arXiv subjects

Lorenza Viola

Publications and source records attributed to Lorenza Viola.

At least 19 recordsLinked to original sources

arXiv2026

Heisenberg scaling under collective non-parallel directional noise via geometric state design

Spin-squeezed states enable entanglement-enhanced frequency estimation; however, the achievable performance is limited in practice by decoherence. We study the problem of parameter estimation under \emph{classical collective noise} that acts along a \emph{fixed} direction during signal encoding. While we restrict our analysis to Gaussian noise statistics, no assumption is made on the nature of the noise temporal correlations. Our approach captures both parallel (dephasing) and single-axis transverse noise as special cases, and covers both Markovian and non-Markovian metrological regimes. In the properly squeezed limit, where a Holstein-Primakoff description is accurate, we identify a geometric noise-immunity mechanism: for \emph{known} non-parallel signal and noise axes, an appropriate one-axis-twisted input encodes the signal in a quadrature that is metric-orthogonal to the direction of noise-induced diffusion. Irrespective of the noise temporal correlations, the resulting estimation precision exhibits Heisenberg scaling in the probe number. Optimal performance is achievable by measuring a single collective spin component. Imperfect knowledge of the noise axis produces a crossover from Heisenberg scaling at moderate probe number back to the known collective-dephasing bounds asymptotically.

quant-ph↗

arXiv2026

Decoupling band topology from criticality in bosonic systems

A new understanding of criticality in systems described by quadratic bosonic Hamiltonians (QBHs) ties the emergence of long-range correlations to boundaries of dynamical, not thermodynamical, stability in the parameter space. This separation occurs because the solution of the Heisenberg equations of motion is determined by an auxiliary pseudo- Hermitian dynamical system. The boundary points of a region of dynamical stability can be either exceptional points, generically associated with long-range correlations, or Krein collisions, where correlations can be either long- or short-range. We investigate the interplay of this landscape of possibilities with band topology and boundary physics, by relying on both specific examples and general arguments. The examples stem from a two-parameter, thermodynamically unstable family of QBHs obtained from the bosonic Su-Schrieffer-Heeger model by breaking particle conservation while preserving a chiral pseudo-symmetry. The dynamically stable regime breaks up into different regions labeled by an integer-valued symplectic analogue of the Berry phase. The topological phase transition is a line of Krein collisions, which coincides with the closing of a band gap at zero and causes the localization length of the topologically mandated boundary zero modes to diverge before disappearing. In the unstable regime, we show that the chiral pseudo-symmetry of our model induces, despite the broken particle-number symmetry, enough structure on its associated dynamical matrices to support a topological classification and a bulk-boundary correspondence, independently of dynamical stability. This strongly suggests that bosonic topological physics extracted from basic index theory is insensitive to dynamical stability and, a posteriori, to non-interacting criticality.

quant-ph↗

arXiv2026

Quantum criticality beyond thermodynamic stability

For a many-body system in equilibrium, described by a thermodynamically stable Hamiltonian, quantum criticality is associated with structural changes of the many-body ground state. However, there exist physically relevant models, notably, certain quadratic bosonic Hamiltonians (QBHs), which fail to have a ground state. QBHs can be dynamically stable or unstable. We show the notion of criticality is meaningful for the entire class of QBHs that are dynamically stable or at the boundary of instability, regardless of thermodynamic stability, and that the key state for such QBHs is a naturally and unambiguously defined quasiparticle vacuum (QPV). This state is Gaussian, and coincides with the ground state if the QBH is thermodynamically stable. We identify a relevant spectral gap, the Krein gap, associated to the minimal spectral separation between creation and annihilation operators, and show that the QPV is unique when the Krein gap is positive. We prove that, for dynamically stable QBHs with finite-range couplings, correlations are exponentially bounded unless the Krein gap closes, which is associated with one of two spectral degeneracies: an exceptional point or a Krein collision. Consequently, long-range QPV correlations can ensue. Thus, the Krein gap takes the role of the spectral gap for dynamically stable QBHs, and the boundary of dynamical stability and criticality (associated to exceptional points) or multicriticality (associated to Krein collisions) are the same. We also find that bosonic critical behavior beyond thermodynamic stability is witnessed by the scaling of the entanglement entropy and other indicators of equilibrium criticality from information geometry. Our framework opens the door to investigating all dynamically stable QBHs through the lens of critical phenomena, including thermodynamically unstable ones from photonics, cavity-QED, and magnonics.

