arXiv subjects

Xiongfeng Ma

Publications and source records attributed to Xiongfeng Ma.

At least 19 recordsLinked to original sources

arXiv2026

Low-Depth Random Unitaries without Ancillae

Random unitaries are fundamental to quantum information and many-body physics, with widespread applications ranging from quantum learning and metrology to device benchmarking. A central pursuit is to minimize the space and circuit depth required to generate them. However, existing methods for generating low-depth random unitaries rely heavily on an extensive number of ancillary qubits, imposing severe spatial overhead. In this work, we prove that random unitaries can be generated in optimal depth without ancillae. For multiplicative-error approximate $k$-designs on $n$ qubits, our circuits achieve a depth of $\widetilde{O} (k) (\log n)^{1/\delta}$ on $\delta$-dimensional architectures and $\widetilde{O}(k) \log \log n$ with all-to-all connectivity. Furthermore, by introducing a general exactification lemma, we lift our construction to optimal-depth exact $k$-designs, yielding an exponential resource reduction over state-of-the-art exact constructions. Our results minimize the space-time costs for a wide range of quantum protocols.

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arXiv2026

Constant-depth adaptive preparation of Dicke and symmetric states

Efficient preparation of Dicke states and, more generally, permutation-symmetric states is important for quantum metrology, quantum networking, and collective quantum information processing. Measurements and classical feedforward enable low-depth preparations of these states, with a cost of ancillary qubits. In this work, we introduce an exact constant-depth adaptive preparation protocol for arbitrary Dicke-$(n,k)$ states and further symmetric states. We first provide a protocol preparing the uniform subset superposition state, as a primitive, using constant-depth adaptive circuit with $O(k^2\log^2 n)$ ancillary qubits and success probability at least $1/k$. This yields an exact, probabilistic, constant-depth Dicke-state preparation protocol using $O\left(n^2+k^2\log^2 n+kn\log n\log\log n\right)$ ancillary qubits. Parallel repetition suppresses the failure probability exponentially without increasing the quantum depth. Moreover, the uniform subset superposition state is also of independent interest as the uniform vertex state of the Johnson graph and as the compact uniform subset state appearing in quantum-walk and topological-data-analysis algorithms. We further establish a general lifting framework that coherently combines clean unitary Dicke-state preparation circuits to prepare arbitrary symmetric states with only polynomial ancillary overhead. Combined with recent constant-depth unitary Dicke-state constructions, this gives an exact constant-depth preparation protocol for arbitrary $n$-qubit symmetric states using $O(n^3\sqrt{\log n})$ ancillary qubits.

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arXiv2026

Quantum-classical crossover in fault-tolerant quantum dynamics simulation

While quantum computers promise to solve classically intractable problems, identifying the point at which fault-tolerant quantum computation outperforms the best classical algorithms for practical applications remains an outstanding challenge. Here we establish a concrete quantum-classical crossover for quantum many-body dynamics under realistic hardware conditions. We introduce a scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations, suppressing the residual logical errors that limit existing partially fault-tolerant approaches. A benchmark against state-of-the-art tensor-network and variational Monte Carlo algorithms reveals a concrete crossover for mixed-field Ising dynamics at modest system sizes. For a physical error rate of $p=10^{-3}$, fault-tolerant simulation requires approximately 2 hours and $3.7 \times 10^5$ physical qubits for a 100-site 1D system, whereas tensor network approaches would require about 100 years. For 2D models, where rapid entanglement growth limits the classical evolution time, we project quantum runtimes within minutes. A physical error rate of $p=10^{-4}$ leads to at least an order of magnitude reduction in qubit count ($3.1 \times 10^4$ physical qubits) and runtime (minutes for 1D and seconds for 2D). The reduction in quantum runtime arises from our improved rotation-state injection and co-design of quantum error correction and observable-estimation protocols, which jointly suppress logical-error accumulation and reduce sampling overhead. Our results establish a scalable route towards practical quantum advantage and identify quantitative engineering targets for future fault-tolerant architectures.

