Papers

The state hidden subgroup problem (StateHSP) is a recent generalization of the hidden subgroup problem. We present an algorithm that solves the non-abelian StateHSP over $N$ copies of the dihedral group of order $8$ (the symmetries of a square). This algorithm is of interest for learning non-Pauli stabilizers, as well as related symmetries relevant for the problem of Hamiltonian spectroscopy. Our algorithm is polynomial in the number of samples and computational time, and requires only constant depth circuits. This result extends previous work on the abelian StateHSP and, as a special case, provides a solution for the ordinary hidden subgroup problem on this specific non-abelian group.

We construct a family of constant-rate highly-symmetric self-dual qLDPC codes on high dimensional expanders. This is the first self-dual code constructed on high dimensional expanders and also the first such code with a rich (e.g. transitive) symmetry group, whose order exceeds the number of qubits. From this symmetry, we identify an extensive set of logical generators that act as permutations or diagonal gates, as well as a handful of other interesting gates (including the logical swap-Hadamard from self-duality). These advantages over prior constructions are in large part due to the fact that our codes are the first to be explicitly defined on expanding (non-product) simplicial complexes. Indeed, our work develops a broader framework toward utilizing high dimensional expanders to construct highly performant quantum codes with fault tolerant gates. While asymptotically good qLDPC codes have been constructed on 2D HDX built from products of graphs, these product constructions have a number of limitations, such as a lack of structure useful for fault-tolerant logic. Our framework for (fold-)transversal logical gates naturally utilizes symmetric non-product simplicial high dimensional expanders, and we demonstrate concretely through our 2D code family how this framework gives a rich set of fault-tolerant logical generators.

We construct a second-quantized representation with a structure of balanced ternary formalism, which involves three substances in organic molecular materials, namely electron, hole and charge-transfer exciton, into a uniform framework. The quantum thermodynamic of excitons is investigated in a closed and compact manner, benefitting from the interplay of the three substances. In order to be friendly with quantum simulations, the interactions among them are all described with unitary transformations. Significantly, the nonconserving dynamics of particle numbers, such as the generation of charge current and the exciton fission in organic semiconductors, is consistently expressed by this unitary formalism on the basis of bosonic coherent states. The spin degree of freedom is further taken into account, and an exotic molecular ferromagnetic ordering is induced in a specific configuration of excitons. This balanced ternary formalism establishes a solid bridge to connect thermodynamics and quantum simulations.

We give a meta-complexity characterization of EFI pairs, which are considered the "minimal" primitive in quantum cryptography (and are equivalent to quantum commitments). More precisely, we show that the existence of EFI pairs is equivalent to the following: there exists a non-uniformly samplable distribution over pure states such that the problem of estimating a certain Kolmogorov-like complexity measure is hard given a single copy. A key technical step in our proof, which may be of independent interest, is to show that the existence of EFI pairs is equivalent to the existence of non-uniform single-copy secure pseudorandom state generators (nu 1-PRS). As a corollary, we get an alternative, arguably simpler, construction of a universal EFI pair.

A tenet of contemporary physics is that novel physics beyond the Standard Model lurks at a scale related to the Planck length. The development and validation of a unified framework that merges general relativity and quantum physics is contingent upon the observation of Planck-scale physics. Here, we present a fully quantum model for measuring the nonstationary dynamics of a ng-mass mechanical resonator, which will slightly deviate from the predictions of standard quantum mechanics induced by modified commutation relations associated with quantum gravity effects at low-energy scalar. The deformed commutator is quantified by the oscillation frequency deviation, which is amplified by the nonlinear mechanism of the detection field. The measurement resolution is optimized to a precision level that is $15$ orders of magnitude below the electroweak scale.

In this work, we study the sample complexity of two variants of product testing when restricted to single-copy measurements. In particular, we consider both bipartite product testing (i.e., does there exist at least one non-trivial cut across which the state is product) and multipartite product testing (i.e., is the state fully product across every cut). For the first variant, we prove an exponential lower bound on the sample complexity of any algorithm for this task which utilizes only single-copy measurements. When comparing this with known efficient algorithms that utilize multi-copy measurements, this establishes an exponential separation for this and several related entanglement learning tasks. For the second variant, we prove another sample lower bound that establishes a separation between single- and multi-copy strategies. To obtain our results, we prove a crucial technical lemma that gives a lower bound on the overlap between tensor products of permutation operators acting on subsystems of states that themselves carry a tensor structure. Finally, we provide an algorithm for multipartite product testing using only single-copy, local measurements, and we highlight several interesting open questions arising from this work.