quant-ph↗

arXiv2026

Precision bounds for frequency estimation under collective dephasing and open-loop control

Dephasing noise is a ubiquitous source of decoherence in current atomic sensors. We address the problem of entanglement-assisted frequency estimation subject to classical dephasing noise with full spatial correlations (collective) and arbitrary temporal correlations. Our contributions are threefold. (i) We derive rigorous, state-independent bounds on the achievable estimation precision, showing how they are entirely determined by the short-time behavior of the decoherence function. For temporally uncorrelated (Markovian) dephasing, precision is limited by a probe-independent constant. For temporally correlated stationary noise, the bound approaches the noiseless limit for classical states, precluding any asymptotic quantum advantage. (ii) We show that these scaling bounds are tight, by constructing generalized Ramsey protocols that saturate them. These optimal protocols use squeezing at the input and before readout, both of which are available in state-of-the-art atomic interferometers. Implementing a perfect-echo protocol, which reaches Heisenberg scaling in the absence of noise, remains optimal in this noisy setting, irrespective of the noise temporal correlations. (iii) We prove that arbitrary collective open-loop control cannot lift the no-go for super-classical precision scaling under either Markovian or colored stationary noise, highlighting the detrimental nature of full spatial correlations. In the latter case, temporal correlations may nonetheless enable constant-factor improvements over the standard quantum limit, which may still be important in practical metrological scenarios.

quant-ph↗

arXiv2026

Approximate Reduced Lindblad Dynamics via Algebraic and Adiabatic Methods

We present an algebraic framework for approximate model reduction of Markovian open quantum dynamics that guarantees complete positivity and trace preservation by construction. First, we show that projecting a Lindblad generator on its center manifold -- the space spanned by eigenoperators with purely imaginary eigenvalue -- yields an asymptotically exact reduced quantum dynamical semigroup whose dynamics is unitary, with exponentially decaying transient error controlled by the generator's spectral gap. Second, for analytic perturbations of a Lindblad generator with a tractable center manifold, we propose a perturbative reduction that keeps the reduced space fixed at the unperturbed center manifold. The resulting generator is shown to remain a valid Lindbladian; explicit finite-time error bounds that quantify leakage from the unperturbed center sector are provided. We further clarify the connection to adiabatic elimination methods, by both showing how the algebraic reduction can be directly related to a first-order adiabatic-elimination and by providing sufficient conditions under which the latter method can be applied while preserving complete positivity. We showcase the usefulness of our techniques in dissipative many-body quantum systems exhibiting non-stationary long-time dynamics.

quant-ph↗

arXiv2026

Dynamical metastability and transient topological magnons in interacting driven-dissipative magnetic systems