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arXiv2026

No Cloning of Quantum Ensembles

Modern quantum physics now enables control of quantum systems at the level of individual trajectories, opening a new frontier that links quantum information theory, quantum many-body physics, and quantum thermodynamics, and uncovers novel non-equilibrium phenomena such as deep thermalization and measurement-induced entanglement. However, a central challenge remains: their characterization relies on measuring nonlinear properties of individual quantum states, a task tantamount to fine-grained cloning of a quantum ensemble. Here, the fundamental laws governing the cloning of quantum ensembles are investigated. First, a general no-cloning theorem for arbitrary ensembles is established from an information-theoretic perspective, even assuming multiple copies of the ensemble's purification. It is then shown that this barrier can be unexpectedly circumvented for physical ensembles generated by finite-time evolutions. Nevertheless, these tasks are proven to remain computationally intractable, even when the full circuit description of state preparation is known. This stands in sharp contrast to the conventional no-cloning theorem, which relies on the state being unknown. Together, these results establish new fundamental principles of quantum mechanics, reveal intrinsic trade-offs among sample complexity, computational complexity, and quantum measurements, and highlight the necessity of problem-specific strategies for probing measurement-induced quantum phenomena.

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arXiv2026

Complexity-driven transitions in quantum observation

Observing the physical world is a foundational pursuit in science. In the quantum realm, however, observation necessitates a fundamental quantum-to-classical conversion: destructive measurements irreversibly project quantum states into classical data, inevitably incurring a loss of information. What physical principles govern this information loss, and how can we construct optimal measurements to maximize the readout? Here, we address these questions by establishing an intrinsic relationship between readout capability--quantified by the ratio of accessible classical Fisher information to the total quantum Fisher information (QFI), and measurement complexity--defined as the quantum circuit depth required prior to projection. Remarkably, we uncover a sudden emergence of observability: a sharp hidden-to-visible transition driven entirely by measurement complexity. We rigorously prove that below critical depth thresholds--$\Theta((\log n)^{1/\delta})$ for $\delta$-dimensional architectures and $\Theta(\log\log n)$ for all-to-all connectivity--readout capability decays exponentially with system size $n$, rendering the quantum information fundamentally inaccessible. Surprisingly, immediately above this threshold, the system enters a visible regime: we demonstrate that randomized measurements universally recover a constant fraction of the QFI using approximate unitary 3-designs, for which we explicitly develop optimal-depth circuit constructions tailored to finite-dimensional architectures. By unveiling the fundamental scaling laws and transitions that govern quantum observation, our results delineate definitive resource boundaries for quantum learning, state certification, and quantum metrology.

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arXiv2026

Can scrambling protect quantum state distinguishability under noise?

Quantum state distinguishability is a fundamental concept in quantum information science that underpins a wide range of important practical tasks. Traditionally formulated for pairs of states, quantum state distinguishability is here extended to quantum state ensembles, which we characterize through the average pairwise trace distance. Motivated by both theoretical and practical interest in noisy quantum information processing, we ask whether ``minimally'' scrambled ensembles modeled by 2-designs protect distinguishability under noise, which sheds light on the fundamental competition between noise and information scrambling. Using a rigorous decoupling approach, we establish tight bounds on noisy ensemble distinguishability. We show that the distinguishability of noisy 2-design ensembles exhibits a sharp threshold and phase-transition behavior governed by channel conditional entropy: below the threshold, the states remain mutually distinguishable with high probability, while above it, distinguishability undergoes a sudden power-law decay and then collapses exponentially. On the other hand, under local purity-shrinking noise, post-measured noisy 2-design ensembles become exponentially indistinguishable for any measurement, precluding a noise threshold for learning tasks such as shadow tomography. These results reveal a sharp difference between unmeasured and post-measured scrambled ensembles: the former can retain high distinguishability for sufficiently small noise, whereas the latter exhibits no such protected regime. We discuss the implications of these results for crucial tasks ranging from quantum communication and cryptography to learning.

