Papers

We investigate how femtoscopic correlations modify the relation between the spin entanglement of emitted particle pairs and that of pairs selected at a given relative momentum. For two spin-$\frac{1}{2}$ particles, we show that the momentum-selected spin state can be entangled even when the corresponding state at emission is separable. We derive a momentum-dependent separability criterion that determines whether the observed spin correlations require entanglement at emission. As an application, we consider a pair of identical $\Lambda$ hyperons, for which quantum statistics and final-state interactions affect the singlet and triplet spin channels differently at low relative momentum. Our results provide a framework for using experimentally accessible spin correlations to investigate entanglement at emission.

Quantum signal processing (QSP) requires the efficient computation of phase factors associated with a polynomial transformation. One existing stable factorization method avoids direct root finding but relies on Prony's method to recover a polynomial from weighted power sums of its roots (arXiv:2202.02671). We present a modification of this approach that eliminates Prony's method by using the logarithmic derivative of an associated polynomial. Because the logarithmic derivative has the same residue at every root after accounting for multiplicity, its Fourier coefficients directly yield the unweighted power sums of the roots inside the unit disk. The Newton–Girard identities then recover the coefficients of the corresponding polynomial without computing its roots. The resulting algorithm has $O(d\log^2 d)$ computational complexity and simplifies the factorization procedure of the original method. In numerical experiments on Hamiltonian simulation, eigenstate filtering, matrix inversion, and the Fermi–Dirac operator, our implementation computes phase factors in seconds with maximum errors on the order of $10^{-12}$.

We deploy a universal fault-tolerant quantum computing (FTQC) architecture based on error-detecting $[\![8,3,2]\!]$ and $[\![4,2,2]\!]$ codes on Quantinuum's Helios-1 trapped-ion quantum computer. We compile and execute ripple-carry adder (RCA) circuits for classical inputs up to five bits on this architecture. Uncomputing a workspace qubit provides an additional “algorithmic check” to detect errors. While available at both the physical and logical levels, this check synergizes with our architecture by increasing the effective fault distance of many circuit locations from two to four. Combining this algorithmic check with the error-detecting codes, we observed only a single logical failure in one-bit addition after burst-error filtering, yielding an estimated logical failure rate of $(6.0 \pm 5.9) \times 10^{-5}$. This is well below the $(3.5 \pm 1.3) \times 10^{-3}$ failure probability observed for one-bit addition on the same hardware in unencoded form. Two- and three-bit adders also showed performance improvements, while the longer four- and five-bit adders executed just above threshold.

The codeword stabilized (CWS) framework provides a systematic method for constructing quantum error correcting codes from a simple undirected graph and a classical code. When the underlying classical code is linear, the resulting quantum code is a stabilizer code. In this work, we investigate the conditions under which an arbitrary $[n,k,d]$ classical binary linear code can be lifted to an $[[n,k,d]]$ quantum stabilizer code using the CWS framework. We analyze the random CWS code constructed from a given $[n,k,d]$ binary linear code $\mathcal{C}$ and an Erdős-Rényi random graph $\mathrm{G}(n, \frac12)$. We establish a lower bound on the probability that the resulting quantum code preserves the minimum distance $d$ of the classical code. This probabilistic analysis yields a Gilbert-Varshamov-type condition on the $n,k,d$ parameters of the classical code that guarantees the existence of a graph resulting in a quantum code with the same $n,k,d$ parameters.