Hamiltonian learning is a cornerstone for advancing accurate many-body simulations, improving quantum device performance, and enabling quantum-enhanced sensing. Existing readily deployable quantum metrology techniques primarily focus on achieving Heisenberg-limited precision in one- or two-qubit systems. In contrast, general Hamiltonian learning theories address broader classes of unknown Hamiltonian models but are highly inefficient due to the absence of prior knowledge about the Hamiltonian. There remains a lack of efficient and practically realizable Hamiltonian learning algorithms that directly exploit the known structure and prior information of the Hamiltonian, which are typically available for a given quantum computing platform. In this work, we present the first Hamiltonian learning algorithm that achieves both Cramer-Rao lower bound saturated optimal precision and robustness to realistic noise, while exploiting device structure for quadratic reduction in experimental cost for fully connected Hamiltonians. Moreover, this approach enables simultaneous in-situ estimation of all Hamiltonian parameters without requiring the decoupling of non-learnable interactions during the same experiment, thereby allowing comprehensive characterization of the system's intrinsic contextual errors. Notably, our algorithm does not require deep circuits and remains robust against both depolarizing noise and time-dependent coherent errors. We demonstrate its effectiveness with a detailed experimental proposal along with supporting numerical simulations on Rydberg atom quantum simulators, showcasing its potential for high-precision Hamiltonian learning in the NISQ era.

We construct a family of distributions $\{\mathcal{D}_n\}_n$ with $\mathcal{D}_n$ over $\{0, 1\}^n$ and a family of depth-$7$ quantum circuits $\{C_n\}_n$ such that $\mathcal{D}_n$ is produced exactly by $C_n$ with the all zeros state as input, yet any constant-depth classical circuit with bounded fan-in gates evaluated on any binary product distribution has total variation distance $1 - e^{-\Omega(n)}$ from $\mathcal{D}_n$. Moreover, the quantum circuits we construct are geometrically local and use a relatively standard gate set: Hadamard, controlled-phase, CNOT, and Toffoli gates. All previous separations of this type suffer from some undesirable constraint on the classical circuit model or the quantum circuits witnessing the separation. Our family of distributions is inspired by the Parity Halving Problem of Watts, Kothari, Schaeffer, and Tal (STOC, 2019), which built on the work of Bravyi, Gosset, and König (Science, 2018) to separate shallow quantum and classical circuits for relational problems.

Previous work on Jackiw-Teitelboim (JT) gravity has shown that, at low temperatures, the annealed entropy becomes negative and departs from the quenched entropy. From the perspective of the random-matrix theory (RMT) dual of JT gravity, this effect is encoded in the continuous spectrum at the spectral edge that is universally described by the Airy model. At low temperature, the quenched entropy exhibits a power law dependence determined by the symmetry class of the RMT ensemble. Here we study the same question in the Sachdev-Ye-Kitaev (SYK) model which possesses much more structure than RMT. Through numerical simulations, we find that the level spacing statistics of the SYK model match the relevant RMT ensembles even near the spectral edge, thus leading to an agreement with the RMT prediction for the power-law behaviour of the quenched entropy at low temperatures. We also show similar effects in supersymmetric wormholes filled with matter, which is modeled by the $\mathcal N = 2$ supersymmetric SYK model. Numerically extracting the spectral edge properties of the BPS operators allows us to compute the quenched entanglement entropy of the wormhole in the large particle number limit.