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arXiv2026

Scalable self-testing of generic multipartite quantum states

Characterizing large quantum systems with minimal assumptions is a central challenge in quantum information science. Self-testing provides the strongest form of certification by identifying the underlying quantum state solely from observed measurement statistics. However, existing self-testing methods for generic $n$-partite states face a scalability barrier, requiring exponentially many samples in the system size. In this work, we overcome this barrier by introducing a protocol that robustly self-tests almost all $n$-qubit states with only polynomial sample complexity. The key ingredient is an efficient scheme for device-independently evaluating multipartite Pauli measurements, which can be implemented using only a linear number of ancillary Bell pairs together with standard projective and Bell measurements, well within the reach of current quantum technology. Beyond self-testing states, our scheme provides a general framework for implementing a wide range of learning and certification protocols in the device-independent setting, thereby opening a scalable route to device-independent quantum information processing in large-scale quantum networks.

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arXiv2026

Limitations of Noisy Quantum Devices in Computational and Entangling Power

Finding solid and practical quantum advantages via noisy quantum devices without error correction is a critical but challenging problem. Conversely, comprehending the fundamental limitations of the state-of-the-art is equally crucial. In this work, we consider the class of strictly contractive unital noise and derive its analytical representation by decomposition. Under such noise, we observe the polynomial-time indistinguishability of $n$-qubit devices from random coins when circuit depths exceed $Ω(\log(n))$. Even with classical processing, we demonstrate the absence of computational advantage in polynomial-time algorithms with super-logarithmic noisy circuit depths. These results impact variational quantum algorithms, error mitigation, and quantum simulation with polynomial depth. Furthermore, we consider noisy quantum devices with a restricted gate topology. For one-dimensional noisy qubit circuits, we rule out super-polynomial quantum advantages in all-depth regimes. We also establish upper limits on entanglement generation: $O(\log(n))$ for one-dimensional circuits and $O(\sqrt{n} \log(n))$ for two-dimensional circuits. Our findings underscore the computational capacity and entanglement scalability constraints in noisy quantum devices.

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arXiv2026

Approximate Quantum Error Correction with 1D Log-Depth Circuits

Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this work, we rigorously prove through information-theoretic analysis that one-dimensional logarithmic-depth random Clifford encoding circuits can achieve high quantum error correction performance. We demonstrate that these random codes typically exhibit good approximate quantum error correction capability by proving that their encoding rate achieves the hashing bound for Pauli noise and the channel capacity for erasure errors. We show that the error correction inaccuracy decays once a threshold of logarithmic depth is exceeded, resulting in negligible recovery errors. This threshold is shown to be lower than that of the simple separate block encoding, and the decay rate is higher. We further establish that these codes are optimal by proving that logarithmic depth is necessary to maintain a constant encoding rate and high error correction performance. To prove our results, we propose decoupling theorems tailored for one-dimensional low-depth circuits. These results also imply strong decoupling and rapid thermalization properties in low-depth random circuits and have potential applications in quantum information science and physics.

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arXiv2025

Bypassing the protection-sensitivity incompatibility in quantum-error-corrected metrology via asymmetric codes

Quantum metrology surpasses the classical precision limit by encoding signals in a probe state such that signal contributions are indistinguishable and their phases accumulate coherently as a collective response. In realistic settings, scalable quantum metrology requires quantum error correction to protect the probe against noise. However, quantum error correction relies on syndrome information that distinguishes errors for identification and correction. Because signals and errors act on the same physical degrees of freedom, there is a structural incompatibility between signal-sensitivity and noise-protection in quantum-error-corrected metrology. We quantify this incompatibility by establishing trade-offs between code distance and the quantum Fisher information of code states for non-degenerate codes, quantum low-density parity-check codes, and generalized Shor codes. We bypass this limitation with asymmetric quantum error correction, in which protection is relaxed along the signal direction while being maintained in complementary directions. We construct such codes for local sensing Hamiltonians, restoring Heisenberg-limited precision while retaining a growing distance and hence protection against local perturbations in complementary directions. Strongly asymmetric quantum low-density parity-check and concatenated asymmetric constructions make the framework sparse, scalable, and continuously tunable. The associated probe states can be prepared by constant-depth adaptive circuits with optimal resource scaling.

