arXiv subjects

Lorenzo Leone

Publications and source records attributed to Lorenzo Leone.

At least 19 recordsLinked to original sources

arXiv2026

Non-local Magic: closed-form solution and equivalence with magic of purification

Non-local magic quantifies the non-stabilizerness of a bipartite quantum state that cannot be removed by local unitary transformations. Despite its natural definition, its evaluation generally requires a difficult optimization over local unitaries. Here, we show that for the log-stabilizer fidelity this optimization admits an exact closed-form analytic solution depending only on the Schmidt spectrum. We then introduce the magic of purification, defined as the minimum pure-state magic over all purifications of a mixed state, and show that it naturally induces a resource theory whose free states are normalized stabilizer-code projectors. For the log-stabilizer fidelity, the magic of purification admits a distance-based formulation in terms of the Uhlmann fidelity. Remarkably, we prove that non-local magic coincides with the minimum magic of purification along the unitary orbit of the reduced density operator. Our results provide both an efficient analytical characterization and a mixed-state resource-theoretic interpretation of non-local magic.

quant-ph↗

arXiv2026

Universal magic state concentration

Magic plays a dual role in quantum computation: it promotes stabilizer dynamics from efficient classical simulability to universality, but it presents a central challenge for fault tolerance, since non-stabilizer operations are harder to protect against noise. Magic state distillation addresses this issue; however, existing protocols typically assume prior structure in the input, such as proximity to the target or a specified noise model. Here we introduce universal magic state concentration: a fixed stabilizer protocol that converts a few copies of an unknown pure non-stabilizer qubit state into an exact target magic state. Motivated by the obstruction to exact $T$-state concentration, we show that $\mathrm{CCZ}$ states behave fundamentally differently. Six input copies are necessary and sufficient to distill one exact $\mathrm{CCZ}$ state, with an optimal success probability determined by the linearized order-three stabilizer R\'enyi entropy $M^{\mathrm{lin}}_3$. Beyond this, we show that $M^{\mathrm{lin}}_3$ governs the optimal state dependence of any protocol up to nine input copies, and we showcase an eight-copy protocol with improved success probability. Furthermore, block repetition of our protocols yields asymptotic distillation rates that achieve optimal scaling up to logarithmic factors. As a corollary, any unknown pure qubit magic state suffices for universal quantum computation via exact $\mathrm{CCZ}$ injection. Together, these results identify the stabilizer R\'enyi entropy as a fundamental operational quantity in magic state distillation.

quant-ph↗

arXiv2026

Fermionic entropy: an efficiently measurable strong monotone for non-Gaussianity

Fermionic Gaussian states form a central class of classically tractable quantum states, while fermionic non-Gaussianity provides the resource required to go beyond free-fermion dynamics. A key challenge is to quantify this resource through monotones that are both mathematically rigorous and experimentally accessible. Here, we show that the fermionic entropy, defined through the squared Frobenius norm of the correlation matrix, is a strong pure-state Gaussian monotone. Its simple closed-form expression also makes it directly measurable: we show that the associated fermionic purity can be unbiasedly estimated up to additive error $\varepsilon$ using $O(\varepsilon^{-2})$ two-copy measurements, independently of the system size. Moreover, we prove that the fermionic entropy obeys asymptotic continuity and, as a direct consequence, establish its operational meaning as the upper bound to the asymptotic rate of non-Gaussianity distillation. We further derive a linear sample complexity bound for tolerant testing of fermionic Gaussian states, providing a quadratic improvement over the state of the art. As a further application of our results, we study unitary designs generated by Matchgate circuits supplemented with Majorana-local non-Gaussian gates. We prove that a linear number of such gates is necessary even to achieve an approximate state $2$-design with error below $0.4\%$. Combined with known nearly linear upper bounds for relative-error designs, this determines the optimal doping level, up to logarithmic factors, across all relevant design notions and reveals the extensive non-Gaussianity cost required to generate Haar-like quantum dynamics in this architecture.

quant-ph↗

arXiv2026

Physically-Aware Preemptive Virtual Channels for Deadlock-Free AXI Networks-on-Chip