A variational quantum state may have many control angles, and its complete gradient contains one derivative for each. The task is to turn access to selected derivatives into a shared finite-shot record for the complete vector. The Hopf ansatz supplies the setting: it constructs any normalized pure state from nested two-way magnitude splits and, for complex states, leaf phases, with one directly programmed angle per split or phase. Earlier Hopf constructions prepare the state, recover coordinates from known amplitudes, and provide indexed derivative access. With a phase-calibrated controlled reflection, the inverse Hopf frame maps each normalized magnitude direction to a computational label, so every all-$X$ outcome contributes to every magnitude derivative. A separate signed leaf record supplies the complex phase block. A checkpoint variant reverses only the suffix below a selected depth and returns that layer's gradient block. For a complete chart with $M$ real-valued parameters, sufficient execution counts are $\mathcal{O}(\log\log M)$ for the global method and $\mathcal{O}(\log M\log\log M)$ for the complete checkpoint schedule at fixed additive coordinate accuracy and confidence. The global saving is record reuse, not a reduction of the $M$-entry output. Under the designated direct-angle schedules, the global method's assigned Hopf CNOT work and input/output-inclusive storage have at most logarithmic overhead relative to a matched scalar evaluation. The same Hopf geometry thus carries a state forward and the objective's complete coordinate response backward.

In de Sitter static patch holography, coupling bulk quantum fields to an observer's dynamical clock yields a type II$_1$ von Neumann algebra $\mathcal{M}_+$ of gauge-invariant observables. However, the unique tracial state on this algebra fails to reproduce semiclassical bulk correlation functions. We resolve this issue by introducing a family of heavy-clock states, representing an observer reference frame with heavy inertia. We prove that in the heavy-clock limit, $n$-point correlation functions of gauge-invariant dressed observables reproduce the bulk quantum field correlation functions on de Sitter spacetime. Furthermore, we investigate a generalized observer Hamiltonian $\widehat{H}_{\rm obs}=|\widehat{\pi}|$ that incorporates both forward-running ($\pi\geq 0$) and backward-running ($\pi <0$) clocks. The resulting von Neumann algebra $\mathcal{M}$ of gauge-invariant observables remains a type~II$_1$ factor and is isomorphic to $\mathcal{M}_+\otimes M_2(\mathbb{C})$, where $M_2(\mathbb{C})$ is the algebra of $2\times2$ complex matrices transforming between the two clock orientations. Time-reversal symmetry is implemented in this setting as an anti-unitary operator that exchanges the two clock orientations, yielding a type~II$_1$ von Neumann algebra $\mathcal{F}$ of gauge-invariant, time-reversal-invariant observables. We generalize the heavy-clock state construction to both $\mathcal{M}$ and $\mathcal{F}$, showing that $n$-point correlation functions calculated in heavy-clock states match the corresponding semiclassical bulk correlation functions. Finally, by coupling Einstein gravity to the Brown–Kuchař dust field, we derive the observer Hamiltonian $\widehat{H}_{\rm obs}=|\widehat{\pi}|$ from a perturbative reduction along the observer's worldline in the $G \to 0$ limit. This provides a field-theoretic foundation for the observer model developed in this work.

Understanding how pairing correlations in superconductors evolve out of equilibrium is a central challenge in quantum many-body physics. In systems with $s$-wave pairing, the character of Cooper pairing evolves continuously from a BCS regime of weakly bound, overlapping pairs to a BEC regime of tightly bound molecules, each with distinct excitation spectra. Here we realize and probe pairing dynamics across these regimes using cold, non-degenerate $^{87}$Rb atoms coupled to an optical cavity with Floquet dressing. Our cavity-QED platform emulates fermionic superfluids through a mapping onto Anderson pseudospins, while optical and microwave control tunes the ratio of interactions to single-particle energies, providing a flexible approach complementary to ultracold Feshbach and ultrafast solid-state platforms. Following a quench, we observe persistent pairing and transient oscillations of the order parameter associated with a collective amplitude (Higgs) mode. We find that the decay of these oscillations sharply distinguishes weak- and strong-pairing regimes: in the weak-pairing regime, oscillations decay with a power-law exponent $|\alpha|=0.65(8)$, whereas in the strong-pairing regime the decay is substantially faster, with $|\alpha|>1$. The oscillation frequency is set by the minimum quasiparticle excitation energy, directly linking nonequilibrium dynamics to the underlying excitation spectrum. Our results establish nonequilibrium dynamics as a direct probe of pairing character and collective excitations in interacting quantum systems.