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arXiv2025

Steering Alternative Realities through Local Quantum Memory Operations

Quantum measurement resolves a superposition into a definite outcome by correlating it with an observer's memory -- a reality register. While the global quantum state remains coherent, the observer's local reality becomes singular and definite. This work introduces reality steering, a protocol that allows an observer to probabilistically access a different reality already supported by the initial quantum state, without reversing decoherence on the environment. The mechanism relies on locally erasing the 'which-outcome' information stored in the observer's brain. Here, 'local' means operations confined to the observer's memory, excluding the environment, which may be cosmically large. Reality steering nevertheless faces intrinsic constraints: successful navigation requires coherent participation from the observer's counterparts across the relevant branches, and any transition is operationally indistinguishable from non-transition. After arriving in a new reality, all memory records are perfectly consistent with that reality, leaving no internal evidence that a switch occurred. This makes conscious confirmation impossible within standard quantum mechanics. We show that nonlinear operations beyond the standard theory could, in principle, enable verifiable and deliberate navigation. Our results shift multi-reality exploration from philosophical speculation toward a concrete -- though fundamentally constrained -- quantum-informational framework.

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arXiv2025

Frequency-matching quantum key distribution

Quantum key distribution (QKD) enables information-theoretically secure communication against eavesdropping. However, phase instability remains a challenge across many QKD applications, particularly in schemes such as twin-field QKD and measurement-device-independent QKD. The most dominant source of phase fluctuation arises from the frequency offset between independent lasers. Here we propose a method to address this issue by employing a classical photodiode to compensate for the laser frequency difference. As an application of this method, we implement this technique in a mode-pairing QKD system, achieving an error rate approaching the theoretical limit and surpassing the linear key-rate bound over a fiber distance of 296.8 km. This approach provides a practical solution for frequency matching between independent lasers and can be extended to other fields requiring precise phase stabilization.

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arXiv2025

Randomness quantification in spontaneous emission

Quantum coherence serves as a fundamental resource for generating intrinsic randomness, yet the quantification of randomness in quantum random number generators (QRNGs) based on spontaneous emission has remained largely phenomenological. Existing randomness analysis lacks rigorous adversarial models and a clear characterization of the role of quantum coherence in these systems. In this work, we develop a comprehensive quantum information-theoretic framework for randomness generation in spontaneous emission processes. We characterize two distinct eavesdropping strategies: one where the adversary directly accesses the atom ensemble, and the other where the adversary accesses only its purification. Our analysis reveals that when randomness is generated through single-photon detection and temporal mode measurements, the QRNG is vulnerable to the first adversary scenario, though it still guarantees a lower bound on intrinsic randomness against the second adversary scenario even under maximal information leakage from the atoms. In contrast, QRNGs based on spatial mode detection and phase fluctuations demonstrate security against both types of adversaries, providing robust randomness generation. Furthermore, we provide a quantitative calculation of intrinsic randomness for these spontaneous-emission-based QRNG schemes.

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arXiv2025

Entanglement Superactivation in Multiphoton Distillation Networks

In quantum networks, after passing through noisy channels or information processing, residual states may lack sufficient entanglement for further tasks, yet they may retain hidden quantum resources that can be recycled. Efficiently recycling these states to extract entanglement resources such as genuine multipartite entanglement or Einstein-Podolsky-Rosen pairs is essential for optimizing network performance. Here, we develop a tripartite entanglement distillation scheme using an eight-photon quantum platform, demonstrating entanglement superactivation phenomena which are unique to multipartite systems. We successfully generate a three-photon genuinely entangled state from two bi-separable states via local operations and classical communication, demonstrating superactivation of genuine multipartite entanglement. Furthermore, we extend our scheme to generate a three-photon state capable of extracting an Einstein-Podolsky-Rosen pair from two initial states lacking this capability, revealing a previously unobserved entanglement superactivation phenomenon. Our methods and findings offer not only practical applications for quantum networks, but also lead to a deeper understanding of multipartite entanglement structures.