As many-core Systems-on-Chip (SoCs) continue to scale, Networks-on-Chip (NoCs) must sustain increasingly high memory bandwidth while preserving deadlock freedom. In AXI4 systems, protocol-level dependencies between read and write traffic can create circular waits at the network endpoints, even when the routing algorithm itself is deadlock-free. Decoupling these traffic classes avoids such dependencies, but exposes a key implementation trade-off: multiplane NoCs duplicate wide physical links and increase routing pressure, whereas conventional Virtual Channel (VC) routers add substantial control complexity, area, and timing overhead. This work revisits this trade-off for modern wide-link NoCs. We evaluate four deadlock-free AXI4 traffic-class separation schemes: a multiplane baseline and three lightweight VC-based designs. Among these designs, we propose Preemptive VCs, a physically-aware architecture that can save up to 76% of link resources with comparable frequency and only 3% router area overhead relative to the multiplane design.

cs.AR↗

arXiv2026

CHIMERA: A Flexible and Scalable 3.1 TOPS/W AI-MCU with Transformer Accelerator and 563 Gb/s Shared-L2 Memory Subsystem with QoS Guarantees

We present Chimera, a flexible and scalable Microcontroller Unit (MCU) designed to accelerate real-time inference of rapidly evolving transformer-based models at the ultra-low-power edge (hundred of mW). The chip, implemented in 22 nm FDX technology, integrates a transformer accelerator tightly coupled within a compute cluster featuring nine general-purpose RV32IMA cores. Scalability extends to the memory hierarchy through a novel L2 memory island subsystem, which enables data sharing across multiple clusters while delivering 563 Gb/s aggregate bandwidth. The L2 subsystem enforces quality-of-service guarantees for latency-critical traffic, achieving up to 16x latency reduction. Chimera achieves peak energy and area efficiencies of 3.1 TOPS/W and 281 GOPS/mm2, demonstrating 1.37x higher energy efficiency and up to 100x higher area efficiency compared to State of the Art (SoA) SoCs. Compared to SoA standalone accelerators, Chimera achieves comparable energy efficiency and up to 1.8x higher area efficiency.

cs.AR↗

arXiv2026

A Lightweight High-Throughput Collective-Capable NoC for Large-Scale ML Accelerators

The exponential increase in Machine Learning (ML) model size and complexity has driven unprecedented demand for high-performance acceleration systems. As technology scaling enables the integration of thousands of computing elements onto a single die, the boundary between distributed and on-chip systems has blurred, making efficient on-chip collective communication increasingly critical. In this work, we present a lightweight, collective-capable Network on Chip (NoC) that supports efficient barrier synchronization alongside scalable, high-bandwidth multicast and reduction operations, co-designed for the next generation of ML accelerators. We introduce Direct Compute Access (DCA), a novel paradigm that grants the interconnect fabric direct access to the cores' computational resources, enabling high-throughput in-network reductions with a small 16.9% router area overhead. Through in-network hardware acceleration, we achieve 5.3x and 2.8x geomean speedups on multicast and reduction operations involving between 1 and 32 KiB of data, respectively. Furthermore, by keeping communication off the critical path in GEMM workloads, these features allow our architecture to scale efficiently to large meshes, resulting in up to 3.8x and 2.4x estimated performance gains through multicast and reduction support, respectively, compared to a baseline unicast NoC architecture, and up to 1.17x estimated energy savings.