We develop a homotopical framework for understanding the space of quantum spin systems based on topological $n$-nets, which assign associative unital algebras to local regions in an $n$-dimensional space in a manner that captures the locality structure of the underlying lattice theories. The net-theoretic perspective admits a natural categorification, in which the category of topological $n$-nets carries the structure of a higher Morita category. Moreover, the nets of greatest physical interest form a Karoubi-complete subcategory that shares many of the characteristic structural features of the category of finite TQFTs. Our main result identifies the group of locality-preserving symmetries of (3+1)-dimensional quantum spin systems (i.e. quantum cellular automata modulo stabilization, finite-depth quantum circuits, and translations) with the full Witt group of nondegenerate braided fusion categories, thereby answering a question posed by Haah.

The nuclear spin of a phosphorus atom in silicon is considered as a promising quantum information carrier for quantum computing due to its long coherence time. Coherent control of the nuclear spin is typically realized using nuclear magnetic resonance (NMR). In this work, we theoretically propose that with the aid of hyperfine interactions and magnetic field gradients, fast electric-dipole-induced nuclear electric resonance (EDNER) can be achieved. The stronger EDNER (compared with NMR) arises from the combined effects of hyperfine interaction between the nuclear and electron spins and coupling between the electron spin and charge degrees of freedom mediated by magnetic field gradients in this scheme. By operating at specific working points, the nuclear-spin splitting becomes less sensitive to electrical noise, enabling long coherence times and high-fidelity quantum operations. All elctrical, addressable control of nuclear spins paves the way for scalable silicon-based quantum computing.

Approximate quantum compilation (AQC) using tensor networks provides a promising route to reducing the circuit resources required for quantum simulation. However, the factors governing the compressibility of many-body dynamics and the extent to which compressed circuits retain physically relevant information on quantum hardware remain poorly understood. We investigate these questions using AQCtensor for an 80-qubit one-dimensional anisotropic XYZ Heisenberg chain initialized in a Néel state. By varying the exchange anisotropy and external magnetic field, we find that compression performance changes systematically with the anisotropic coupling configuration and field orientation. These variations are strongly associated with a nested-commutator measure related to second-order Trotter error, with corresponding directional trends also reflected in the target-state MPS bond dimension. For an 80-qubit quantum-hardware evaluation, AQCtensor compresses a 10-repetition target evolution to 5 repetitions while retaining a target-state fidelity of 0.995474, reducing the total circuit depth by 45.9% and the two-qubit gate count by 47.6%. The compressed circuit exhibits comparable behavior across magnetization, nearest-neighbor correlation, and Hamiltonian expectation measurements, while process-level diagnostics and local reduced-state tomography provide complementary characterization beyond these observables. Together, these results link AQCtensor compressibility to Hamiltonian commutator structure and target-state complexity and demonstrate substantial circuit reduction while retaining physically relevant features in an 80-qubit quantum-hardware experiment.

Scattering of quasiparticles provides direct access to the interactions that govern strongly correlated systems. In this work, we realize the quasiparticle scattering experiment of the Fermi-Hubbard model on a digital quantum processor by colliding a doublon and a holon in the half-filled chain of 21 sites encoded on 42 qubits of the ibm_boston processor. For the first time, we measure the transmission probability of quasiparticles of the Hubbard model on quantum hardware, which agrees with the Bethe-ansatz scattering matrix without free parameters. Beyond the scattering probabilities, the collision generates entanglement by superposing the transmitted and reflected components, which we infer from the particle-number fluctuation. In sharp contrast, a control collision between two doublons shows neither the interaction dependence nor the number fluctuation, as expected for indistinguishable particles. Our work demonstrates that the ability to create quasiparticles of a chosen flavor on demand and program their motion and interactions makes a digital quantum processor a new experimental toolset for probing the entanglement structure generated by quasiparticle scattering.

