Papers

Can synchronization – the widespread spontaneous emergence of coordinated dynamics in classical nonlinear systems – also occur in the quantum regime? This question has recently sparked intense research into collective behavior and temporal self-organization in quantum systems. Typical quantum features such as the linearity of time evolution and the presence of quantum noise seem to hinder the appearance of synchrony at the microscopic level. At the same time, quantum coherence and quantum correlations may provide novel mechanisms for enhancing synchronization beyond its classical counterpart. We here survey recent theoretical and experimental advances in quantum synchronization, ranging from the characterization of synchronous oscillations and genuinely nonclassical forms of synchrony to many-body synchronization on quantum networks.

Fault-tolerant quantum computing based on lattice surgery requires place-and-route compilation with low spacetime overhead. Routing, in particular, faces a basic tension between suppressing path conflicts through greater spatial allocation and exploiting the time direction to realize ancilla-efficient spacetime routing. Existing approaches do not fully resolve this trade-off while retaining compatibility with inner factory layouts and termination guarantees. Here we introduce double-slice routing, a constant-depth spacetime-routing method that uses two consecutive time slices with a guarantee that its kink-parity correction terminates under both planar and stacked architectures. We numerically benchmark the resulting compiler on Hamiltonian-simulation workloads to show that double-slice routing reduces compilation cost by up to a factor of 2.4 over a single-slice baseline. Compared to projective routing, an existing method that allows an unbounded number of time slices per path, double-slice routing achieves smaller circuit volume with only a marginal execution-time penalty. Combined with a cultivation-compatible mapping optimization, the overall improvement reaches up to 7.5-fold over a naive single-slice compilation baseline. These results identify double-slice routing as a practically useful operating point in lattice-surgery compilation and show the substantial benefit in joint optimization of mapping and routing.

Topology has become a central concept in understanding physical phenomena, leading to important advances in condensed matter and photonics. Recent work has established a universal upper bound on the energy gap of Chern insulators in electronic systems, revealing a fundamental connection between topology, quantum geometry, and optical absorption. Here, we generalize this framework to photonic systems, deriving rigorous upper bounds on gap Chern numbers without requiring explicit topological analysis. Our approach enables the estimation of the topological charge of band gaps in both dispersive and nondispersive regimes.

The maximum field-free orientation attainable from a thermal molecular ensemble within a finite rotational subspace has not been characterised analytically. Here we derive a Schur–Horn-type upper bound on the field-free orientation $\avg{\cos\theta}$ achievable by any $M$-conserving unitary control acting on a Boltzmann ensemble truncated to rotational levels $J\le\Jmax$. The bound is the sum, over magnetic-quantum-number sectors, of the sorted Boltzmann weights paired with the sorted spectrum of $\cos\theta$; it is purely kinematic, set by temperature, the rotational constant, and $\Jmax$ alone, and interpolates exactly between the zero-temperature subspace eigenvalue and a finite-temperature ceiling fixed by the rotational partition function. Benchmarked on LiH against the analytical $N$-subpulse resonant protocol of Hong et al. [Phys.\ Rev.\ Research 7, L012049 (2025)], it reveals three regimes: the protocol saturates the bound to within about $1.6\%$ for $T\le\SI{5}{\kelvin}$, loses roughly $10\%$ of its zero-temperature orientation at $T=B/\kB\approx\SI{10.8}{\kelvin}$, and leaves a $10$–$40\%$ gap above $\SI{10}{\kelvin}$. Optimising the subpulse areas and carrier phases within the fixed layout closes only $\approx7\%$ of that gap, the optimal phase offsets vanishing, which localises the dominant loss in the rigidity of the analytic layout rather than in the choice of areas or phases. The bound is a control-independent target for coherent-control design, applies unchanged to any linear polar molecule in a $^1\Sigma^+$ state, and is mapped across the $(\Jmax,T)$ plane.

