arXiv subjects

Beatrice Magni

Publications and source records attributed to Beatrice Magni.

6 recordsLinked to original sources

arXiv2026

Universal purification dynamics of monitored Clifford circuits

Quantum circuits under sufficiently weak monitoring purify on a timescale $T_P$ exponentially long in the system size. This slowness underlies a universal purification dynamics, whose quantitative description has so far required the replica trick, with a delicate analytic continuation. We show that monitored Clifford circuits on $L$ qudits of prime dimension $q$ bypass this construction entirely: in the scaling limit at fixed $x = t/T_P(L)$, purification reduces to the Markovian decay of the density-matrix rank, an exactly solvable death process descending from infinity. We compute the full scaling functions in compact form: all R\'enyi entropies collapse onto a universal curve $\langle S(x) \rangle$. Exact stabilizer simulations at $q=2,3,5$ confirm the predictions, with no fitting parameter for the global model and $T_P$ as the only fitted scale for local brick-wall circuits. Also, the replica problem amounts to a tilted version of the same Markov process, in agreement with exact computations from the Clifford commutant. Finally, the quantization of the rank leaves two hallmarks that distinguish Clifford dynamics from generic monitored circuits: the entropy fluctuations saturate at short scaled times $x\to0$ to an $O(1)$ variance, instead of vanishing, and observables develop a temporal modulation periodic in $\log_q x$, which cannot be captured by the replica approach.

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arXiv2026

Non-Local Magic Resources for Fermionic Gaussian States

Entanglement and magic are fundamental resources that capture the complexity of quantum many-body systems. Non-local magic isolates the irreducible nonstabilizerness intrinsically tied to entanglement. However, evaluating this quantity generally requires a prohibitive minimization over the full Hilbert space, making it computationally inaccessible beyond a few qubits. Here, we overcome this bottleneck by establishing a closed-form expression for the non-local stabilizer entropies of fermionic Gaussian states over local Gaussian unitaries, which we prove at R\'enyi index $\alpha=2$ for arbitrary subsystem size, and which can be evaluated in polynomial time directly from the eigenvalues of the reduced Majorana covariance matrix. We apply this framework to characterize fermionic non-local magic across diverse physical regimes: we derive an exact Page-like curve for typical random states, reveal logarithmic scaling at the quantum critical point of the XY model, and establish a quasiparticle picture for magic generation during out-of-equilibrium quantum quenches. Crucially, because our result relies solely on two-point correlation functions, it provides a scalable route for the experimental estimation of fermionic non-local magic in large-scale quantum processors via fermionic shadow tomography.

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arXiv2025

Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks

We investigate the statistical properties of orthogonal, or real, Clifford circuits doped with magic and imaginary resources. By developing the Weingarten calculus for the real Clifford group, we derive the exact overlap distribution of real stabilizer states, identifying a new universality class: the orthogonal Clifford Porter-Thomas distribution. We prove that local real architectures recover this global statistic in logarithmic depth. Furthermore, we uncover a sharp hierarchy in resource requirements: while retrieving Haar statistics necessitates a polylogarithmic amount of magic states, recovering the full unitary Clifford statistics requires only a single phase gate.

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arXiv2025

Quantum Complexity and Chaos in Many-Qudit Doped Clifford Circuits

We investigate the emergence of quantum complexity and chaos in doped Clifford circuits acting on qudits of odd prime dimension $d$. Using doped Clifford Weingarten calculus and a replica tensor network formalism, we derive exact results and perform large-scale simulations in regimes challenging for tensor network and Pauli-based methods. We begin by analyzing generalized stabilizer entropies, computable magic monotones in many-qudit systems, and identify a dynamical phase transition in the doping rate, marking the breakdown of classical simulability and the onset of Haar-random behavior. The critical behavior is governed by the qudit dimension and the magic content of the non-Clifford gate. Using the qudit $T$-gate as a benchmark, we show that higher-dimensional qudits converge faster to Haar-typical stabilizer entropies. For qutrits ($d=3$), analytical predictions match numerics on brickwork circuits, showing that locality plays a limited role in magic spreading. We also examine anticoncentration and entanglement growth, showing that $O(\log N)$ non-Clifford gates suffice for approximating Haar expectation values to precision $\varepsilon$, and relate antiflatness measures to stabilizer entropies in qutrit systems. Finally, we analyze out-of-time-order correlators and show that a finite density of non-Clifford gates is needed to induce chaos, with a sharp transition fixed by the local dimension, twice that of the magic transition. Altogether, these results establish a unified framework for diagnosing complexity in doped Clifford circuits and deepen our understanding of resource theories in multiqudit systems.

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arXiv2025

Universality in the Anticoncentration of Chaotic Quantum Circuits

We identify a \emph{universal functional form} that governs anticoncentration in random quantum circuits-one that holds across diverse circuit architectures and depths, and crucially remains valid even at finite system sizes and shallow depth. We support this claim through analytical results for ensembles of random tensor-network states and random-phase models. This compact, universal expression for the output bitstring probability distribution is fully characterized by just two fitting parameters, as validated through extensive numerical simulations. Our findings underscore the pivotal role of finite-size and finite-depth effects in shaping anticoncentration and introduce a practical framework for benchmarking quantum devices using shallow circuits, thereby enabling validation of systems significantly larger than previously accessible.

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arXiv2025

Anticoncentration in Clifford Circuits and Beyond: From Random Tensor Networks to Pseudo-Magic States

Anticoncentration describes how an ensemble of quantum states spreads over the allowed Hilbert space, leading to statistically uniform output probability distributions. In this work, we investigate the anticoncentration of random Clifford circuits toward the overlap distribution of random stabilizer states. Using exact analytical techniques and extensive numerical simulations based on Clifford replica tensor networks, we demonstrate that random Clifford circuits fully anticoncentrate in logarithmic circuit depth, namely higher-order moments of the overlap distribution converge to those of random stabilizer states. Moreover, we investigate the effect of introducing a controlled number of non-Clifford (magic) resources into Clifford circuits. We show that inserting a polylogarithmic in qudit number of $T$-states is sufficient to drive the overlap distribution toward the Porter-Thomas statistics, effectively recovering full quantum randomness. In short, this fact presents doped tensor networks and shallow Clifford circuits as pseudo-magic quantum states. Our results clarify the interplay between Clifford dynamics, magic-state injection, and quantum complexity, with implications for quantum circuit sampling, many-body quantum physics, and the benchmarking of quantum computational advantage.

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