Quantum mechanics seems to be an incredibly delicate theory. Slight alterations to nearly any part of its structure can lead to huge qualitative differences and wildly unphysical predictions. Here, we explore the many-body consequences of replacing the Born rule $p(m)\propto\|P_m|\psi \rangle|^2$ by a warped rule $p_b(m)\propto\|P_m|\psi\rangle\|^{2b}$. Specifically, in systems with conserved particle number, evolution punctuated by repeated local particle observations acquires a probabilistic bias over measurement histories with an effect controlled by the sign of $b-1$. For $b>1$, this bias generically drives the gas to collect into nearly frozen configurations. Similar to the action of Maxwell's demon, the simple act of observation seems to extract entropy from a closed system. For $b<1$, the bias is reversed, generically scouring out long-wavelength fluctuations to produce a hyperuniform gas. We study this effect in a one-dimensional quantum gas, where these two phases are derived analytically for a particular measurement scheme and corroborated numerically for more general procedures with discrete-time projective-measurement circuit models using matrix product state simulations. We additionally discuss how this bias manifests in a common technique that often employs this warped rule, the “replica trick,” implying qualitative differences between finite-replica and replica-limit calculations.

A scalable ground-state solver to be used in sample-based quantum diagonalization (SQD) is presented. The solver is built on JAX API, and is intended to be run on GPU platforms and possibly many-GPU high-performance computing facilities. It is capable of subspace diagonalization in up to $2^{30}$-dimensional subspace, with possible upgrades to enable even larger-scale operations. The two main components, a general-purpose eigensolver and an SQD-specific matrix-vector operation function, are described in detail. Efficiency of the eigensolver with respect to the GPU memory is demonstrated using a simple physics model. Furthermore, good strong scaling of the eigensolver in many-GPU environment is observed.

We study the quantum query complexity of several basic graph problems. 1) We prove a tight $\Theta(n^{3/2})$ bound for finding a maximum-out-degree vertex in an $n$-vertex tournament, resolving a conjecture of Mande, Paraashar, and Saurabh [FSTTCS'23]. 2) Using the same proof idea, we give a direct proof that finding a maximum-degree vertex in an $n$-vertex undirected graph requires $\Theta(n^{3/2})$ quantum queries, a bound implicit in the work of Apers and Lee [CCC'21]. Both lower bounds above hold even for computing only the maximum degree or maximum out-degree. 3) We also study Maximum $(k,n-k)$-Cut, which asks for the largest cut with one side of size $k$. For every constant $k\geq 1$, we give an $O(n^{2-1/(k+1)})$-query quantum algorithm. 4) We establish a reduction to Maximum $(k,n-k)$-Cut involving $k$-Graph Collision, which asks whether the marked vertices of a known graph contain a $k$-clique. For $k\geq 3$, this yields unconditional lower bounds with exponents strictly larger than $3/2$, showing that this problem is strictly harder than computing maximum degree. Additionally, under a conjecture we propose for $k$-Graph Collision, the reduction yields a lower bound matching our upper bound above.

Fermionic Gaussian states are completely characterized by their two-point correlations, making the covariance matrix a natural reference for quantifying non-Gaussian structure. Motivated by fermionic antiflatness, we study its extremal form for pure number-conserving states and ask which states can be maximally antiflat and how they can be constructed. We show that, at fixed particle number, maximal first antiflatness is equivalent to a completely flat one-body reduced density matrix, and we obtain a complete existence classification together with explicit block and cyclic-orbit constructions of all allowed sectors. We then investigate the structure that appears beyond the covariance level. Maximally antiflat states with identical one-body data can exhibit distinct connected four-point correlations, which we characterize through the four-point Majorana Wick error and, equivalently, the connected two-body reduced density matrix cumulant. We show that this quartic structure is necessarily nonzero and formulate its extremization as a two-body reduced density matrix (2RDM) purity problem. Combining this framework with a Hilbert–Schmidt estimate of Christiansen for truncated two-body correlations, we obtain an upper bound on the connected quartic structure in terms of first antiflatness. Our results establish both a complete characterization of maximal fermionic antiflatness at fixed particle number and a constrained hierarchy linking covariance-level flatness to higher-order non-Gaussian correlations.