As quantum control approaches hardware-imposed performance limits, weak effects omitted by reduced models become consequential. Assumptions required for analytic tractability then cease to guide control design and instead constrain further improvement. Here, we relax such assumptions and use simulation-guided stochastic tree search to navigate combinatorially large, discrete pulse-sequence spaces for robust many-body spin control. Experimentally, in a solid-state spin ensemble, the resulting computationally discovered pulse sequences substantially outperform analytically optimized baselines, despite being excluded by construction from analytic design criteria. Importantly, these unconventional sequences expose predictive structural features that enable rapid neural network–based performance evaluation. This efficiency gain makes the combinatorial scaling tractable and expands the control alphabet from 8 symmetry-restricted pulses to over 26,000 hardware-resolved options. The resulting fine-grained design freedom provides the control resolution required to reliably address weak, performance-limiting effects, unlocking qualitatively different spin-control capabilities beyond decades of traditional sequence design. Together, these results show that near performance limits, simplifying assumptions can become a primary constraint on quantum control in realistic hardware, and must be repurposed to guide computational discovery.

Learning the closest matrix product state (MPS) representation of a quantum state enables useful tools for quantum machine learning and analysis of complex quantum systems. In this work, we study the problem of learning MPS in the following setting: given many copies of an input MPS, the task is to recover a classical description of the state. The best known polynomial-time algorithm, introduced by [LCLP10, CPF+10], requires linear circuit depth and $\widetilde O(n^5)$ samples, and has seen no improvement in over a decade. These costs, neither known to be optimal, renders existing algorithms impractical for near-term quantum devices with limited resources. We introduce parallel disentangling algorithms for MPS learning. For exact MPS learning, our algorithm runs in polynomial time and uses circuit depth $O(\log n)$ and sample complexity $\widetilde O(n^3)$, improving both the depth and the dependence on the system size $n$. The key idea is to exploit the bounded-rank structure of reduced states on middle blocks of an MPS and organize the disentangling operations in a tree structure. We further extend the algorithm to closest MPS learning, improving the sample complexity dependence on $n$ from $n^9$ to $n^7$ and complement the algorithms with an $\Omega(n)$ product-state lower bound. We also investigate MPS learning under hardware constraints, including restricted measurements and geometric connectivity. Under the Learning Parity with Noise (LPN) assumption, we show computational hardness for learning an MPS(2) family with non-adaptive single-qubit measurements. Finally, we show that our algorithm can be implemented with depth $O(q n^{1/q})$ on a $q$-dimensional hypercubic lattice, giving an asymptotic reduction in depth. Together, our work provides a complete characterization of the quantum resources needed for efficient MPS learning.

Edge excitations are the defining signature of chiral topologically ordered systems. In continuum fractional quantum Hall (FQH) states, these excitations are described by the chiral Luttinger liquid ($\chi$LL) theory. Whether these field theory predictions can be precisely identified in discrete lattice systems of finite width, however, remains a longstanding question. Here we numerically demonstrate that the charge-one edge spectral function of a $\nu=1/2$ FCI on an infinitely long strip with width $L_y=10$ quantitatively follows the predictions of $\chi$LL theory. The edge spectrum is gapless, chiral, and linear, with spectral weight increasing linearly with both momentum and energy. We further analyze the influence of lattice size, particle number, trapping potential, and charge sector of excitations on the edge properties. Our results establish a clear correspondence between lattice FCIs and continuum FQH systems and provide guidance for future experimental detection of chiral edge modes.

In the problem of quantum state tomography, one is given $n$ copies of an unknown rank-$r$ mixed state $\rho \in \mathbb{C}^{d \times d}$ and asked to produce an estimator of $\rho$. In this work, we present the debiased Keyl's algorithm, the first estimator for full state tomography which is both unbiased and sample-optimal. We derive an explicit formula for the second moment of our estimator, with which we show the following applications. (1) We give a new proof that $n = O(rd/\varepsilon^2)$ copies are sufficient to learn a rank-$r$ mixed state to trace distance error $\varepsilon$, which is optimal. (2) We further show that $n = O(rd/\varepsilon^2)$ copies are sufficient to learn to error $\varepsilon$ in the more challenging Bures distance, which is also optimal. (3) We consider full state tomography when one is only allowed to measure $k$ copies at once. We show that $n =O\left(\max \left(\frac{d^3}{\sqrt{k}\varepsilon^2}, \frac{d^2}{\varepsilon^2} \right) \right)$ copies suffice to learn in trace distance. This improves on the prior work of Chen et al. and matches their lower bound. (4) For shadow tomography, we show that $O(\log(m)/\varepsilon^2)$ copies are sufficient to learn $m$ given observables $O_1, \dots, O_m$ in the "high accuracy regime", when $\varepsilon = O(1/d)$, improving on a result of Chen et al. More generally, we show that if $\mathrm{tr}(O_i^2) \leq F$ for all $i$, then $n = O\Big(\log(m) \cdot \Big(\min\Big\{\frac{\sqrt{r F}}{\varepsilon}, \frac{F^{2/3}}{\varepsilon^{4/3}}\Big\} + \frac{1}{\varepsilon^2}\Big)\Big)$ copies suffice, improving on existing work. (5) For quantum metrology, we give a locally unbiased algorithm whose mean squared error matrix is upper bounded by twice the inverse of the quantum Fisher information matrix in the asymptotic limit of large $n$, which is optimal.

