restricted subset of trajectories rather than a single one. Using an exactly-solvable Liouvillian model, I will show that varying degrees of trajectory averaging impact long-time spatial correlations, most notably by introducing an effective finite length scale that suppresses long-range coherence. This suggests that imperfect postselection of quantum trajectories conceals the critical features of individual realizations, thereby blurring the signatures of distinct measurement-induced phases.

We explore, both analytically and numerically, the quantum dynamics of a many-body free-fermion system subjected to local density measurements. We begin by extending the mapping to the nonlinear sigma-model (NLSM) field theory for the case of finite evolution time $T$ and different classes of initial states, which lead to different NLSM boundary conditions. The analytical formalism is then used to study how quantum correlations gradually develop, with increasing $T$, from those determined by the initial state towards their steady-state form. The analytical results are confirmed by numerical simulations for several types of initial states. We further consider the long-time limit, when the system in $d+1$ space-time dimensions becomes quasi-one-dimensional, and analyze the scaling of the ``localization'' time (which is simultaneously the purification time and the charge-sharpening time for this class of problems). The analytical predictions for scaling properties are fully confirmed by numerical simulations in a $d=2$ model around the measurement-induced phase transition. We use this dynamical approach to determine numerically the measurement-induced transition point and the associated correlation-length critical exponent.

We study a system of three qubits subject to blind continuous stabilizer measurements and stochastic bit-flip errors. The resulting open-system dynamics are governed by a non-Hermitian Liouvillian super-operator, which exhibits an exceptional point (EP) at a specific critical error rate: two eigenvalues coalesce and their eigenmodes merge into a single vector, forming a nontrivial Jordan chain. Motivated by this structure, we construct a logical-qubit basis directly from the Liouvillian eigenmodes, thereby incorporating both measurement-induced dissipation and error processes into the encoded subspace. By analyzing the Jordan chain at the EP, we identify dynamical features that enhance logical-state stability over short and intermediate times. We then optimize the logical basis to reproduce these EP-induced properties for arbitrary error rates, effectively extending the favorable dynamical behavior beyond the singular point.

We consider the Lindblad quantum-state-diffusion dynamics of the XXZ-staggered spin chain, also focusing on its noninteracting XX-staggered limit, and of the Sachdev-Ye-Kitaev (SYK) model. We describe the process through quantum trajectories and evaluate along the trajectories the nonstabilizerness, quantifying it by the stabilizer Rényi entropy (SRE). In the absence of measurements, we find that the SYK model is the only one in which the time-averaged SRE saturates the random state bound and has a scaling with the system size that is well described by the theoretical prediction for quantum chaotic systems. In the presence of measurements, we numerically find that the steady-state SRE versus the coupling strength to the environment is well fitted by a generalized Lorentzian function. The scaling of the fitting parameters with the system size suggests that the steady-state SRE linearly increases with the system size in all the considered cases and displays no measurement-induced quantum transition, as confirmed by the curves of the steady-state SRE versus the system size. We contrast these results with the case of a driven-dissipative Lipkin-Meshkov-Glick model, where dynamics is restricted to a total-spin eigenspace, the steady-state SRE scales as a power law with the system size, and quantum chaos is marked by plateaus in the exponent of this power law.

We investigate the effect of dissipation on the dynamics of edge modes in the monitored Su-Schrieffer-Heeger model. Our study considers both a linear observable and a nonlinear entanglement measure, namely the two-point correlation function and the disconnected entanglement entropy, as diagnostic tools. While dissipation inevitably alters the entanglement properties observed in the closed system, statistical analysis of quantum trajectories reveals that by protecting the chain's edges from dissipation, it is possible to recover characteristic features analogous to those found in the unitary limit. This highlights the fundamental role of spatial dissipation patterns in shaping the dynamics of edge modes in monitored systems.

Open quantum systems can be approximately described by non-Hermitian Hamiltonians (NHHs) and Lindbladians. The two approaches differ by quantum jump terms corresponding to a measurement of the system by its environment. We analyze the emergence of exceptional points (EPs) in NHHs and Lindbladians. In particular, we show how EPs in NHHs relate to a novel type of EPs -- multi-block EPs -- in the non-Hermitian Liouvillian, i.e. the Lindbladian in absence of quantum jump terms. We further analyze how quantum jump terms modify the multi-block structure. To illustrate our general findings, we present two prime examples: qubits and qutrits coupled to additional ground state levels that serve as sinks of the population. In those examples, we can navigate through the EP block structure by a variation of physical parameters. We analyze how the dynamics of the population of the states is affected by the order of the EPs. Additionally, we demonstrate that the quantum geometric tensor serves as a sensitive indicator of EPs of different kinds.

Controlling, in particular, the acceleration of relaxation dynamics in many-body quantum systems is crucial in various contexts, including quantum computation and state preparation. In this study, we demonstrate that such acceleration can be universally achieved via transient stochastic resetting. This means that during an initial time interval of finite duration, the dynamics is interrupted by resets that take the system to a designated state at randomly selected times. We illustrate this idea for few-body open systems and also for the extreme case of many-body open systems, which exhibit first-order phase transitions, associated with a divergence of relaxation time. In all scenarios, a significant and sometimes even exponential acceleration in reaching the stationary state is observed, similar to the Mpemba effect. The universal nature of this speedup lies in the fact that the design of the reset protocol only requires knowledge of a few macroscopic properties of the target state, such as the order parameter of the phase transition, while it does not necessitate any fine-tuned manipulation of the initial state.