Air pollution poses a significant threat to public health, exacerbated by the rapid industrialization and urbanization of modern society. While traditional deep learning offers predictive capabilities, recent advancements in quantum machine learning (QML) present a compelling alternative. Here, we introduce a scalable hybrid framework that integrates variational quantum circuits with quantum annealing. Leveraging a neuromorphic quantum computing platform to transcend the qubit limitations of the NISQ era, we model particulate matter (PM$_{2.5}$) dynamics using high-density urban data from the UK. We demonstrate that our Quantum Neural Networks (QNNs) exhibit an intrinsic resilience to input volatility, significantly outperforming classical baselines (MLP and LSTM) on raw, high-entropy environmental data. Furthermore, we successfully scaled the model to 172 qubits, observing a synergistic enhancement when coupled with wavelet decomposition that achieves state-of-the-art predictive fidelity. These findings establish a critical benchmark for quantum utility, proving that scalable, neuromorphic quantum machine learning can now address complex, non-linear real-world problems.

Two-block group-algebra codes are among the simplest quantum LDPC codes, and many of them are translation invariant on a twisted torus, which suits neutral-atom arrays and other platforms with movable qubits. We ask how far they go at small sizes when searched systematically across all groups. We use algebraic constraints and screens to design a search pipeline capable of enumerating broad and complete swathes of two-block codes on a laptop. With it we census about $10^8$ two-block codes with up to $320$ qubits at check weights five to nine. Several of these censuses are exhaustive, and support complete statements; for instance, the Gross code is, up to equivalence, the only abelian weight-six two-block code with $n \le 200$ to reach $kd^2/n=12$, no weight-six two-block code with $n \le 300$ beats $[[288,16,16]]$, and the known $[[64,18,8]]$ is the best two-block code by $kd^2/n$ across weights five to nine with $n \le 94$. The censuses are also large enough to give insights into where good codes live - they concentrate in a handful of groups; abelian groups give the best codes at small $n$ and non-abelian groups at large $n$, with the crossover appearing to move out as the check weight grows; and high quality codes become $100$ to $1000$ times rarer per draw from weight six to weights eight and nine. Using the group algebra and the census data to steer a statistical search finds four to fifteen times as many good codes as uniform draws in equal time. Among the codes found are $[[102,20,10]]$ and $[[120,24,10]]$ at check weight nine, which we simulate in noisy syndrome-extraction circuits, and $[[186,20,18]]$, a weight-nine code with every check in a $5\times5$ window. At check weights seven to nine, our best codes exceed the best published $kd^2/n$ with exact distance at the same check weight in most length bands up to $320$ qubits. All codes are available in a public database.

Quantum low-density parity-check (qLDPC) decoding requires reliable corrections and low latency over long syndrome histories. We extend BP-SF, an oscillation-guided belief-propagation (BP) decoder with independent syndrome-flip trials, by introducing windowed and streaming operations. Our CUDA implementation combines disordered-memory retries, sliding windows, correlation-aware graphs, and layered scheduling. Circuit-level simulations test fixed-basis memory and complete logical Pauli-frame recovery. On the [[144,12,12]] bivariate bicycle code at physical error rate p = 0.002, parallel BP-SF reduces 99.9th-percentile call latency by a factor of 13.15 relative to an eight-chain Relay-BP GPU baseline on 100,000 matched samples for which every tested method's initial BP stage fails within 80 iterations. Windowed BP-SF maintains a flat logical error rate and nearly constant per-round compute time through 512 rounds, reaching a 17.1-fold speedup over monolithic decoding. In 512-round full-frame streaming decoding with 2.97-ms syndrome arrivals, layered BP-SF on a transformed joint graph with 20 retries reduces 99.9th-percentile correction-release age from 166.29 to 36.25 ms relative to the joint graph with flooding updates and 100 retries. These results connect parallel BP post-processing to lower decoding costs and earlier correction release in streaming quantum memory.