Metastability, i.e., partial relaxation to long-lived, quasi-stationary states before true asymptotic equilibrium sets in, emerges ubiquitously in classical and quantum dynamical systems as a result of timescales separation. In open quantum systems, an intrinsically nonequilibrium analogue, dynamical metastability, can originate from the spectral geometry of a non-Hermitian operator. In noninteracting models, this mechanism produces boundary-sensitive anomalous relaxation, transient amplification, and topologically mandated long-lived edge modes, all of which are enhanced as system size grows. Here we extend dynamical metastability into the nonlinear, interacting regime and identify magnetic heterostructures as a natural platform for its exploration. We introduce an interacting spin Lindbladian whose linearized magnon dynamics map onto a dynamically metastable Hatano-Nelson chain, and show that dynamical metastability in the noninteracting limit seeds genuinely nonlinear phenomena, including size-dependent spin dipping and anomalous attraction to unstable equilibria. Long-lived edge states associated to topologically mandated Dirac bosons persist under nonlinearities and disorder. We further analyze the magnetization dynamics in magnetic multilayers within the classical Landau-Lifshitz-Gilbert-Slonczewski framework, identifying Dzyaloshinskii-Moriya interaction, nonlocal damping, and spin-transfer torque as control parameters governing bulk-boundary stability mismatch and band topology. While all the distinctive dynamical phenomena previously identified reappear in this experimentally relevant setting, the LLGS framework also supports multistability and limit cycles that are absent in the quantum model. Our results constitute the first systematic study of dynamical metastability in nonlinear dynamics, directly relevant to spin-torque oscillator arrays, magnonic devices, and beyond.

cond-mat.mes-hall↗

arXiv2025

Testing the weak equivalence principle for nonclassical matter with torsion balances

We propose tests of the weak equivalence principle (WEP) using a torsion balance, in which superposition of energy eigenstates are created in a controllable way for the test masses. After general considerations on the significance of tests of the WEP using quantum states and the need for considering inertial and gravitational masses as operators, we develop a model to derive the matrix elements of the free-fall operator, showing that the variance of the acceleration operator, in addition to its mean, enables estimation of violations of the WEP due to quantum coherence in a way that is robust with respect to shot-to-shot fluctuations. Building on this analysis, we demonstrate how the validity of the WEP may be tested in a torsion balance setup, by accessing the mean and variance of a torque operator we introduce and quantize. Due to the long acquisition times of the signal as compared to the timescale on which coherent superposition states may survive, we further propose a dynamical setting, where the torsion balance is subject to a time-dependent gravitational field, and measurements of angular acceleration encode possible violations of the WEP.

quant-ph↗

arXiv2025

Generation of Ultrahigh Anomalous Hall Conductivities via Optimally Prepared Topological Floquet States

Ultrafast quantum matter experiments have validated predictions from Floquet theory - notably, the dynamical modification of the electronic band structure and the light-induced anomalous Hall effect, via monotonic modulation of the driving amplitude. Here, we demonstrate how new physics is uncovered by leveraging quantum optimal control techniques to design Floquet amplitude modulation profiles. We discover a fundamentally different regime of topological transport, whereby the optimal oscillatory preparation protocol functions as a non-adiabatic topological pump: as a result, ultrahigh time-averaged anomalous Hall conductivities emerge, that reach up to around seventy times the values one would expect from the Chern number of the targeted Floquet state. The optimal protocols achieve >99% fidelity at the topological energy gap closing point - a twenty-fold improvement over standard monotonic approaches in as little as ten Floquet cycles - while unexpectedly generating the predicted ultrahigh conductivities. Our findings demonstrate that optimally prepared non-equilibrium quantum states can access transport regimes not achievable in the corresponding equilibrium system or even by applying conventional Floquet approaches, opening new avenues for ultrafast quantum technologies and topological device applications.

cond-mat.mes-hall↗

arXiv2025

Model Reduction for Controlled Quantum Markov Dynamics

We consider the problem of model reduction for Markovian quantum systems whose dynamics are described by a time-dependent Lindblad generator -- notably, as arising in the presence of external control. Our approach, which builds upon Krylov operator subspaces and operator-algebraic techniques introduced for time-independent generators, returns a reduced model that reproduces exactly the evolution of observables of interest and is guaranteed to be in Lindblad form.

quant-ph↗

arXiv2025

Separate and efficient characterization of state-preparation and measurement errors using single-qubit operations

