arXiv subjects

Daniel Malz

Publications and source records attributed to Daniel Malz.

At least 19 recordsLinked to original sources

arXiv2026

Collective decay of interacting bosons

We study a bosonic analog of the paradigmatic Dicke model of superradiance, comprising interacting bosonic modes subject to fully symmetric collective decay. Depending on the interaction strength, we uncover qualitatively distinct regimes of emission. For strong interactions, the emission closely resembles Dicke superradiance, with perturbative corrections arising from the presence of additional levels. For weaker interactions, the bosonic statistics qualitatively changes the dynamics, leading to a crossover to subradiant emission. Remarkably, we show that the dynamics in this regime can be described by rate equations analogous to those of the Dicke model despite the large accessible bosonic Hilbert space. Our findings are based on a combination of analytical arguments and large-scale numerics enabled by the permutational symmetry of the problem and may be probed in circuit QED experiments.

quant-ph↗

arXiv2026

Algorithmic Locality via Provable Convergence in Quantum Tensor Networks

Belief propagation has recently emerged as a powerful framework for evaluating tensor networks in higher dimensions, combining computational efficiency with provable analytical guarantees. In this work, we develop the first end-to-end theory of tensor network belief propagation for a class of projected entangled pair states satisfying \emph{strong injectivity}. We show that when the injectivity parameter exceeds a constant threshold, BP fixed points can be found efficiently, and a cluster-corrected BP algorithm computes physical quantities to $1/\mathrm{poly}(N)$ error in $\mathrm{poly}(N)$ time for an $N$ qubit system. We identify a striking phenomenon we term \emph{algorithmic locality}: local perturbations of the tensor network affect the BP fixed point with an influence decaying rapidly with distance. As a result, updates to the fixed point after a local perturbation can be carried out using only local recomputation. Moreover, through the cluster expansion, this locality extends to observables, implying that local expectation values can be approximated from local data with controlled accuracy. Our results provide the first rigorous guarantee for the effectiveness of tensor-network belief propagation on a wide class of many-body states, bridging a gap between widely used numerical practice and provable algorithmic performance.

quant-ph↗

arXiv2026

Constraints on phantom codes from automorphism group bounds

Executing a logical quantum circuit fault-tolerantly incurs a large spacetime overhead. Recent work has proposed and investigated phantom codes, defined by the property that every in-block logical $\mathrm{CNOT}$ circuit can be implemented with a physical permutation, a property that has the potential to greatly reduce the depth of compiled circuits. Here we show that phantomness comes at the cost of low encoding rate. Specifically, we prove that any binary phantom code encoding $k$ logical qubits into $n$ physical qubits with distance $d\geq 2$ obeys the bound $k\leq \log_2(n+1)$ for all $k\neq 4$. For $k=4$ we explicitly construct a nonstabiliser $(\!(8, 2^4, 2)\!)$ phantom code that violates the bound and has a transversal non-Clifford gate. We further show that, within the class of nontrivial CSS phantom codes with $k\neq 4$, there is a unique family of codes saturating this bound. In addition, we prove that this logarithmic ceiling cannot be circumvented by permitting additional local unitary gates, or by making use of subsystem codes: any subspace or subsystem code admitting a $\mathrm{SWAP}$-transversal implementation of every logical $\mathrm{CNOT}$ circuit is constrained to satisfy the same bound. These bounds follow from a general theorem relating the length of a quantum code to the structure of its automorphism group, a result which may find applications beyond phantom codes.

quant-ph↗

arXiv2026

Noise-induced contraction of MPO truncation errors in noisy random circuits and Lindbladian dynamics