We prove that four capacities of single-mode bosonic dephasing channels coincide under an average photon-number constraint: the unassisted quantum capacity, the unassisted private capacity, the two-way classically assisted quantum capacity, and the two-way public-classically assisted private capacity. The assistance may be interactive: the parties can exchange classical messages between channel uses and choose subsequent inputs based on earlier outcomes. For every finite value of the constraint, their common value is the coherent information optimized over Fock-diagonal input states satisfying the constraint. The proof uses a relative entropy comparison with the completely dephasing channel to derive chain rules for the Rains relative entropy and the relative entropy of entanglement. These chain rules give an upper bound on the rates achievable by adaptive protocols whose mean input photon number is constrained on average over all channel uses. We also show that both chain rules are attained by canonical purifications of finite-energy Fock-diagonal states.

The introduction of two-body XX interactions has been shown to improve the performance of quantum annealing in solving certain combinatorial optimisation problems and would enable the simulation of a broader class of many-body Hamiltonians. Due to experimental constraints, such interactions are typically not natively available on analogue quantum devices. To overcome this limitation we introduce the truss gadget. This is an exact construction that generates two-body XX interactions using only one-body X and Z fields and two-body ZZ interactions which are readily accessible on, for instance, superconducting quantum annealers. We experimentally validate the construction by reproducing the dynamics of a target XX Hamiltonian on a trapped-ion quantum processor. We then apply the gadget to an illustrative set of instances of the weighted maximum-independent-set problem on a superconducting quantum annealer. We empirically determine an approximate thousand-fold improvement in the probability of finding a state close to the ground state for these instances, over implementation without an XX interaction.

Scaling trapped-ion processors by adding ions remains challenging. A complementary route exploits the multilevel internal structure of each ion to increase the computational Hilbert space per ion. We introduce a hardware-native hybrid qudit-oscillator instruction set for a general d-level internal register coupled to bosonic modes and prove that three of its native operation families suffice for universality of one qudit coupled to several modes. Adding an entangling operation between ions extends universality to a connected register of several qudits. The architecture natively supports both phase-space and sideband instruction sets and is implemented in the open-source framework HybridLane. As a representative application, we reproduce the dissipative vibronic dynamics of a three-chromophore complex previously simulated on a hybrid qubit-oscillator superconducting platform. Moving from a one-qubit-per-state register to a single qudit stores the entire electronic manifold in one ion, so every electronic coupling becomes a local intra-ion transition and the lab-frame Hamiltonian compiles directly into the ISA. Under the stated sequential timing model from a 40Ca+ qudit processor, one Trotter step is projected to run about ten times faster on the qudit, with an average RMSE of approximately 1.1 percent against the published reference.

Large language models (LLMs) have shown strong results in classical code generation and are increasingly used to write the unit tests that safeguard that code. Whether they can do the same for quantum software is less clear, because quantum programs are probabilistic, depend on numerical tolerances, and are judged by domain-specific checkers, so a well-formed test can still disagree with the benchmark's verdict. Existing quantum benchmarks measure whether a model produces a correct solution, but not whether its tests can distinguish correct implementations from faulty ones. We introduce QTestBench, a framework that evaluates LLM-generated quantum test suites against independent benchmark checkers, never treating the tests themselves as ground truth. For each task, QTestBench prompts models to produce syntactic, semantic, and behavioral tests, injects candidate solutions at runtime, and compares each test verdict with the checker's label under three validation cohorts, each answering a distinct diagnostic question. We benchmark five LLMs on eight PennyLane QHack challenges and ten Qiskit HumanEval tasks. Generated suites almost always execute, but discrimination lags behind: the best generator reaches a test quality of 0.71 on QHack and 0.34 on Qiskit HumanEval, so executability alone overstates test quality. Oracle-verified synthetic mutants stabilize bug-detection estimates when natural faulty solutions are scarce, as on three of ten Qiskit tasks that yield none. QTestBench offers a reproducible, cross-framework benchmark for the trustworthiness of LLM-generated quantum tests.