In many platforms, errors from state-preparation and measurement (SPAM) dominate over single-qubit gate errors. To inform further hardware improvements and the development of more effective SPAM mitigation strategies, it is necessary to separately characterize the error contributions from state-preparation (SP) and measurement (M). Here, we show how to construct a protocol that can efficiently and separately characterize the SP and M error parameters by using only high-fidelity single-qubit gates and repeated single-qubit measurements without reset. The measurements are assumed to be non-destructive and M errors are taken to be (spatially and temporally) uncorrelated and classical. Notably, the circuit depth of the protocol is independent of system size, and the target parameters may be characterized to a precision that is only limited by the number of experimental repetitions. We employ our protocol for the parallel characterization of SPAM errors on multiple qubits in the IBM Quantum Platform devices, where we find SP infidelities up to $6.57\%$ and readout assignment errors up to $19.1\%$. Using numerical simulations, we also demonstrate how measurement-error mitigation that does not properly account for SP errors generally leads to a biased estimate of measured observable expectation values.

quant-ph↗

arXiv2025

Demonstration of a Tunable Non-Hermitian Nonlinear Microwave Dimer

Achieving and controlling non-reciprocity in engineered photonic structures is of fundamental interest in science and engineering. Here, we introduce a tunable, non-Hermitian, nonlinear microwave dimer designed to precisely implement phase-non-reciprocal hopping dynamics between two spatially separated cavities at room temperature. Our system incorporates simple components such as three-dimensional microwave cavities, unidirectional amplifiers, digital attenuators, and a digital phase shifter. By dividing the energy transfer into forward and backward paths, our platform enables precise control over the amplitude and phase of the propagating signals in each direction. Through a combination of theoretical and numerical analysis, we model the dynamics of the system under different operating conditions, including a parameter regime where the gain not only compensates for but significantly exceeds the inherent loss. Our model quantitatively reproduces the observed weak-drive transmission spectra, the amplitude and frequency of self-sustained limit cycles, and the phase locking synchronization effect between the limit cycle and an external microwave tone. Our results may have implications in areas ranging from sensing and synthetic photonic materials to neuromorphic computing and quantum networks, while providing new insight into the interplay between non-Hermitian and nonlinear dynamics.

quant-ph↗

arXiv2024

Optimal asymptotic precision bounds for nonlinear quantum metrology under collective dephasing

Interactions among sensors can provide, in addition to entanglement, an important resource for boosting the precision in quantum estimation protocols. Dephasing noise, however, remains a leading source of decoherence in state-of-the-art quantum sensing platforms. We analyze the impact of classical {\em collective dephasing with arbitrary temporal correlations} on the performance of generalized Ramsey interferometry protocols with \emph{quadratic} encoding of a target frequency parameter. The optimal asymptotic precision bounds are derived for both product coherent spin states and for a class of experimentally relevant entangled spin-squeezed states of $N$ qubit sensors. While, as in linear metrology, entanglement offers no advantage if the noise is Markovian, a precision scaling of $N^{-1}$ is reachable with classical input states in the quadratic setting, which is improved to $N^{-5/4}$ when temporal correlations are present and the Zeno regime is accessible. The use of nonclassical spin-squeezed states and a nonlinear readout further allows for an $N^{-3/2}$ precision scaling, which we prove is asymptotically optimal. We also show how to counter {\em noise-induced bias} by introducing a simple ratio estimator which relies on detecting two suitable system observables, and show that it remains asymptotically unbiased in the presence of dephasing, without detriment to the achievable precision.