We study how matrix-product-operator (MPO) truncation errors evolve when simulating two setups: (1) 1D Haar-random circuits under either depolarizing noise or amplitude-damping noise, and (2) 1D Lindbladian dynamics of a non-integrable quantum Ising model under either depolarizing or amplitude-damping noise. We first show that the average purity of the system density matrix relaxes to a steady value on a timescale that scales inversely with the noise rate. We then show that truncation errors contract exponentially in both system size $N$ and the evolution time $t$, as the noisy dynamics maps different density matrices toward the same steady state. This yields an empirical bound on the $L_1$ truncation error that is exponentially tighter in $N$ than the existing bound. Together, these results provide empirical evidence that MPO simulation algorithms may efficiently sample from the output of 1D noisy random circuits [setup (1)] at arbitrary circuit depth, and from the steady state of 1D Lindbladian dynamics [setup (2)].

quant-ph↗

arXiv2026

Contractivity of time-dependent driven-dissipative systems

In a number of physically relevant contexts, a quantum system interacting with a decohering environment is simultaneously subjected to time-dependent controls and its dynamics is thus described by a time-dependent Lindblad master equation. Of particular interest in such systems is to understand the circumstances in which, despite the ability to apply time-dependent controls, they lose information about their initial state exponentially with time i.e., their dynamics are exponentially contractive. While there exists an extensive framework to study contractivity for time-independent Lindbladians, their time-dependent counterparts are far less well understood. In this paper, we study the contractivity of Lindbladians, which have a fixed dissipator (describing the interaction with an environment), but with a time-dependent driving Hamiltonian. We establish exponential contractivity in the limit of sufficiently small or sufficiently slow drives together with explicit examples showing that, even when the fixed dissipator is exponentially contractive by itself, a sufficiently large or a sufficiently fast Hamiltonian can result in non-contractive dynamics. Furthermore, we provide a number of sufficient conditions on the fixed dissipator that imply exponential contractivity independently of the Hamiltonian. These sufficient conditions allow us to completely characterize Hamiltonian-independent contractivity for unital dissipators and for two-level systems.

quant-ph↗

arXiv2026

Polaron-Polaritons in Subwavelength Arrays of Trapped Atoms

Subwavelength arrays of atoms trapped in optical lattices or tweezers are inherently susceptible to deformations: Optomechanical forces displace atoms within their trapping potential and produce lattice distortions, which in turn modify the optical response of the array. We show that this optomechanical coupling hybridizes collective atomic excitations (polaritons) with phonons, forming polaron-polaritons -- the fundamental quasiparticles governing light-matter interactions in arrays of trapped atoms. Using analytical polaron theory and numerical simulations, we find that: (1) phonons can strongly enhance the decay of subradiant states, but also enable their efficient excitation; (2) transport of dark excitations remains remarkably robust even at low trap frequencies, except when a polariton can resonantly scatter phonons; and (3) motion reduces the reflectivity of a two-dimensional atomic mirror; by identifying design principles that mitigate this degradation, we recover reflectivity above 99% under realistic conditions. Our findings lay the foundation for analyzing motional effects in key applications and suggest new ways to harness them in state-of-the-art experiments.

quant-ph↗

arXiv2025

Gibbs state postulate from dynamical stability -- Redundancy of the zeroth law

Gibbs states play a central role in quantum statistical mechanics as the standard description of thermal equilibrium. Traditionally, their use is justified either by a heuristic, a posteriori reasoning, or by derivations based on notions of typicality or passivity. In this work, we show that Gibbs states are completely characterized by assuming dynamical stability of the system itself and of the system in weak contact with an arbitrary environment. This builds on and strengthens a result by Frigerio, Gorini, and Verri (1986), who derived Gibbs states from dynamical stability using an additional assumption that they referred to as the "zeroth law of thermodynamics", as it concerns a nested dynamical stability of a triple of systems. We prove that this zeroth law is redundant and that an environment consisting solely of harmonic oscillators is sufficient to single out Gibbs states as the only dynamically stable states.

math-ph↗

arXiv2025

Renormalization-group-based preparation of matrix product states on up to 80 qubits

