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 beyond the local choice of basis. Its evaluation is a hard problem requiring 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 address the open problem of non-stabilizerness of mixed states by introducing the magic of purification and show that it naturally induces a resource theory whose free states are the states with zero stabilizer entropy. For the log-stabilizer fidelity, the magic of purification admits a distance-based formulation in terms of the Uhlmann fidelity. We prove that non-local magic coincides with the minimum magic of purification along the unitary orbit of the reduced density operator. This framework introduces non-local magic as the relevant resource for non-trivial steering and the characterization of entangling and non-stabilizer resources in measurements. These results provide both an efficient analytical characterization and a mixed-state resource-theoretic interpretation of non-local magic.

quant-ph↗

arXiv2026

Universal quantum coding

Entanglement distillation from noisy bipartite states and reliable quantum communication over noisy channels are fundamental tasks in quantum information theory. Yet existing coding schemes typically require prior knowledge of the underlying state or channel, or assume independent or weakly correlated quantum information sources. Here, using Schur-Weyl duality, we establish a universal quantum error-correction principle that overcomes these limitations. We show that the irreducible permutation spaces arising from the local Schur-Weyl decomposition of multiple copies of an unknown bipartite mixed state form maximally entangled quantum code spaces whose error structure is governed entirely by representation theory. Correcting these symmetry-resolved errors yields protocols for entanglement distillation and quantum communication that achieve coherent-information rates with exponentially vanishing error and optimal second-order corrections, even in the case of almost i.i.d. resources. Our approach also provides sharp finite-copy guarantees that are worst-case optimal at every finite block length, including in the sample-efficient regime, where the number of copies scales only polynomially with the number of qubits. Together, these results establish Schur-Weyl duality as a general mechanism for universal, robust, and optimal quantum coding, unifying entanglement distillation, quantum error correction, and quantum communication within a common representation-theoretic framework.

quant-ph↗

arXiv2026

Infinite magic and the emergence of the continuum

Which features of a quantum state are needed for a relativistic quantum field theory to emerge from a lattice system? We address this question by establishing a quantitative relationship between the type classification of hyperfinite von Neumann algebras and the quantum-information-theoretic resource of nonstabilizerness, also called magic. Our results establish two complementary parts of this relationship. First, we prove that any stabilizer system on a lattice defines a canonical GNS Hilbert space in which local von Neumann algebras do not contain type III factors in their central decomposition. As an explicit example, we prove that for stabilizer systems with short-range order, the local algebras are isomorphic to tensor products of hyperfinite factors of type I or type II. This demonstrates that the absence of magic is accompanied by the absence of type III factors in the local algebras, therefore prohibiting the appearance of a quantum field theory. Second, for the hyperfinite factors of Araki, Woods and Powers, we prove a quantitative equivalence: The limiting factor is of type III if and only if the locally optimized min-relative entropy of magic diverges. This divergence is necessary to generate the continuous spectrum associated to a type III factor. Thus, in this setting, the emergence of a type III factor requires not merely the presence of magic, but an infinite amount of it. These results provide a rigorous setting supporting the proposal that infinite magic is a necessary structural ingredient for the emergence of a relativistic continuum from lattice systems.

quant-ph↗

arXiv2026

Computational entanglement distillation beyond pure states: efficient protocols and fundamental limitations

The information-theoretic approach to entanglement typically relies on arbitrarily many input copies and unboundedly complex operations; however, the available resources are constrained in reality. This motivates the study of entanglement theory with limited resources. One of its central questions is which quantities characterize entanglement manipulations, and so far, only the idealized case of pure states has been well explored. In this work, we address entanglement distillation from mixed states and identify the Rényi coherent information as the quantity determining the optimal rate in the worst case under two distinct resource constraints. We first characterize the sample-efficient regime, in which unbounded computational power is allowed. Our universal protocol achieves this rate without knowledge of the input state under certain polynomial rank constraints. This rate is optimal among universal protocols: we construct states whose distillable entanglement is nearly extensive, yet from which no universal sample-efficient protocol attains a rate above their Rényi coherent information. We then push this characterization to the computationally efficient frontier: the same bound holds for any efficient protocol even when the input state is known, and another universal protocol achieves this rate efficiently under additional polynomial constraints on the marginal ranks. Overall, our results give the Rényi coherent information a novel operational meaning in two computational settings: universal distillation with limited copies and efficient distillation even with knowledge of the input state.