quant-ph↗

arXiv2024

Exact Model Reduction for Continuous-Time Open Quantum Dynamics

We consider finite-dimensional many-body quantum systems described by time-independent Hamiltonians and Markovian master equations, and present a systematic method for constructing smaller-dimensional, reduced models that exactly reproduce the time evolution of a set of initial conditions or observables of interest. Our approach exploits Krylov operator spaces and their extension to operator algebras, and may be used to obtain reduced linear models of minimal dimension, well-suited for simulation on classical computers, or reduced quantum models that preserve the structural constraints of physically admissible quantum dynamics, as required for simulation on quantum computers. Notably, we prove that the reduced quantum-dynamical generator is still in Lindblad form. By introducing a new type of observable-dependent symmetries, we show that our method provides a non-trivial generalization of techniques that leverage symmetries, unlocking new reduction opportunities. We quantitatively benchmark our method on paradigmatic open many-body systems of relevance to condensed-matter and quantum-information physics. In particular, we demonstrate how our reduced models can quantitatively describe decoherence dynamics in central-spin systems coupled to structured environments, magnetization transport in boundary-driven dissipative spin chains, and unwanted error dynamics on information encoded in a noiseless quantum code.

quant-ph↗

arXiv2024

Limitations to Dynamical Error Suppression and Gate-Error Virtualization from Temporally Correlated Nonclassical Noise

Realistic multi-qubit noise processes often result in error mechanisms that are not captured by the probabilistic, Markovian error models commonly employed in circuit-level analyses of quantum fault-tolerance. By working within an open-quantum system Hamiltonian formulation, we revisit the validity of the notion of a constant gate error in the presence of noise that is both temporally correlated and nonclassical, and whose impact is mitigated through perfect instantaneous dynamical decoupling subject to finite timing constraints. We study a minimal exactly solvable single-qubit model under Gaussian quantum dephasing noise, showing that the fidelity of a dynamically protected idling gate can depend strongly on its location in the circuit and the history of applied control, even when the system-side error propagation is fully removed through perfect reset operations. For digital periodic control, we prove that, under mild conditions on the low-frequency behavior of the nonclassical noise spectrum, the gate fidelity saturates at a value that is strictly smaller than the one attainable in the absence of control history; the presence of high-frequency noise peaks is also found as especially harmful, due to the possible onset of control-induced resonance effects. We explicitly relate these features to the evolution of the bath statistics during the computation, which has not been fully accounted for in existing treatments. We find that only if decoupling can keep the qubit highly pure over a timescale larger than the correlation time of the noise, the bath approximately converges to its original statistics and a stable-in-time control performance is recovered. Implications of this costly re-equilibration of the quantum bath statistics for layered quantum fault-tolerant architectures are discussed.

quant-ph↗

arXiv2024

The Interplay of Finite and Infinite Size Stability in Quadratic Bosonic Lindbladians

We provide a framework for understanding dynamical metastability in open many-body systems of free bosons, whereby the dynamical stability properties of the system in the infinite-size (thermodynamic) limit may sharply differ from those of any finite-size truncation, and anomalous transient dynamics may arise. By leveraging pseudospectral techniques, we trace the discrepancy between asymptotic and transient dynamics to the non-normality of the underlying quadratic bosonic Lindbladian (QBL) generator, and show that two distinct flavors of dynamical metastability can arise. QBLs exhibiting type I dynamical metastability, previously discussed in the context of anomalous transient amplification [Phys. Rev. Lett. 127, 245701 (2021)], are dynamically unstable in the infinite-size limit, yet stable once open boundaries are imposed. Type II-dynamically metastable QBLs, which we uncover in this work, are dynamically stable for infinite size, but become unstable under open boundary conditions for arbitrary finite system size. We exhibit representative models for both types of metastability in the dissipative, as well as the limiting closed-system (Hamiltonian) settings, and analyze distinctive physical behavior they can engender. We show that dynamical metastability manifests itself in the generation of entanglement entropy, by way of a transient which reflects the stability phase of the infinite (rather than the actual finite) system and, as a result, is directly tied to the emergence of super-volume scaling in type I systems. Finally, we demonstrate how, even in Hermitian, and especially in highly non-normal regimes, the spectral properties of an infinite-size QBL are reflected in the linear response functions of the corresponding finite QBLs, by way of resonant pseudospectral modes.