cs.AR↗

arXiv2026

Non-Clifford Cost of Random Unitaries

Recent years have enjoyed a strong interest in exploring properties and applications of random quantum circuits. In this work, we explore the ensemble of $t$-doped Clifford circuits on $n$ qubits, consisting of Clifford circuits interspersed with $t$ single-qubit non-Clifford gates. We establish rigorous convergence bounds towards unitary $k$-designs, revealing the intrinsic cost in terms of non-Clifford resources in various flavors. First, we analyze the $k$-th order frame potential, which quantifies how well the ensemble of doped Clifford circuits is spread within the unitary group. We prove that a quadratic doping level, $t = \tildeΘ(k^2)$, is both necessary and sufficient to approximate the frame potential of the full unitary group. As a consequence, we refine existing upper bounds on the convergence of the ensemble towards state $k$-designs. Second, we derive tight bounds on the convergence of $t$-doped Clifford circuits towards relative-error $k$-designs, showing that $t = \tildeΘ(nk)$ is both necessary and sufficient for the ensemble to form a relative $\varepsilon$-approximate $k$-design. Similarly, $t = \tildeΘ(n)$ is required to generate pseudo-random unitaries. All these results highlight that generating random unitaries is extremely costly in terms of non-Clifford resources, and that such ensembles fundamentally lie beyond the classical simulability barrier. Additionally, we introduce doped-Clifford Weingarten functions to derive analytic expressions for the twirling operator over the ensemble of random doped Clifford circuits, and we establish their asymptotic behavior in relevant regimes.

quant-ph↗

arXiv2026

Operational interpretation of the Stabilizer Entropy

Magic-state resource theory is a fundamental framework with far-reaching applications in quantum error correction and the classical simulation of quantum systems. Recent advances have significantly deepened our understanding of magic as a resource across diverse domains, including many-body physics, nuclear and particle physics, and quantum chemistry. Central to this progress is the stabilizer Rényi entropy, a computable and experimentally accessible magic monotone. Despite its widespread adoption, a rigorous operational interpretation of the stabilizer entropy has remained an open problem. In this work, we provide such an interpretation in the context of quantum property testing. By showing that the stabilizer entropy is the most robust measurable magic monotone, we demonstrate that the Clifford orbit of a quantum state becomes exponentially indistinguishable from Haar-random states, at a rate governed by the stabilizer entropy $M_α(ψ)$ and the number of available copies. This implies that the Clifford orbit forms an approximate state $k$-design, with an approximation error $\exp(-Θ(M_α(ψ)))$ for $α\ge2$. Conversely, we establish that the optimal probability of distinguishing a given quantum state from the set of stabilizer states is also governed by its stabilizer entropy. These results reveal that the stabilizer entropy quantitatively characterizes the transition from stabilizer states to universal quantum states, thereby offering a comprehensive operational perspective of the stabilizer entropy as a quantum resource.

quant-ph↗

arXiv2026

Computational relative entropy

Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For computationally bounded observers the situation is quite different -- they can, for example, be fooled to believe that distributions are more random than they actually are. In our work, we build a new foundation for a computational quantum information theory that captures the essence of complexity-constrained information theory while retaining the look and feel of the unbounded asymptotic theory. As our fundamental quantity, we define the computational relative entropy as the optimal error exponent in asymmetric hypothesis testing when restricted to polynomially many copies and quantum gates, defined in a mathematically rigorous way. Building on this foundation, we prove a computational analogue of Stein's lemma, establish computational versions of fundamental inequalities like Pinsker's bound, and demonstrate a computational smoothing property showing that computationally indistinguishable states yield equivalent information measures. We derive a computational entropy that operationally characterizes optimal compression rates for quantum states under computational limitations and show that our quantities apply to computational entanglement theory, proving a computational version of the Rains bound. Our framework reveals striking separations between computational and unbounded information measures, including quantum-classical gaps that arise from cryptographic assumptions, demonstrating that computational constraints fundamentally alter the information-theoretic landscape and open new research directions at the intersection of quantum information, complexity theory, and cryptography.

quant-ph↗

arXiv2026

Constant Overhead Entanglement Distillation via Scrambling

High-fidelity quantum entanglement enables key quantum networking capabilities such as secure communication and distributed quantum computing, but long-distance entanglement distribution is limited by noise and loss. Entanglement distillation protocols address this problem by extracting high-fidelity Bell pairs from multiple noisy ones. The primary objective is minimizing the resource overhead: the number of noisy input pairs needed to distill each high-fidelity output pair. While protocols achieving optimal overhead are known in theory, they often require complex decoding operations that make practical implementation challenging. We circumvent this challenge by introducing protocols that use quantum scrambling -- the spreading of quantum information under chaotic dynamics -- through random Clifford operations. Based on this scrambling mechanism, our protocol maintains asymptotically \emph{constant} overhead, independent of the desired output error rate $\bar{\varepsilon}$, and can be implemented with shallow quantum circuits of depth $O(\mathrm{poly} \log \log \bar{\varepsilon}^{-1})$ and memory $O(\mathrm{poly} \log \bar{\varepsilon}^{-1})$. Our protocol remains effective even with noisy quantum gates. By incorporating error correction, our protocol achieves state-of-the-art performance: starting with pairs of 10% initial infidelity, we require only 7 noisy inputs per output pair to distill a single Bell pair with infidelity $\bar{\varepsilon}=10^{-12}$, substantially outperforming existing schemes. We demonstrate the utility of our protocols for quantum repeater networks.