A key challenge for quantum computers is the efficient preparation of many-body entangled states across many qubits. In this work, we demonstrate the preparation of matrix product states (MPS) using a renormalization-group(RG)-based quantum algorithm on superconducting quantum hardware. Compared to sequential generation, it has been shown that the RG-based protocol asymptotically prepares short-range correlated MPS with an exponentially shallower circuit depth (when scaling system size), but it is not yet clear for which system sizes it starts to convey an advantage. We thus apply this algorithm to prepare a class of MPS exhibiting a phase transition between a symmetry-protected topological (SPT) and a trivial phase for systems of up to 80 qubits. We find that the reduced depth of the RG-based circuits makes them more resilient to noise, and that they generally outperform the sequential circuits for large systems, as we showcase by measuring string-order-like local expectation values and energy densities. We thus demonstrate that the RG-based protocol enables large-scale preparation of MPS and, in particular, SPT-ordered states beyond the fixed point.

quant-ph↗

arXiv2025

Estimating applied potentials in cold atom lattice simulators

Cold atoms in optical lattices are a versatile and highly controllable platform for quantum simulation, capable of realizing a broad family of Hubbard models, and allowing site-resolved readout via quantum gas microscopes. In principle, arbitrary site-dependent potentials can also be implemented; however, since lattice spacings are typically below the diffraction limit, precisely applying and calibrating these potentials remains challenging. Here, we propose a simple and efficient experimental protocol that can be used to measure any potential with high precision. The key ingredient in our protocol is the ability in some atomic species to turn off interactions using a Feshbach resonance, which makes the evolution easy to compute. Given this, we demonstrate that collecting snapshots from the time evolution of a known, easily prepared initial state is sufficient to accurately estimate the potential. Our protocol is robust to state preparation errors and uncertainty in the hopping rate. This paves the way toward precision quantum simulation with arbitrary potentials.

cond-mat.quant-gas↗

arXiv2025

Gaussian tomography for cold-atom simulators

A limitation of analog quantum simulators based on cold atoms in optical lattices is that readout is typically limited to observables diagonal in the charge basis, i.e., densities and density correlation functions. To overcome this limitation, we propose experiment-friendly schemes to measure charge-off-diagonal correlations (such as currents). Our protocols use non-interacting dynamics for random times followed by standard quantum gas microscope measurements to effectively measure in random bases. The main requirement of our scheme is the ability to turn off interactions, which can be done in many atomic species using Feshbach resonances. Importantly, our scheme requires no local control and otherwise also exhibits modest requirements in terms of total evolution time and number of repetitions. We numerically demonstrate efficient estimation of bilinear correlation functions, requiring less than $4000$ samples to measure local currents to 5% error (system-size independent) and $\sim 10^4$ samples to simultaneously measure all non-local correlations in 70-site systems. Due to its simplicity, our protocol is implementable in existing platforms and thus paves the way to precision measurements beyond particle number measurements.

quant-ph↗

arXiv2025

Robust Superradiance and Spontaneous Spin Ordering in Disordered Waveguide Quantum Electrodynamics

We study the collective emission of a disordered array of $N$ excited two-level atoms into a one-dimensional photonic waveguide. In the perfectly ordered case, where atoms are spaced by exact integer multiples of the wavelength, the system exhibits the characteristic superradiant burst with a peak emission rate scaling as $N^2$. Using large-scale semiclassical simulations, we find that this key signature of superradiance remains asymptotically robust under strong spatial and spectral disorder, but also exhibits subtle finite-size scaling toward this limit. To explain our observations, we provide an analytical variational estimate for the maximal decay rate, which tightly bounds the numerical results and reveals how disorder shapes the collective decay. Specifically, we find that even in the presence of strong disorder, the spins tend to self-organize spontaneously according to their locations, which overall optimizes constructive interference effects and explains the emergence of mirror-asymmetric correlations in superradiant decay. These findings resolve important open questions regarding the existence and nature of superradiance in strongly disordered arrays and offer valuable insights for understanding collective quantum optical phenomena in realistic systems.