quant-ph↗

arXiv2024

SPAM-Robust Multi-axis Quantum Noise Spectroscopy in Temporally Correlated Environments

Characterizing temporally correlated (``non-Markovian'') noise is a key prerequisite for achieving noise-tailored error mitigation and optimal device performance. Quantum noise spectroscopy can afford quantitative estimation of the noise spectral features; however, in its current form it is highly vulnerable to implementation non-idealities, notably, state-preparation and measurement (SPAM) errors. Further to that, existing protocols have been mostly developed for dephasing-dominated noise processes, with competing dephasing and relaxation effects being largely unaccounted for. We introduce quantum noise spectroscopy protocols inspired by spin-locking techniques that enable the characterization of arbitrary temporally correlated multi-axis noise on a qubit with fixed energy splitting, while remaining resilient to realistic static SPAM errors. By validating our protocol's performance in both numerical simulation and cloud-based IBM quantum processors, we demonstrate the successful separation and estimation of native noise spectrum components as well as SPAM error rates. We find that SPAM errors can significantly alter or mask important noise features, with spectra overestimated by up to 26.4% in a classical noise regime. Clear signatures of non-classical noise are manifest in the reconstructed IBM-qubit dephasing spectra, once SPAM-error effects are compensated for. Our work provides a timely tool for benchmarking realistic sources of noise in qubit devices.

quant-ph↗

arXiv2024

Topological zero modes and edge symmetries of metastable Markovian bosonic systems

Tight bosonic analogs of free-fermionic symmetry-protected topological phases, and their associated edge-localized excitations, have long evaded the grasp of condensed-matter and AMO physics. In this work, building on our initial exploration [PRL 127, 245701 (2021)], we identify a broad class of quadratic bosonic systems subject to Markovian dissipation that realize tight bosonic analogs of the Majorana and Dirac edge modes characteristic of topological superconductors and insulators, respectively. To this end, we establish a general framework for topological metastability for these systems, by leveraging pseudospectral theory as the appropriate mathematical tool for capturing the non-normality of the Lindbladian generator. The resulting dynamical paradigm, which is characterized by both a sharp separation between transient and asymptotic dynamics and a nontrivial topological invariant, is shown to host edge-localized modes, which we dub Majorana and Dirac bosons. Generically, these consist of one conserved mode and a canonically conjugate generator of an approximate symmetry of the dynamics. The general theory is exemplified through several models exhibiting a range of exotic boundary physics that topologically metastable systems can engender. In particular, we explore the extent to which Noether's theorem is violated in this dissipative setting and the interplay between symmetries and these edge modes. We also demonstrate the possibility of anomalous parity dynamics for a bosonic cat state prepared in a topologically metastable system. Observable multitime signatures in the form of anomalously long-lived quantum correlations and divergent zero-frequency power spectral peaks are proposed and discussed in detail. Our results point to a new paradigm of genuine symmetry-protected topological physics in free bosons, embedded deeply in the long-lived transient regimes of metastable dynamics.

quant-ph↗

arXiv2023

Nearly Heisenberg-limited noise-unbiased frequency estimation by tailored sensor design

We consider entanglement-assisted frequency estimation by Ramsey interferometry, in the presence of dephasing noise from spatiotemporally correlated environments.By working in the widely employed local estimation regime, we show that even for infinite measurement statistics, noise renders standard estimators biased or ill-defined. We introduce ratio estimators which, at the cost of doubling the required resources, are insensitive to noise and retain the asymptotic precision scaling of standard ones. While ratio estimators are applicable also in the limit of Markovian noise, we focus on non-Markovian dephasing from a bosonic bath and show how knowledge about the noise spectrum may be used to maximize metrological advantage, by tailoring the sensor's geometry. Notably, Heisenberg scaling is attained up to a logarithmic prefactor by maximally entangled states.

quant-ph↗