Variational quantum circuits (VQCs) are highly sensitive to circuit architecture, yet most quantum machine learning pipelines select a single best design and discard the remaining candidates. This paper addresses whether the structural diversity across quantum circuit search spaces can be used to produce stronger predictions through model fusion. We apply Combinatorial Fusion Analysis (CFA), a model fusion framework that selects and combines multiple scoring systems using rank-score function (RSF) and cognitive diversity (CD), to a pool of 29 architecturally diverse classical models and quantum circuits. Using a diversity-aware model selection method, we identify subsets of maximally diverse models and combine them with both score and rank combination. Experiments on four binary classification benchmarks covering different domains demonstrate that CFA-based hybrid classical-quantum fusion consistently outperform the best individual model on every dataset considered with improvements up to 6.03% in accuracy. When comparing with relevant literatures, the CFA framework further achieves superior performance across all four datasets.

Performing measurements on gapless quantum ground states can give rise to new universal phenomena, whose origins remain poorly understood even for the paradigmatic Ising critical point. Replica methods offer a natural framework to study such post-measurement ensembles, with the replica limit $Q\to 1$ describing physical Born-averaged observables. Here we show that, for the monitored critical Ising chain, the replicated post-measurement ensemble of states itself undergoes a phase transition precisely at the physically relevant replica limit $Q \to 1$, preventing standard replica treatments. We use boundary conformal field theory (BCFT) methods to explain the underlying mechanism of this transition. Our methods yield a perturbative analytic calculation of the universal $O(1)$ constant in the Shannon entropy of the measurement record, previously known only numerically. We also apply our tools to study measurement-averaged spin correlators, providing a unified description of the universal properties of measurement outcomes and post-measurement states in the critical Ising chain.

Dissipative state preparation engineers quantum many-body states as steady states of an open-system dynamics. The spatial range of the required dissipation sets both the feasibility of analog implementations and the connectivity and control complexity of digital ones. Yet how this locality quantitatively constrains preparation times remains largely unknown. Here, we establish an exact locality-preparation time relation for quadratic fermionic systems and develop a construction that optimizes the locality of the dissipative dynamics while preserving the target state. Applied to the Kitaev chain, our framework reveals sharply different locality-preparation time tradeoffs in critical and gapped regimes. At criticality, suppressing the algebraic tails of the jump operators necessarily forces the preparation time to grow algebraically with system size. By contrast, both trivial and topological gapped phases admit exponentially localized dissipation with a finite preparation time in the thermodynamic limit. Our results identify when fast dissipative preparation is compatible with local control and when criticality imposes an unavoidable dynamical cost.

Parameterized Quantum Circuits have emerged as a central framework for variational quantum algorithms in the NISQ regime, with major applications in quantum simulation, combinatorial optimization, and, more recently, quantum machine learning (QML). By developing a new approach for computing dynamical Lie algebras associated with quantum circuits combining parametrized gates and non-parametrized entangling gates, we aim to extend the applicability of recent algebraic results to architectures that are actually used in quantum machine learning.