Precisely addressing single nanostructures inside dense ensembles remains a bottleneck for scalable photonic and quantum information devices. Here we demonstrate, through comprehensive finite element and variational Monte-Carlo modelling, that a reconfigurable three-dimensional array of needle shaped beams can selectively switch the quantum optical response of individual InAs nanorods embedded in GaAs. By tuning the local non resonant intensity pattern the exciton and biexciton energies were calculated, electromagnetically induced transparency (EIT) windows were examined, and correspondingly near-field diffraction carpets were dynamically reshaped. A single parameter the activation ratio between illuminated and dark nanorods provides continuous control over photoluminescence peak position (80 meV) and EIT bandwidth (six times). We further predict fully programmable Talbot self-imaging in nanorod arrays with sub-wavelength pitch. Importantly, the observed Talbot carpets enable spatially resolved identification of which nanorods were excited, offering a powerful diagnostic for verifying structured-light activation schemes. The concept offers a low crosstalk, wafer scale route toward reconfigurable quantum emitters, tunable diffractive optics and on-chip slow-light components.

We study the connection between quantum secret sharing (QSS) schemes and $k$-uniform states of qubits beyond the equivalence between threshold QSS schemes and AME states. Specifically, we show that $3$-uniformity is a necessary but not sufficient condition for constructing a $3$-homogeneous QSS scheme using states of qubits. To the best of our knowledge, this is the first result connecting non-threshold QSS schemes with $k$-uniform states. As an application of our result, we classify QSS schemes for up to 7 players and provide explicit characterizations of their existence. Our results offer new insights into the role of $k$-uniform states in the design of QSS schemes (not necessarily threshold) and provide a foundation for future classifications of QSS schemes with more complex structures.

The speed of elementary quantum gates sets a limit on the speed at which quantum circuits can be applied and, as a result, the size of the computations that can be performed on a quantum computer. This limitation stems from the fact that present-day quantum hardware systems have finite coherence times that limit the total computation time. The speeds of qubit gates in various hardware settings have been well studied over the past few decades. The recent interest in multi-level quantum systems naturally creates a need for similar investigations of the speeds of multi-level or qudit gates. In this work, we perform an empirical study of the speed limit for the three-level or qutrit CZ gate. Our analysis focuses on a theoretical model for capacitively coupled superconducting transmons but can be extended to other systems. We generate CZ gate protocols using optimal control theory techniques and observe when the fidelity crosses certain thresholds. In addition to the empirical approach, we derive an analytical speed limit for the qutrit CZ gate using traditional quantum speed limit techniques. We compare the speed limits derived using these two different approaches and discuss the gap that remains between them. We also compare the time needed to implement the qutrit CZ gate with its qubit counterpart.

One of the key aspects of Shannon's theory is that it provides guidance for designing the most efficient systems, such as minimizing errors and clarifying the limits of coding. Such theories have made great developments in the 50 years since 1948. It has played a vital role in enabling the development of modern ultra-fast, stable, and highly dependable information and communication systems. The Shannon theory is supported by the statistical communication theory such as detection and estimation theory. The theory of communication systems that transmit Shannon information using quantum media is called quantum Shannon information theory, and research began in the 1960s. The theoretical formulation comparable to conventional Shannon theory has been completed. Its important role is to suggest that application of quantum effect will surpass existing communication performance. It would be meaningless if performance, efficiency, and utility were to deteriorate due to quantum effects, even if certain new function is given. This paper suggests that there are various limitations to utilizing quantum Shannon information theory to benefit real-world communication systems and presents a theoretical framework for achieving the ultimate goal. Finally, we introduce the perfect secure cipher that overcome the Shannon impossibility theorem without degrading communication performance and sensor et al as the examples.