quant-ph↗

arXiv2026

Gravitational back-reaction is magical

We study the interplay between magic and entanglement in quantum many-body systems. We show that non-local magic, which is supported by the quantum correlations is lower bounded by the non-flatness of entanglement spectrum and upper bounded by the amount of entanglement in the system. We then argue that a smoothed version of non-local magic bounds the hardness of classical simulations for incompressible states. In conformal field theories, we conjecture that the non-local magic should scale linearly with entanglement entropy but sublinearly when an approximation of the state is allowed. We support the conjectures using both analytical arguments based on unitary distillation and numerical data from an Ising CFT. If the CFT has a holographic dual, then we prove that the non-local magic vanishes if and only if there is no gravitational back-reaction. Furthermore, we show that non-local magic is approximately equal to the rate of change of the minimal surface area in response to the change of cosmic brane tension in the bulk.

hep-th↗

arXiv2026

The unbearable hardness of deciding about magic

Identifying the boundary between classical and quantum computation is a central challenge in quantum information. In multi-qubit systems, entanglement and magic are the key resources underlying genuinely quantum behaviour. While entanglement is well understood, magic - essential for universal quantum computation - remains relatively poorly characterised. Here we show that determining membership in the stabilizer polytope, which defines the free states of magic-state resource theory, requires super-exponential time $\class{exp} ( n^2)$ in the number of qubits $n$, even approximately. We reduce the problem to solving a $3$-\class{SAT} instance on $n^2$ variables and, by invoking the exponential time hypothesis, the result follows. As a consequence, both quantifying and certifying magic are fundamentally intractable: any magic monotone for general states must be super-exponentially hard to compute, and deciding whether an operator is a valid magic witness is equally difficult. As a corollary, we establish the robustness of magic as computationally optimal among monotones. This barrier extends even to classically simulable regimes: deciding whether a state lies in the convex hull of states generated by a logarithmic number of non-Clifford gates is also super-exponentially hard. Together, these results reveal intrinsic computational limits on assessing classical simulability, distilling pathological magic states, and ultimately probing and exploiting magic as a quantum resource.

quant-ph↗

arXiv2026

The computational two-way quantum capacity

Quantum channel capacities are fundamental to quantum information theory. Their definition, however, does not limit the computational resources of sender and receiver. In this work, we initiate the study of computational quantum capacities. These quantify how much information can be reliably transmitted when imposing the natural requirement that en- and decoding have to be computationally efficient. We focus on the computational two-way quantum capacity and showcase that it is closely related to the computational distillable entanglement of the Choi state of the channel. This connection allows us to show a stark computational capacity separation. Under standard cryptographic assumptions, there exists a quantum channel of polynomial complexity whose computational two-way quantum capacity vanishes while its unbounded counterpart is nearly maximal. More so, we show that there exists a sharp transition in computational quantum capacity from nearly maximal to zero when the channel complexity leaves the polynomial realm. Our results demonstrate that the natural requirement of computational efficiency can radically alter the limits of quantum communication.

