arXiv subjects

Zhenhuan Liu

Publications and source records attributed to Zhenhuan Liu.

At least 19 recordsLinked to original sources

arXiv2026

Fermionic quantum error correction is never free

Fermionic platforms offer compelling architectures for quantum computing, ranging from topologically protected Majorana-based qubits to fermionic cold atoms. To achieve scalability, however, they require quantum error correction. In this work, we prove that any exact and sufficiently accurate approximate fermionic quantum error correction necessarily requires non-Gaussian operations, beyond the free-fermion regime of quadratic dynamics. This is in sharp contrast to the qubit setting, where the efficiently classically simulable stabilizer operations form the standard framework for quantum error correction. Specifically, we show that the logical space of any non-trivial fermionic error-correcting code contains no pure fermionic Gaussian state, utilizing a fundamental incompatibility between fermionic error correction and Wick's theorem. We further show that the required number of bounded-weight non-Gaussian gates for unitary codeword preparation grows at least linearly with both the code distance and the number of encoded modes, revealing an intrinsic resource overhead that increases simultaneously with error-protection strength and logical capacity. Furthermore, we analyze the performance of fermionic Gaussian operations in entanglement distillation, revealing a distinction from their bosonic counterparts. Our results reveal fundamental difficulties for fermionic error correction from the perspectives of both physical implementation and classical simulation, suggesting connections to fermionic phases of matter and state preparation complexity.

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arXiv2026

On the geometry and typicality of quantum magic

We prove that, for an $n$-qubit system of dimension $d=2^n$, every state satisfying $\operatorname{Tr}(ρ^2)\le 1/(d-a_\ast)$, with $a_\ast=0.458327\cdots$, lies inside the stabilizer polytope and is therefore magic-free. Combining this result with general geometric properties of high-dimensional polytopes, we establish quantitative estimates for the Hilbert--Schmidt inradius and volume radius of the stabilizer polytope, and use them to characterize the typicality of magic in random induced states obtained by tracing out a $k$-dimensional subsystem from a $d\times k$-dimensional Haar-random pure state. We prove a sharp phase transition in the probability of such states having magic, whose transition dimension $k_\star$ is bounded between $Ω(d^2/\log^2d)$ and $\mathcal{O}(d^2)$. We further prove that the number of facets of the stabilizer polytope lies between $\exp[Ω(d^2/\log^2 d)]$ and $\exp[\mathcal{O}(d^2\log^2 d)]$ employing a result of Bourgain and Milman in convex geometry, substantially improving upon the previous quasipolynomial lower bound and implying that doubly-exponentially many linear inequalities in the number of qubits are required for an exact description of the magic-free region. Overall, our results reveal the near-extremal geometry of the stabilizer polytope and provide a quantitative foundation for understanding the typicality, robustness, and detectability of magic.

quant-ph↗

arXiv2026

Non-Markovian Noise Suppression Simplified through Channel Representation

Non-Markovian noise, arising from memory effects in the environment, poses substantial challenges to conventional quantum noise suppression protocols, including quantum error correction and mitigation. We introduce a channel representation for arbitrary non-Markovian quantum dynamics, termed the Choi channel, which translates the complex dynamics of non-Markovian noise into the familiar picture of noise channels. It therefore provides a systematic way to design non-Markovian noise suppression protocols: one can apply existing channel-level error-suppression techniques in the Choi-channel picture and then translate them back to the circuit picture. The performance of the resulting non-Markovian protocols, including their noise-suppression effects and complexity, can often be inherited directly from the corresponding Choi-channel protocols without requiring a separate analysis. With this framework, we devise new protocols using Pauli twirling, probabilistic error cancellation, and virtual channel purification. Pauli twirling reduces non-Markovian noise to noise with only classical temporal correlations; probabilistic error cancellation can fully cancel non-Markovian noise; and virtual channel purification can suppress non-Markovian noise without detailed knowledge of its specific form. Through these examples, the Choi channel serves as a foundational bridge for systematically converting existing channel-level techniques into non-Markovian noise suppression protocols.