quant-ph↗

arXiv2025

Measurement-induced entanglement in noisy 2D random circuits

We study measurement-induced entanglement (MIE) generated by column-by-column sampling of noisy 2D random circuits of size $N$ and depth $T$. Focusing primarily on Clifford circuits and using the operator entanglement $S_{\rm op}$ of the sampling-induced boundary state as a proxy for computational complexity, first, we reproduce in the noiseless limit a finite-depth transition from area- to volume-law scaling at a threshold depth $T_c=6$. In contrast, in the presence of single-qubit depolarizing noise at any constant rate $p>0$, we find that the operator entanglement $S_{\rm op}$ obeys an area law, with its maximum value scaling approximately linearly with $T/p$ in the regime $T>T_c$. By analyzing the spatial distribution of stabilizer generators, we observe exponential localization of stabilizer generators; this both accounts for the scaling of the maximal $S_{\rm op}$ and implies an exponential decay of conditional mutual information across buffered tripartitions, which we also confirm numerically. Together, these results indicate that constant local noise destroys long-range MIE in 2D random Clifford circuits, and that a tensor-network based algorithm can efficiently sample from noisy 2D random Clifford circuits (i) at sub-logarithmic depths $T = o(\log N)$ for any constant noise rate $p = \Omega(1)$, and (ii) at constant depths $T = O(1)$ for noise rates $p = \Omega(\log^{-1}N)$. Finally, we turn to depth $T=4$ Haar-random and measurement-based quantum computing-type circuits, providing evidence that MIE in noisy 2D Haar-random circuits exhibits the same qualitative behavior as in random Clifford circuits, and that noise destroys the volume-law scaling of MIE in non-Clifford circuits.

quant-ph↗

arXiv2025

Computational complexity of injective projected entangled pair states

Projected entangled pair states (PEPS) constitute a variational family of quantum states with area-law entanglement. PEPS are particularly relevant and successful for studying ground states of spatially local Hamiltonians. However, computing local expectation values in these states is known to be \postBQP-hard. Injective PEPS, where all constituent tensors fulfil an injectivity constraint, are generally believed to be better behaved, because they are unique ground states of spatially local Hamiltonians. In this work, we therefore examine how the computational hardness of contraction depends on the injectivity. We establish that below a constant positive injectivity threshold, evaluating local observables remains \postBQP-complete, while above a different constant nontrivial threshold there exists an efficient classical algorithm for the task, resolving an open question from (Anshu et al., STOC `24). We do this by proving that noisy postselected quantum computation can be made fault-tolerant.

quant-ph↗

arXiv2025

Random Permutation Circuits Beyond Qubits are Quantum Chaotic

Random permutation circuits were recently introduced as minimal models for local many-body dynamics that can be interpreted both as classical and quantum. Standard dynamical complexity indicators such as damage spreading and out-of-time-order correlators (OTOCs), show that these systems exhibit sensitivity to initial conditions in the classical setting and operator scrambling in the quantum setting. Here, we address their quantum chaoticity - a stricter property - by studying the time evolution of local operator entanglement (LOE). We show that the behaviour of LOE in random permutation circuits depends on the dimension of the local configuration space q. When q = 2, i.e. the circuits act on qubits, random permutations are Clifford and the LOE of any local operator is bounded by a constant, indicating that they are not truly chaotic. On the other hand, when the dimension of the local configuration space exceeds two, the LOE grows linearly in time. We prove this in the limit of large q and present numerical evidence that a three-dimensional local configuration space is sufficient for a linear growth of LOE. Our findings highlight that quantum chaos can be produced by essentially classical dynamics. Moreover, we show that LOE can be defined also in the classical realm and put it forward as a universal indicator chaos, both quantum and classical.

cond-mat.stat-mech↗

arXiv2025

Unraveling superradiance: Entanglement and mutual information in collective decay