quant-ph↗

arXiv2026

Quantum State Designs via Magic Teleportation

We investigate how non-stabilizer resources enable the emergence of quantum state designs within the projected ensemble. Starting from initial states with finite magic and applying resource-free Clifford circuits to scramble them, we analyze the ensemble generated by performing projective Pauli measurements on a subsystem of the final state. Using both analytical arguments and large-scale numerics, we show that the projected ensemble converges towards a state $k$-design with an error that decays exponentially with the $k$-th Stabilizer Rényi Entropy of the pre-measurement state, via a Magic-Induced Design Ansatz (MIDA) that we introduce. We identify a universal scaling form, valid across different classes of magic initial states, and corroborate it through numerical simulations and analytical calculations of the frame potential. For finite-depth Clifford unitaries, we show that the timescales at which state designs emerge are controlled by the transport of magic. We identify a ``magic teleportation'' mechanism whereby non-Clifford resources injected locally spread through Clifford scrambling and measurements across distances beyond the lightcone. Our results demonstrate how a small and controlled amount of magic suffices to generate highly random states, providing a systematic route toward generating quantum state designs in early fault-tolerant devices.

quant-ph↗

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.

quant-ph↗

arXiv2025

Toward Open-Source Chiplets for HPC and AI: Occamy and Beyond

We present a roadmap for open-source chiplet-based RISC-V systems targeting high-performance computing and artificial intelligence, aiming to close the performance gap to proprietary designs. Starting with Occamy, the first open, silicon-proven dual-chiplet RISC-V manycore in 12nm FinFET, we scale to Ramora, a mesh-NoC-based dual-chiplet system, and to Ogopogo, a 7nm quad-chiplet concept architecture achieving state-of-the-art compute density. Finally, we explore possible avenues to extend openness beyond logic-core RTL into simulation, EDA, PDKs, and off-die PHYs.

cs.AR↗

arXiv2025

Adaptively secure unitary designs with constant non-Clifford cost

Randomness is a fundamental resource in quantum information, with crucial applications in cryptography, algorithms, and error correction. A central challenge is to construct unitary $k$-designs that closely approximate Haar-random unitaries while minimizing the costly use of non-Clifford operations. In this work, we present a protocol able to generate unitary $k$-designs on $n$ qubits, secure against any adversarial quantum measurement, with a system-size-independent number of non-Clifford gates. Our construction applies a $k$-design only to a subsystem of size $\Theta(k)$, independent of $n$. This ``seed'' design is then ``diluted'' across the entire $n$-qubit system by sandwiching it between two random Clifford operators. The resulting ensemble forms an $\varepsilon$-approximate unitary $k$-design on $n$ qubits. We prove that this construction achieves full quantum security against adaptive adversaries using only $\tilde{O}(k^2 \log\varepsilon^{-1})$ non-Clifford gates. If one requires security only against polynomial-time adaptive adversaries, the non-Clifford cost decreases to $\tilde{O}(k + \log^{1+c} \varepsilon^{-1})$. This is optimal, since we show that at least $\Omega(k)$ non-Clifford gates are required in this setting. Compared to existing approaches, our method significantly reduces non-Clifford overhead while strengthening security guarantees to adaptive security as well as removing artificial assumptions between $n$ and $k$. These results make high-order unitary designs practically attainable in near-term fault-tolerant quantum architectures.

quant-ph↗

arXiv2025

Optimal trace-distance bounds for free-fermionic states: Testing and improved tomography

Free-fermionic states, also known as fermionic Gaussian states, represent an important class of quantum states ubiquitous in physics. They are uniquely and efficiently described by their correlation matrix. However, in practical experiments, the correlation matrix can only be estimated with finite accuracy. This raises the question: how does the error in estimating the correlation matrix affect the trace-distance error of the state? We show that if the correlation matrix is known with an error $\varepsilon$, the trace-distance error also scales as $\varepsilon$ (and vice versa). Specifically, we provide distance bounds between (both pure and mixed) free-fermionic states in relation to their correlation matrix distance. Our analysis also extends to cases where one state may not be free-fermionic. Importantly, we leverage our preceding results to derive significant advancements in property testing and tomography of free-fermionic states. Property testing involves determining whether an unknown state is close to or far from being a free-fermionic state. We first demonstrate that any algorithm capable of testing arbitrary (possibly mixed) free-fermionic states would inevitably be inefficient. Then, we present an efficient algorithm for testing low-rank free-fermionic states. For free-fermionic state tomography, we provide improved bounds on sample complexity in the pure-state scenario, substantially improving over previous literature, and we generalize the efficient algorithm to mixed states, discussing its noise-robustness.

quant-ph↗