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arXiv2026

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection

Quantum information science aims to harness different kinds of quantum resources to accomplish specific information-processing tasks. These resources also play an increasingly important role in addressing fundamental questions concerning quantum phases and dynamics. Therefore, developing powerful and practical methods for identifying and detecting quantum resources is of great significance, with applications ranging from benchmarking quantum devices to understanding the fundamental structure of quantum theory. In this work, we propose witness expansion, a unified framework for constructing nonlinear criteria for detecting quantum resources that are associated with a well-defined group of free unitaries. These criteria apply to both pure and mixed quantum states and are based on polynomial functions of the target state, which can be estimated experimentally using multiple copies of the state and evaluated analytically in certain physical models. We show how several well-known resource-detection quantities naturally emerge from our framework, including the $l_2$ norm of coherence, partial-transpose moments for entanglement, stabilizer entropy for nonstabilizerness (quantum magic), and fermionic antiflatness for fermionic non-Gaussianity. Beyond recovering these existing structures, our framework also yields new criteria for detecting qubit and qudit magic states, substantially enhancing witness-based detection capabilities. In addition, it gives, to the best of our knowledge, the first analytical criterion for detecting mixed-state fermionic non-Gaussianity with respect to the convex hull of pure fermionic Gaussian states that remains nontrivial for arbitrary numbers of qubits, demonstrating the broad applicability and conceptual unifying power of the framework.

quant-ph↗

arXiv2026

No Universal Purification in Quantum Mechanics

Many central tasks in fundamental physics and quantum information processing are possible only insofar as mixed quantum states can be made purer. In this work, we prove that the linearity and positivity of quantum mechanics impose general restrictions on quantum purification, unveiling a new fundamental principle of quantum information processing. We first establish that no quantum operation can transform a finite number of copies of an unknown quantum state or channel into an exactly pure output that depends non-trivially on the input, thereby ruling out an important form of universal purification in both static and dynamical settings. Building on this, we show that, upon relaxing the requirement of exact purity, one can establish quantitative sample-complexity lower bounds for approximate purification that hold for arbitrary physically allowed strategies, whose scaling matches the performance of purification-related tasks across several different areas of quantum information processing. Moreover, this lower bound leads to a generalized standard quantum limit for learning arbitrary functions of a quantum state, greatly extending earlier results based on quantum Fisher information and revealing a deep connection between purification and quantum learning. Extending this principle to other important settings, we establish, for the first time, an exponential sample-complexity lower bound for approximate pure dilation state preparation and a no-go theorem for approximate bosonic Gaussian state purification with passive Gaussian operations, establishing much more stringent limitations under practical operational constraints.

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arXiv2026

Triangle Criterion: a mixed-state magic criterion with applications in distillation and detection

We introduce a mixed-state magic criterion, the Triangle Criterion, which plays a role for magic analogous to the Positive Partial Transposition (PPT) Criterion for entanglement: it combines strong detection capability, a clear geometric interpretation, and an operational link to magic distillation. Using this criterion, we uncover several new features of multi-qubit magic distillation and detection. We prove that genuinely multi-qubit magic distillation protocols are strictly more powerful than all single-qubit schemes by showing that the Triangle Criterion is not stable under tensor products. Moreover, we show that, with overwhelming probability, multi-qubit magic states with relatively low rank cannot be distilled by any single-qubit distillation protocol. We derive an upper bound on the minimal purity of magic states, which is conjectured to be tight with both numerical and constructive evidences. Using this minimal-purity result, we predict the existence of unfaithful magic states, namely states that cannot be detected by any fidelity-based magic witness, and reveal fundamental limitations of mixed-state magic detection in any single-copy scheme.

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arXiv2026

Exponential speedup in measurement property learning with post-measurement states

Learning properties of quantum states and channels is known to benefit from resources such as entangled operations, auxiliary qubits, and adaptivity, whereas the resource structure of measurement learning, namely, learning properties of quantum measurement operators, remains poorly understood. In this work, we identify a measurement learning task for which access limited to classical measurement outcomes leads to an exponential lower bound on the query complexity, established via a distinguishing task between a genuine quantum projective measurement and a purely classical random number generator. Remarkably, this hardness persists even when arbitrary entangled operations, auxiliary systems, and fully adaptive strategies are allowed, indicating that conventional resources for state and channel learning are ineffective in this task. In contrast, when access to the post-measurement quantum state is available, the same task can be solved with constant query complexity using a simple measuring-twice protocol, without requiring resources that are useful for state and channel learning. Our results reveal post-measurement states as a qualitatively new and decisive resource for measurement learning, suggesting potential implications for the design of practical quantum certification protocols.