The speed of evolution between perfectly distinguishable states is thoroughly analyzed in a closed three-level (qutrit) quantum system. Considering an evolution under an arbitrary time-independent Hamiltonian, we fully characterize the relevant parameters according to whether the corresponding quantum speed limit is given by the Mandelstam-Tamm, the Margolus-Levitin, or the Ness-Alberti-Sagi (dual) bound, thereby elucidating their hierarchy and relative importance. We revisit the necessary and sufficient conditions that guarantee the evolution of the initial state towards an orthogonal one in a finite time, and pay special attention to the full characterization of the speed of evolution, offering a speed map in parameter space that highlights regions associated with faster or slower dynamics. The general analysis is applied to concrete physical settings, particularly a pair of bosons governed by an extended Bose-Hubbard Hamiltonian, and a single particle in a triple-well potential. Our findings provide a framework to explore how the energetic resources and the initial configurations shape the pace of the dynamics in higher-dimensional systems.

We show that $n = \Omega(rd/\varepsilon^2)$ copies are necessary to learn a rank $r$ mixed state $\rho \in \mathbb{C}^{d \times d}$ up to error $\varepsilon$ in trace distance. This matches the upper bound of $n = O(rd/\varepsilon^2)$ from prior work, and therefore settles the sample complexity of mixed state tomography. We prove this lower bound by studying a special case of full state tomography that we refer to as projector tomography, in which $\rho$ is promised to be of the form $\rho = P/r$, where $P \in \mathbb{C}^{d \times d}$ is a rank $r$ projector. A key technical ingredient in our proof, which may be of independent interest, is a reduction which converts any algorithm for projector tomography which learns to error $\varepsilon$ in trace distance to an algorithm which learns to error $O(\varepsilon)$ in the more stringent Bures distance.

Arrays of hundreds or thousands of low temperature detectors have been deployed for many experiments, both bolometers for long wavelength applications and calorimeters for shorter wavelength applications. One challenge that is common to many of these arrays is the efficient use of focal plane area to achieve a large fill fraction of absorbers coupled to detectors. We are developing an integrated fabrication of soft X-ray transition edge sensors (TES) and microwave SQUID multiplexers ($\mu$MUX) with the goal of maximizing the fill fraction of the focal plane area on a scale of many thousand pixel detectors. We will utilize lithographically defined high density interconnects to circumvent limitations in existing solutions that use wirebonds or flip-chip bonds. Here we report the first demonstration of combining TES and $\mu$MUX processes into a single TES-System-on-a-Chip (TES-SoC) fabrication on a silicon wafer. The $\mu$MUX SQUIDs and TES electrothermal feedback circuits are microfabricated first and protected with passivating SiO$_2$, then the TES devices and TES-to-SQUID interconnects are fabricated, and finally the protective layer is removed before the fabrication of the microwave resonators. We show that the microwave SQUIDs are functional and have reasonable yield, and that we are able to read out the transition temperature of the connected TESs using those SQUIDs.

We propose cascaded spontaneous four-wave mixing (SFWM) in microring resonators as a scalable and efficient approach for directly generating non-Gaussian states of light. Focusing on the well-understood "low-gain" regime, we demonstrate that triplet generation through cascaded SFWM can be achieved with high efficiency and favorable spectral characteristics using realistic microring sources in AlGaAs. The ability to achieve the generation of light in a single set of supermodes – and the predicted accessibility of the "high-gain" regime at realistic pump powers – makes this source a promising candidate as a direct and deterministic source of non-Gaussian light for photonic quantum information processing.