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arXiv2025

Resource analysis of Shor's elliptic curve algorithm with an improved quantum adder on a two-dimensional lattice

Quantum computers have the potential to break classical cryptographic systems by efficiently solving problems such as the elliptic curve discrete logarithm problem using Shor's algorithm. While resource estimates for factoring-based cryptanalysis are well established, comparable evaluations for Shor's elliptic curve algorithm under realistic architectural constraints remain limited. In this work, we propose a carry-lookahead quantum adder that achieves Toffoli depth $\log n + \log\log n + O(1)$ with only $O(n)$ ancillas, matching state-of-the-art performance in depth while avoiding the prohibitive $O(n\log n)$ space overhead of existing approaches. Importantly, our design is naturally compatible with the two-dimensional nearest-neighbor architectures and introduce only a constant-factor overhead. Further, we perform a comprehensive resource analysis of Shor's elliptic curve algorithm on two-dimensional lattices using the improved adder. By leveraging dynamic circuit techniques with mid-circuit measurements and classically controlled operations, our construction incorporates the windowed method, Montgomery representation, and quantum tables, and substantially reduces the overhead of long-range gates. For cryptographically relevant parameters, we provide precise resource estimates. In particular, breaking the NIST P-256 curve, which underlies most modern public-key infrastructures and the security of Bitcoin, requires about $4300$ logical qubits and logical Toffoli fidelity about $10^{-9}$. These results establish new benchmarks for efficient quantum arithmetic and provide concrete guidance toward the experimental realization of Shor's elliptic curve algorithm.

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arXiv2025

Benchmarking non-Clifford gates using only Pauli twirling group

Quantum gate benchmarking is unavoidably influenced by state preparation and measurement errors. Randomized benchmarking addresses this challenge by employing group twirling to regularize the noise channel, then provides a characterization of quantum channels that is robust to these errors through exponential fittings. In practice, local twirling gates are preferred due to their high fidelity and experimental feasibility. However, while existing RB methods leveraging local twirling gates are effective for benchmarking Clifford gates, they face fundamental challenges in benchmarking non-Clifford gates. In this work, we solve this problem by introducing the Pauli Transfer Character Benchmarking. This protocol estimates the Pauli transfer matrix elements for a quantum channel using only local Pauli operations. Building on this protocol, we develop a fidelity benchmarking method for non-Clifford gates $U$ satisfying $U^2=I$. We validate the feasibility of our protocol through numerical simulations applied to Toffoli gates as a concrete example.

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arXiv2025

Certifying localizable quantum properties with constant sample complexity

Characterizing increasingly complex quantum systems is a central task in quantum information science, yet experimental costs often scale prohibitively with system size. Certifying key properties using simple local measurements is highly desirable but challenging. In this work, we introduce a highly general certification framework based on a physical phenomenon that we call localizable quantumness: for generic many-body states, essential quantum properties are robustly preserved within the projected ensembles on small subsystems after performing local projective measurements on the rest of the system. Leveraging this insight, we develop protocols to certify global properties -- including multipartite entanglement, circuit complexity, and quantum magic -- by witnessing them on a small, accessible subsystem. Remarkably, randomizing the local measurement bases extends this capability to certify state fidelity. Relying solely on local Pauli measurements, these protocols achieve constant sample complexity and robustness for almost all quantum states, including a wide range of physically relevant states. For certifying the fidelity of $n$-qubit states, this $O(1)$ scaling dramatically improves upon state-of-the-art protocols requiring $O(n^4)$ samples. Our unified framework provides both a practical toolkit for large-scale quantum certification and a novel lens into complex many-body systems.

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arXiv2025

State complexity and phase identification in adaptive quantum circuits

Adaptive quantum circuits, leveraging measurements and classical feedback, significantly expand the landscape of realizable quantum states compared to their non-adaptive counterparts, enabling the preparation of long-range entangled states and topological phases at constant depths. However, the ancilla overhead for preparing arbitrary states can be prohibitive, raising a fundamental question: which states can be efficiently realized with limited ancilla and low depth? Addressing this question requires a rigorous quantitative characterization of state complexity, or the minimum depth and ancillas, to realize a state in adaptive circuits. In this work, we tackle this problem by introducing two properties of quantum states: state weight and anti-shallowness, connected to the correlation range and correlation strength within a state, respectively. We prove that these quantities are bounded under limited circuit resources, thereby providing rigorous bounds on the approximate complexity of state preparation and gate implementation. Illustrative examples include the GHZ state, W state, QLDPC code states, and the Toffoli gate. Besides complexity, we show that states within the same quantum phase, defined by a set of quantum states connected with constant-depth circuits, must share the same scaling of weight or anti-shallowness. This establishes these quantities as indicators of quantum phases and their essential roles in many-body physics.

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