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arXiv2026

Entanglement Detection with Variational Quantum Interference: Theory and Experiment

Entanglement detection is a fundamental task in quantum information science, serving as a cornerstone for quantum benchmarking and foundational studies. With an increasing qubit number that can be effectively controlled, there is a pressing need for a scalable and robust detection protocol which requires minimal resources while maintaining high detection capability. By integrating the Positive Partial Transposition criterion with variational quantum interference, we propose an entanglement detection protocol that requires moderate classical and quantum computation resources. We numerically show that this protocol achieves a high detection capability with shallow quantum circuits, surpassing some widely-used entanglement detection methods. The protocol also exhibits strong resilience to circuit noise, ensuring its applicability across different physical platforms. We further demonstrate the protocol experimentally on an eight-photon linear-optical platform, where it successfully detects the entanglement of a three-qubit mixed state that is inaccessible to conventional entanglement witnesses. By combining quantum interference with classical optimization, our protocol provides a scalable and resource-efficient route toward practical entanglement detection.

quant-ph↗

arXiv2026

Optimal randomized measurements for a family of non-linear quantum properties

Quantum learning encounters fundamental challenges when estimating non-linear properties, owing to the inherent linearity of quantum mechanics. Although recent advances in single-copy randomized measurement protocols have achieved optimal sample complexity for specific tasks like state purity estimation, generalizing these protocols to estimate broader classes of non-linear properties without sacrificing optimality remains an open problem. In this work, we introduce the observable-driven randomized measurement (ORM) protocol enabling the estimation of ${\rm Tr}(Oρ^2)$ for an arbitrary observable $O$ -- an essential quantity in quantum computing and many-body physics. We establish an upper bound for ORM's sample complexity and show its optimality for observables with a large trace-norm, including Pauli and local observables, closing a gap in the literature. For these observables, ORM admits an efficient implementation with Clifford circuits. Numerical experiments validate that ORM requires substantially fewer state samples to achieve the same precision compared to classical shadows. Additionally, we introduce a braiding randomized measurement protocol for multiple low-rank non-linear observables, reducing circuit complexities in practical applications.

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arXiv2025

Realizing Universal Non-Markovian Noise Suppression

Non-Markovian noise, arising from environmental memory effects, is the most general and challenging form of noise in quantum computing, and is typically difficult to characterize and suppress. Here, we analyze and experimentally demonstrate a non-Markovian noise suppression scheme inspired by quantum purification protocols. We theoretically prove that, even without noise calibration and assumptions on specific noise models, the scheme can exponentially reduce non-Markovian error rates with respect to the ancillary system size. We implement the protocol using nuclear spins, demonstrating that non-Markovian noise can be suppressed for both unitary operations and non-unitary channels. The observed fidelities and process tomography show close agreement with theoretical predictions, confirming the practicality and effectiveness of the scheme.

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arXiv2025

Experimental Quantum Channel Purification

Quantum networks, which integrate multiple quantum computers and the channels connecting them, are crucial for distributed quantum information processing but remain inherently susceptible to channel noise. Channel purification emerges as a promising technique for suppressing noise in quantum channels without complex encoding and decoding operations, making it particularly suitable for remote quantum information transmission in optical systems. In this work, we introduce an experimental setup for efficient channel purification, harnessing the spatial and polarization properties of photons. Our design employs two Fredkin gates to enable coherent interference between independent noise channels, achieving effective noise suppression across a wide range of noise levels and types. Through application to entanglement distribution, our protocol demonstrates a superior capability to preserve entanglement against channel noise compared to conventional entanglement purification methods.

quant-ph↗

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.

quant-ph↗

arXiv2025

Expectation value estimation with parametrized quantum circuits

Estimating properties of quantum states, such as fidelities, molecular energies, and correlation functions, is a fundamental task in quantum information science. Due to the limitation of practical quantum devices, including limited circuit depth and connectivity, estimating even linear properties encounters high sample complexity. To address this inefficiency, we propose a framework that optimizes sample complexity for estimating the expectation value of any observable using a shallow parameterized quantum circuit. Within this framework, we introduce two decomposition algorithms, a tensor network approach and a greedy projection approach that decompose the target observable into a linear combination of multiple observables, each of which can be diagonalized with the shallow circuit. Using this decomposition, we then apply an importance sampling algorithm to estimate the expectation value of the target observable. We numerically demonstrate the performance of our algorithm by estimating the expectation values of some specific Hamiltonians and inner product of a Slater determinant with a pure state, highlighting advantages compared to some conventional methods. Additionally, we derive the fundamental lower bound for the sample complexity required to estimate a target observable using a given shallow quantum circuit, thereby enhancing our understanding of the capabilities of shallow circuits in quantum learning tasks.