Generalized quantum measurements, described by positive operator-valued measures (POVMs), are essential for modeling realistic processes in open quantum systems. While quantum process tomography can fully characterize a POVM, it is resource-intensive and impractical when only specific POVM elements or matrix elements of a particular POVM element are of interest. Direct quantum measurement tomography offers a more efficient alternative but typically relies on weak interactions and complex structures of the system, environment, and probe as the dimension of the system increases, limiting its precision and scalability. Furthermore, characterizing a POVM element alone is insufficient to determine the underlying physical mechanism, as multiple Kraus operators can yield the same measurement statistics. In this work, we present a unified framework for the direct characterization of individual matrix elements of Kraus operators associated with specific POVM elements and arbitrary input states without requiring weak interaction, complex structures of the system-environment-probe or full process and state tomography. This framework naturally extends to projective measurements, enabling direct observable tomography, and to the characterization of unitary operations. Our method also captures modular and weak values of observables and Kraus operators, without invoking weak interaction approximations. We demonstrate potential implementations in optical systems, highlighting the experimental feasibility of our approach.

Entanglement underpins the power of quantum technologies, yet it is fragile and typically destroyed by dissipation. Paradoxically, the same dissipation, when carefully engineered, can drive a system toward robust entangled steady states. However, this engineering task is nontrivial, as dissipative many-body systems are complex, particularly when they support multiple steady states. Here, we derive analytic expressions that predict how the steady state of a system evolving under a Lindblad equation depends on the initial state, without requiring integration of the dynamics. These results extend the frameworks developed in Refs. [Phys. Rev. A 89, 022118 (2014) and Phys. Rev. X 6, 041031 (2016)], showing that while the steady-state manifold is determined by the Liouvillian kernel, the weights within it depend on both the Liouvillian and the initial state. We identify a special class of Liouvillians for which the steady state depends only on the initial overlap with the kernel. Our framework provides analytical insight and a computationally efficient tool for predicting steady states in open quantum systems. As an application, we propose schemes to generate metrologically useful entangled steady states in spin ensembles via balanced collective decay.

We study ancilla-free approximation of single-qubit unitaries $U\in {\rm SU}(2)$ by gate sequences over Clifford+$G$, where $G\in\{T,V\}$ or their generalization. Let $p$ denote the characteristic factor of the gate set (e.g., $p=2$ for $G=T$ and $p=5$ for $G=V$). We prove three asymptotic bounds on the minimum $G$-count required to achieve approximation error at most $\varepsilon$. First, for Haar-almost every $U$, we show that $3\log_{p}(1/\varepsilon)$ $G$-count is both necessary and sufficient; moreover, probabilistic synthesis improves the leading constant to $3/2$. Second, for unitaries whose ratio of matrix elements lies in a specified number field, $4\log_p(1/\varepsilon)$ $G$-count is necessary. Again, the leading constant can be improved to $2$ by probabilistic synthesis. Third, there exist unitaries for which the $G$-count per $\log_{p}(1/\varepsilon)$ fails to converge as $\varepsilon\to 0^+$. These results partially resolve a generalized form of the Ross–Selinger conjecture.

We give a natural problem over input quantum oracles $U$ which cannot be solved with exponentially many black-box queries to $U$ and $U^\dagger$, but which can be solved with constant many queries to $U$ and $U^*$, or $U$ and $U^{\mathrm{T}}$. We also demonstrate a quantum commitment scheme that is secure against adversaries that query only $U$ and $U^\dagger$, but is insecure if the adversary can query $U^*$. These results show that conjugate and transpose queries do give more power to quantum algorithms, lending credence to the idea put forth by Zhandry that cryptographic primitives should prove security against these forms of queries. Our key lemma is that any circuit using $q$ forward and inverse queries to a state preparation unitary for a state $\sigma$ can be simulated to $\varepsilon$ error with $n = \mathcal{O}(q^2/\varepsilon)$ copies of $\sigma$. Consequently, for decision tasks, algorithms using (forward and inverse) state preparation queries only ever perform quadratically better than sample access. We also identify a motif, which we call the "acorn trick", where generically strengthening a quantum resource can be possible if the output is allowed to be random, bypassing no-go theorems for deterministic algorithms. We demonstrate this idea for several settings, including controlization and purification.