quant-ph↗

arXiv2026

Universal magic state concentration

Magic plays a dual role in quantum computation: it promotes stabilizer dynamics from efficient classical simulability to computational universality, but also challenges fault-tolerant architectures, since non-stabilizer operations are harder to protect against noise. Magic state distillation addresses this issue, yet existing protocols remain largely tailored to specific assumptions about the input or noise model and, more fundamentally, no general information-theoretic theory of optimal magic-state conversion currently exists. Here we develop such a characterization for pure qubit states through 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 impossibility of exact $T$-state concentration, we build six- and eight-copy protocols producing an exact $\mathrm{CCZ}$ state, with six copies being minimal. Their success probabilities are governed by the linearized order-three stabilizer Rényi entropy $M^{\mathrm{lin}}_3$. We show that this connection is structural: for up to nine input copies, $M^{\mathrm{lin}}_3$ fully determines the success probability of every universal Clifford-invariant stabilizer protocol. Remarkably, this characterization persists asymptotically: our constructions achieve optimal rates among universal single-output protocols and remain optimal up to logarithmic factors among arbitrary stabilizer protocols. As a corollary, we show that any unknown pure non-stabilizer state suffices for universal quantum computation via probabilistic $\mathrm{CCZ}$-state injection. Together, these results identify the stabilizer Rényi 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

A complete theory of the Clifford commutant

The Clifford group plays a central role in quantum information science. It is the building block for many error-correcting schemes and matches the first three moments of the Haar measure over the unitary group-a property that is essential for a broad range of quantum algorithms, with applications in pseudorandomness, learning theory, benchmarking, and entanglement distillation. At the heart of understanding many properties of the Clifford group lies the Clifford commutant: the set of operators that commute with $k$-fold tensor powers of Clifford unitaries. Previous understanding of this commutant has been limited to relatively small values of $k$, constrained by the number of qubits $n$. In this work, we develop a complete theory of the Clifford commutant. Our first result provides an explicit orthogonal basis for the commutant and computes its dimension for arbitrary $n$ and $k$. We also introduce an alternative and easy-to-manipulate basis formed by isotropic sums of Pauli operators. We show that this basis is generated by products of permutations, which generate the unitary group commutant, and at most three other operators. Additionally, we develop a graphical calculus allowing a diagrammatic manipulation of elements of this basis. These results enable a wealth of applications: among others, we characterize all measurable magic measures and identify optimal strategies for stabilizer property testing, whose success probability also offers an operational interpretation to stabilizer entropies. Finally, we show that these results also generalize to multi-qudit systems with prime local dimension.

quant-ph↗

arXiv2026

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 $Θ(k)$, 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 $Ω(k)$ 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↗

arXiv2026

Experimental measurement and a physical interpretation of quantum shadow enumerators

Throughout its history, the theory of quantum error correction has heavily benefited from translating classical concepts into the quantum setting. In particular, classical notions of weight enumerators, which relate to the performance of an error-correcting code, and MacWilliams' identity, which helps to compute enumerators, have been generalized to the quantum case. In this work, we establish a distinct relationship between the theoretical machinery of quantum weight enumerators and a seemingly unrelated physics experiment: we prove that Rains' quantum shadow enumerators - a powerful mathematical tool - arise as probabilities of observing fixed numbers of triplets in a Bell sampling experiment. This insight allows us to develop here a rigorous framework for the direct measurement of quantum weight enumerators, thus enabling experimental and theoretical studies of the entanglement structure of any quantum error-correcting code or state under investigation. On top of that, we derive concrete sample complexity bounds and physically-motivated robustness guarantees against unavoidable experimental imperfections. Finally, we experimentally demonstrate the possibility of directly measuring weight enumerators on a trapped-ion quantum computer. Our experimental findings are in good agreement with theoretical predictions and illuminate how entanglement theory and quantum error correction can cross-fertilize each other once Bell sampling experiments are combined with the theoretical machinery of quantum weight enumerators.

quant-ph↗

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↗