The most widely studied class of Exceptional Points (EPs) is characterized by all the eigenvectors coalescing into a single eigenvector at the EP. Recently, the attention has been brought to a new class of EPs, which corresponds to the case, where the eigenvectors do not coalesce fully and instead form several distinct eigenvectors at the EP. Such Exceptional Points have been named "multiblock" [1] or "fragmented" [2]. They arise naturally in the spectrum of Lindbladian superoperator, if the quantum jump terms are neglected and the underlying effective non-Hermitian Hamiltonian is itself tuned to an EP. As a result, understanding the properties of multiblock EPs is important to discuss the Lindbladian eigenspectrum. In this talk, we demonstrate that multiblock EPs can be converted into each other by infinitesimally small perturbations. In addition to that, we determine which conversions are allowed. To this end, we demonstrate that all EPs of the given algebraic multiplicity form an hierarchy: if we want to tell which EPs we can get from a given one by infinitesimal perturbations, we need to move up the hierarchy. We discuss the results for the non-symmetric case as well as for the case of pseudo-Hermitian symmetry. The latter case is relevant for the discussion of the Lindbladian eigenspectrum: Lindbladian superoperator is known to exhibit a generalized PT-symmetry, which is deeply connected to the pseudo-Hermitian one. [1] A. Shiralieva, G.A. Starkov, B. Trauzettel, Multi-block exceptional points in open quantum systems, arXiv:2509.11856 (2025) [2] S. Bid, H. Schomerus, Fragmented exceptional points and their bulk and edge realizations in lattice models, arXiv:2507.22158 (2025)

Persistent current is a hallmark of quantum phase coherence. We will discuss the fate of the persistent current in a non-equilibrium setting, where a tight-binding ring is subjected to stochastic disorder as well as a fermionic reservoir attached to each site. The current is calculated using the Keldysh technique, and we find that it exhibits non-monotonic behaviour, suggesting two distinct mechanisms of decoherence. While coupling to the reservoirs introduces a coherence length scale given by the inverse of the coupling strength, the other mechanism is more subtle and driven by the ratio of noise strength to reservoir coupling. The interplay of noise and reservoir constitutes a purely non-equilibrium steady state with a flatter distribution function that we effectively describe using classical rate equations.

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Time plays a central role across theoretical physics, from dynamics to thermodynamics. Recent work has explored the quantitative thermodynamic aspects of timekeeping by studying the operation and performance of quantum clocks. In parallel, condensed matter research has uncovered time crystals—quantum phases that spontaneously break time-translation symmetry. Beyond their fundamental interest, such systems may also serve as platforms for quantum technologies.This prompts a natural question: can time crystals serve as quantum clocks, and what are their thermodynamic limitations? In this talk, I will address these questions by discussing dissipative time crystals that function as clocks under continuous monitoring. Note: As it is mandatory to choose a format, I'm choosing "oral", but either (oral or poster) would work the same for me.

Lindbladian dynamics of open systems may be employed to steer a many-body system towards a non-trivial ground state of a local Hamiltonian. Such protocols provide us with tunable platforms facilitating the engineering and study of non-trivial many-body states. Steering towards a degenerate ground state manifold provides us with a protected platform to employ many-body states as a resource for quantum information processing. Notably, ground states of frustrated local Hamiltonians have been known not to be amenable to steering protocols. Revisiting this intricate physics we report two new results: (i) we find a broad class of (geometrically) frustrated local Hamiltonians for which steering of the ground state manifold is possible through a sequence of discrete steering steps. Following the steering dynamics, states within the degenerate ground-state manifold keep evolving in a non-stationary manner. (ii) For the class of Hamiltonians with ground states which are non-steerable through local superoperators, we derive a "glass floor" on how close to the ground state one can get implementing a steering protocol. This is expressed invoking the concept of cooling-by-steering (a lower bound of the achievable temperature), or through an upper bound of the achievable fidelity. Our work provides a systematic outline for studying quantum state manipulation of a broad class of strongly correlated states.

In this talk/poster, I introduce distinct dynamical signatures of bulk and boundary modes in the quantum dynamics of non-Hermitian systems. Although these modes typically appear together, their individual roles and observable signatures have often been intertwined. Chiral damping is a known manifestation of the non-Hermitian skin effect in quantum dynamics, serving as a signature of bulk states. However, boundary modes also contribute to the skin effect, and their separation from bulk behavior—as well as their distinguishable dynamical signatures—has so far remained unexplored. Here, we identify experimentally accessible signatures of boundary modes and establish fundamental criteria for separating bulk and boundary dynamics. We show that such a separation is possible when governed by the Liouvillian separation gap.

We present a single-quench protocol that generates unitary $k$-designs with minimal control. A system first evolves under a random Hamiltonian $H_1$; at a switch time $t_s \geq t_{\mathrm{Th}}$ (the Thouless time), it is quenched to an independently drawn $H_2$ from the same ensemble and then evolves under $H_2$. This single quench breaks residual spectral correlations that prevent strictly time-independent chaotic dynamics from forming higher-order designs. The resulting ensemble approaches a unitary $k$-design using only a single control operation -- far simpler than Brownian schemes with continuously randomized couplings or protocols that apply random quenches at short time intervals. Beyond offering a direct route to Haar-like randomness, the protocol yields an operational, measurement-friendly definition of $t_{\mathrm{Th}}$ and provides a quantitative diagnostic of chaoticity. It further enables symmetry-resolved and open-system extensions, circuit-level single-quench analogs, and immediate applications to randomized measurements, benchmarking, and tomography.