An attractive approach for stabilizing entangled many-body spin states is to employ engineered dissipation. Most existing proposals either target relatively simple collective spin states, or require numerous independent and complex dissipative processes. Here, we show a surprisingly versatile scheme for many-body reservoir engineering that relies solely on fully collective single-excitation decay, augmented with local Hamiltonian terms. Crucially, all these ingredients are readily available in cavity QED setups. Our method is based on splitting the spin system into groups of sub-ensembles, and provides an easily tunable setup for stabilizing a broad family of pure, highly entangled states with closed-form analytic descriptions. Our results have immediate application to multi-ensemble quantum metrology, enabling Heisenberg-limited sensing of field gradients and curvatures. Notably, our approach solves an important challenge in differential quantum sensing by providing the first example of Heisenberg-limited differential sensing immune to common-mode noise and accessible with only simple one-body measurements. The same setup also allows the stabilization of an entire family of entangled states in a 1D chain of spin ensembles with symmetry-protected topological (SPT) order, and have a direct connection to the outputs of sequential unitary circuits. A special case of our protocol efficiently stabilizes the celebrated Affleck-Kennedy-Lieb-Tasaki (AKLT) state.

The paper presents variational formulae for entropy-like functionals, including Segal and Rényi entropies, for normal states on semifinite von Neumann algebras. The considered functionals are of the form $\tau(f(h))$ where $\tau$ is a normal faithful semifinite trace on this algebra, $h$ is a positive selfadjoint operator from $L^1(\mathscr{M},\tau)$, and $f$ is an appropriate convex or concave function. The results cover both finite and semifinite algebras, and the obtained formulae generalise known results, in particular, those concerning relative entropy. Moreover, the connection between quantum entropies and the structure of abelian subalgebras is highlighted, providing new interpretations in the context of quantum information theory.

Hypergraph product codes are a prototypical family of quantum codes with state-of-the-art decodability properties. In this work we consider the "noisy" syndrome decoding problem and exact recovery problem for hypergraph product codes and show a reduction to the decoding and exact recovery of classical codes in the noisy syndrome setting. Our results hold for a broad class of codes admitting efficient syndrome decoding, including Sipser-Spielman codes and Reed-Solomon codes.

The ultimate limits of quantum state discrimination are often thought to be captured by asymptotic bounds that restrict the achievable error probabilities, notably the quantum Chernoff and Hoeffding bounds. Here we study hypothesis testing protocols that are permitted a probability of producing an inconclusive discrimination outcome, and investigate their performance when this probability is suitably constrained. We show that even by allowing an arbitrarily small probability of inconclusiveness, the limits imposed by the quantum Hoeffding and Chernoff bounds can be significantly exceeded. This completely circumvents the conventional trade-offs between error exponents in hypothesis testing while incurring only a vanishingly small overhead over conventional approaches. Such improvements over standard state discrimination are robust and can be obtained even when an exponentially vanishing probability of inconclusive outcomes is demanded. Relaxing the constraints on the inconclusive probability can enable even larger advantages, but this comes at a price. We show a 'strong converse' property of this setting: targeting error exponents beyond those achievable with vanishing inconclusiveness necessarily forces the probability of inconclusive outcomes to converge to one. By exactly quantifying the rate of this convergence, we give a complete characterisation of the trade-offs between error exponents and rates of conclusive outcome probabilities. Overall, our results provide a comprehensive asymptotic picture of how the allowance for inconclusive measurement outcomes reshapes optimal quantum hypothesis testing.

Trapped-ion crystals are a leading platform for quantum information science, but achieving the high-fidelity entangling gates required for fault-tolerant quantum computing becomes harder as system size increases. As systems scale, spectral crowding makes low-order nonlinear resonances between collective motional modes increasingly common and can limit gate performance, especially in monolithic or global-mode architectures. We develop a general model to identify and simulate nonlinear motional-mode coupling (NoMoCou) arising from third-order Coulomb terms and quantify its impact on the Molmer-Sorensen gate across linear chains and 2D crystals in rf and Penning traps. We delineate the regimes where NoMoCou dominates the error budget and provide design rules: detune operating points from low-order resonances, tune trap anisotropy to reshape spectra, and shape gate waveforms.