Resource constraints and imperfect quantum operations remain major challenges for quantum machine learning (QML) on noisy intermediate-scale quantum (NISQ) devices, particularly for fault-diagnosis tasks involving imbalanced and heterogeneous data. This work proposes QTN-RQNN, a Quantum Tensor Network-Based Recurrent Quantum Neural Network that integrates tensor-network-inspired nearest-neighbor interactions with recurrent quantum processing. The model sequentially encodes input features while propagating quantum memory across recurrent steps and incorporates QSMOTE for class balancing. QTN-RQNN is evaluated on four heterogeneous fault-diagnosis datasets SPID, CWRUBD, EFDD, and SFDD and compared with QNN, QTN-QNN, and RQNN baselines through classification, ablation, multi-seed, convergence, and quantum-resource analyses. Results show dataset-dependent predictive behavior, indicating that increased quantum architectural complexity does not universally improve classification. On SPID, QTN-RQNN improves the RQNN F1-score from 0.3077 to 0.4516 and ROC-AUC from 0.4485 to 0.6970, while the remaining datasets exhibit different performance-resource trade-offs and sensitivity to recurrent timesteps and circuit depth. Across all datasets, QTN-RQNN reduces the two-qubit-gate count from 32 to 24 per sample relative to RQNN, corresponding to a 25% reduction without increasing the four-qubit requirement; the same relative reduction is obtained for QTN-QNN over QNN. These findings establish QTN-RQNN as a resource-conscious recurrent quantum architecture and highlight the need to jointly consider predictive performance and circuit-resource requirements for near-term quantum fault diagnosis.

Rare-earth-ion based molecular crystals are emerging as a promising platform for quantum information applications, combining long optical coherence times with the chemical tunability of coordination chemistry. Here we present a comprehensive optical characterisation of twelve Eu$^{3+}$-based molecular complexes, with a focus on the coherent $^{5}\text{D}_{0} \longrightarrow \ ^{7}\text{F}_{0}$ transition at $\sim$580 nm. Judd-Ofelt analyses are performed across all complexes, providing insights into ligand-field environments, local point-group symmetries, and the resulting branching ratios of the coherent transition. We find that lower point-group symmetry (C$_1$, C$_2$) yields higher branching ratios of the $^{5}\text{D}_{0} \longrightarrow \ ^{7}\text{F}_{0}$ transition, exceeding 1% in several complexes. Optical inhomogeneous linewidths measured at 4.2 K reveal narrow linewidths for some complexes of below ten GHz, indicative of a highly ordered crystalline environment. Optical coherence measurements of one of the complexes, 5-Eu, yields an optical coherence time of $T_{\text{2}}^{\text{opt}} = 2.3~\mu\mathrm{s}$ at 4.2 K, comparable to the best-performing molecular systems reported to date. Systematic characterisation and quantitative comparison will be key to find structure-property relations guiding rational design of optimised complexes for quantum information applications.

Can quantum data reliably answer questions chosen from earlier results? We prove that $M$ adaptive Pauli predictions on $n$ qubits require $\Omega(\sqrt{\min\{n,M\}})$ copies at fixed accuracy. Published upper bounds make this tight for $M\le n$. Thus $n$ adaptive predictions cost $\Theta(\sqrt n)$ copies, whereas a fixed list costs only $O(\log n)$. The lower bound uses diagonal states and commuting observables, identifying a statistical cost of adaptation. We also quantify how this cost increases with precision.

Exceptional points (EPs) are usually introduced as defective degeneracies of non-Hermitian Hamiltonians and, in fully open quantum dynamics, of Liouvillian generators. Here we formulate an operational theory of exceptional points that does not invoke a Hamiltonian or a master equation. The primitive dynamical object is a completely positive trace-preserving (CPTP) quantum channel $\Phi$, applied an integer number $n$ of times, while physical data are probabilities $p_n^{\mathbf A}(x|\rho)$ associated with states $\rho$ and observables $\mathbf A$ having measurements results $x$. We define exceptional channels through nontrivial Jordan chains of $\Phi$ and show that a Jordan block of order $m$ generates discrete polynomial-exponential terms with maximal degree $m-1$. This places the physics of exceptional points in contact with what can be directly measured in experiments.