quant-ph↗

arXiv2025

No Practical Quantum Broadcasting: Even Virtually

Quantum information cannot be broadcast -- an intrinsic limitation imposed by quantum mechanics. However, recent advances in virtual operations offer new insights into the no-broadcasting theorem. Here, we focus on the practical utility and introduce sample efficiency as a fundamental constraint, requiring any practical broadcasting protocol perform no worse than the naïve approach of direct preparation and distribution. We prove that no linear process -- whether quantum or beyond -- can simultaneously uphold sample efficiency, unitary covariance, permutation invariance, and classical consistency. This leads to a no-practical-broadcasting theorem, which places strict limits on the practical distribution of quantum information. By applying Schur-Weyl duality, we establish the uniqueness of the canonical 1-to-$N$ virtual broadcasting map that satisfies the latter three conditions, provide its construction, and determine its sample complexity through semidefinite programming. Finally, we explore the interplay between virtual broadcasting and a quantum spacetime framework, known as the pseudo-density operator, showing that their correspondence holds only in the 1-to-2 case, underscoring the fundamental asymmetry between spatial and temporal statistics in the quantum world.

quant-ph↗

arXiv2025

Exponential Advantage from One More Replica in Estimating Nonlinear Properties of Quantum States

Inferring nonlinear features of quantum states is fundamentally important across quantum information science, but remains challenging due to the intrinsic linearity of quantum mechanics. It is widely recognized that quantum memory and coherent operations help avoid exponential sample complexity, by mapping nonlinear properties onto linear observables over multiple copies of the target state. In this work, we prove that such a conversion is not only sufficient but also necessary. Specifically, we prove that the estimation of $\mathrm{tr}(ρ^{k} O)$ for a broad class of observables $O$ is exponentially hard for any protocol restricted to $(k-1)$-replica joint measurements, whereas access to one additional replica reduces the complexity to a constant. These results establish, for the first time, an exponential separation between $(k-1)$- and $k$-replica protocols for any integer $k>2$, thereby introducing a fine-grained hierarchy of replica-based quantum advantage and resolving an open question in the literature. The technical core is a general indistinguishability principle showing that any ensemble constructed from large Haar random states via tensor products and mixtures is hard to distinguish from its average. Leveraging this principle, we further prove that $k$-replica joint measurements are also necessary for distinguishing rank-$k$ density matrices from rank-$(k-1)$ ones. Overall, our work delineates sharp boundaries on the power of joint measurements, highlighting resource-complexity trade-offs in quantum learning theory and deepening the understanding of quantum mechanics' intrinsic linearity.

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arXiv2025

CD-NGP: A Fast Scalable Continual Representation for Dynamic Scenes

Novel view synthesis (NVS) in dynamic scenes faces persistent challenges in memory consumption, model complexity, training efficiency, and rendering quality. Offline methods offer high fidelity but suffer from high memory usage and limited scalability, while online approaches often trade quality for speed and compactness. We propose Continual Dynamic Neural Graphics Primitives (CD-NGP), a continual learning framework that reduces memory overhead and enhances scalability through parameter reuse. To avoid feature interference in dynamic scenes and improve rendering quality, our method combines spatial and temporal hash encodings, which compactly represent scene structures and motion patterns. We also introduce a new dataset comprising multi-view, long-duration ($>1200$ frames) videos with both rigid and non-rigid motion, which is not found in existing benchmarks. CD-NGP is evaluated on public datasets and our long video dataset, demonstrating superior scalability and reconstruction quality. It significantly reduces training memory usage to <14GB and requires only 0.4MB/frame in streaming bandwidth on DyNeRF -- substantially lower than most online baselines.

cs.CV↗

arXiv2025

Exponential Separations between Quantum Learning with and without Purification

In quantum learning tasks, quantum memory can offer exponential reductions in statistical complexity compared to any single-copy strategies, but this typically necessitates at least doubling the system size. We show that such exponential reductions can also be achieved by having access to the purification of the target mixed state. Specifically, for a low-rank mixed state, only a constant number of ancilla qubits is needed for estimating properties related to its purity, cooled form, principal component and quantum Fisher information with constant sample complexity, which utilizes single-copy measurements on the purification. Without access to the purification, we prove that these tasks require exponentially many copies of the target mixed state for any strategies utilizing a bounded number of ancilla qubits, even with the knowledge of the target state's rank. Our findings also lead to practical applications in areas such as quantum cryptography. With further discussions about the source and extent of the advantages brought by purification, our work uncovers a new resource with significant potential for quantum learning and other applications.

quant-ph↗

arXiv2025

Practical Quantum Advantage for Boosting Citations

Realizing practical quantum advantage with meaningful economic impact is the holy grail of the quantum information field. Recent quantum technology advances have driven exponential growth in quantum information research, with resultant publications achieving significantly elevated impact. Within academia, citation counts serve as a key metric for evaluating research impact, often directly influencing career advancement and compensation structures. Motivated by these observations, we propose a potential protocol for practical quantum advantage in boosting citations.

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