We study the collective decay of an initially inverted ensemble of two-level emitters in two distinct scenarios: when coupled to a squeezed photonic reservoir and when interacting with a one-dimensional waveguide. Using a quantum-state diffusion approach to unravel the emission process, we investigate entanglement and classical correlations along individual quantum trajectories over time. This numerical analysis shows that despite an initial build-up of entanglement and a significant amount of entanglement due to either spin squeezing or dark states at late times, the essential features of the superradiant burst are well described by averages over fully factorizable states. We explain this observation in terms of an almost complete factorization of all 2-local observables, which we identify as a generic property of superradiant decay. Based on this insight, we provide a purely classical theory for the burst in squeezed superradiance, which is both intuitive and exact for a large number of emitters. Moreover, we find that our numerical approach also performs well in the presence of subradiant states, which dominate the slow residual decay of non-uniform ensembles at late times.

quant-ph↗

arXiv2025

Theory of quantum-enhanced interferometry with general Markovian light sources

Quantum optical systems comprising quantum emitters interacting with engineered optical modes generate non-classical states of light that can be used as resource states for quantum-enhanced interferometry. However, outside of well-controlled systems producing either single-mode states (e.g. Fock states or squeezed states) or highly symmetric multi-mode states (e.g. superradiant states), their potential for quantum advantage remains uncharacterized. In this work, we develop a framework to analyze quantum enhanced interferometry with general Markovian quantum light sources. First, we show how to compute the quantum Fisher Information (QFI) of the photons emitted by a source efficiently by just tracking its internal dynamics and without explicitly computing the state of the emitted photons. We then use this relationship to elucidate the connection between the level structure and spectrum of the source to a potential quantum advantage in interferometry. Finally, we analyze optimal measurement protocols that can be used to achieve this quantum advantage with experimentally available optical elements. In particular, we show that tunable optical elements with Kerr non-linearity can always be harnessed to implement the optimal measurement for any given source. Simultaneously, we also outline general conditions under which linear optics and photodetection is enough to implement the optimal measurement.

quant-ph↗

arXiv2025

State preparation with parallel-sequential circuits

We introduce parallel-sequential (PS) circuits, a family of quantum circuit layouts that interpolate between brickwall and sequential circuits, which introduces control parameters governing a trade-off between the amount of entanglement and the maximum correlation range they can express. We provide numerical evidence that PS circuits can efficiently prepare many-body ground states in one dimension. On noisy devices, characterized through both idling errors and two-qubit gate errors, we show that in a wide parameter regime, PS circuits outperform brickwall, sequential, and the log-depth circuits from [Malz, Styliaris, Wei, Cirac, PRL 132, 040404 (2024)]. Additionally, we demonstrate that properly chosen noisy random PS circuits suppress error proliferation and, when employed as a variational ansatz, exhibit superior trainability.

quant-ph↗

arXiv2024

Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits

We analyse the entanglement structure of states generated by random constant-depth two-dimensional quantum circuits, followed by projective measurements of a subset of sites. By deriving a rigorous lower bound on the average entanglement entropy of such post-measurement states, we prove that macroscopic long-ranged entanglement is generated above some constant critical depth in several natural classes of circuit architectures, which include brickwork circuits and random holographic tensor networks. This behaviour had been conjectured based on previous works, which utilize non-rigorous methods such as replica theory calculations, or work in regimes where the local Hilbert space dimension grows with system size. To establish our lower bound, we develop new replica-free theoretical techniques that leverage tools from multi-user quantum information theory, which are of independent interest, allowing us to map the problem onto a statistical mechanics model of self-avoiding walks without requiring large local Hilbert space dimension. Our findings have consequences for the complexity of classically simulating sampling from random shallow circuits, and of contracting tensor networks: First, we show that standard algorithms based on matrix product states which are used for both these tasks will fail above some constant depth and bond dimension, respectively. In addition, we also prove that these random constant-depth quantum circuits cannot be simulated by any classical circuit of sublogarithmic depth.

quant-ph↗