The phonon laser realized in a trapped ion, i.e., a self-sustained mechanical oscillator, has demonstrated the unique characteristics in practically detecting externally applied electric signals without the prerequisite of sideband cooling. Entering the quantum regime via sideband cooling is expected to further improve its sensing performance. Here we report the first experimental realization of a quantum-regime single-ion phonon laser ($\bar{n}<10$) using a trapped $^{40}\mathrm{Ca}^+$ ion and demonstrate electrometry based on its phase-space symmetry-breaking response to weak resonant electric fields. By tuning the phonon-laser parameters, we reveal that the sensing performance is fundamentally governed by the finite-time relaxation dynamics of the underlying open quantum system. We find that a slow Liouvillian relaxation, correlated with the finite experimental interaction window, effectively enhances the dynamic susceptibility while maintaining the structural robustness of the limit cycle. This regime, when applied to the detection of electric fields, produces a shot-noise-limited peak sensitivity of $14.15 \pm 0.77~\mu\mathrm{V/m}/\sqrt{\mathrm{Hz}}$ and a minimum detectable field variation of $\delta E_{\mathrm{min}} \approx 1.83~\mu\mathrm{V/m}$. Our results establish quantum phonon lasers as a practical platform for advanced sensing and highlight the central role of Liouvillian dynamics in non-equilibrium electrometry.

The Unruh effect predicts that accelerated observers perceive the inertial vacuum as populated by particles, providing a flat-spacetime analogue of Hawking radiation. Its direct observation, however, remains experimentally challenging, since an Unruh temperature of $1\,\mathrm{K}$ requires accelerations of order $10^{20}\,\mathrm{m/s^2}$. Here, we show that the Lamb shift of a centripetally accelerated atom inside a high-$Q$ cavity provides a sensitive spectroscopic probe of the Unruh effect at dramatically lower accelerations. The cavity reshapes the electromagnetic density of states and converts otherwise tiny noninertial corrections into tunable level shifts. Depending on the atomic angular velocity and cavity detuning, the Lamb shift can be enhanced, strongly quenched, or completely screened. Remarkably, for experimentally realistic parameters, a rotation-induced shift of order $10\;\mathrm{Hz}$ can arise already at accelerations as low as $0.5\,\mathrm{m/s^2}$, more than twenty orders of magnitude below the acceleration scale conventionally associated with direct Unruh detection. These results identify cavity-controlled Lamb-shift spectroscopy as a viable route toward laboratory tests of the circular Unruh effect in the ultralow-acceleration regime.

Nuclear spin diffusion is often summarized by a single diffusion coefficient, but this coarse-grained description can fail in dilute solids where positional disorder and long-range dipolar couplings generate a broad distribution of hopping rates. We develop a continuous-time random-walk (CTRW) description of $^{13}$C polarization transport in natural-abundance diamond (1.1%), constructing the rate matrix from dipolar-mediated flip-flop couplings and sampling exact continuous-time trajectories. Although site-to-site hopping is Markovian, the disorder-averaged dynamics give rise to emergent, anomalous transport. The empirical waiting-time distribution exhibits a heavy tail with exponent $\alpha=0.64$ and exponential cutoff $t_{\rm cutoff}=19$ s; the mean jump length becomes correlated with the waiting time $\tau$ for $\tau\gtrsim0.1$ s; and the mean-squared displacement grows sublinearly in both step number and physical time, with exponents $\gamma=0.56$ and $\delta=0.87$ respectively. We trace the microscopic origin of these signatures to geometric trapping: polarization can rapidly exchange within strongly coupled clusters, including dimers, while weak inter-cluster links control long-range exploration. A kinetic percolation construction links global transport to inter-cluster crossing times, and identifies a corresponding crossing time of $\sim20$ s, consistent with $t_{\rm cutoff}$. Finally, mapping paramagnetic impurities onto hard-sphere traps connects the CTRW framework to classic studies of trapping in reaction-diffusion theory and reproduces the qualitative timescale of experimentally measured relaxation, whereas a continuum diffusion equation description does not. These results show that dilute dipolar spin networks require a microscopic, network-resolved transport description beyond the Fickian diffusion equation.

In recent times there has been growing interest in Raman optical activity (ROA) for its label free detection of absolute configuration, conformation, and stereochemical structure in chiral biosamples and drug molecules. Since ROA signals are generally small, techniques such as stimulation by a probe beam can be used to enhance the signal strength. However, with a classical probe, the measurement precision is still fundamentally limited by its shot noise. To solve this problem we propose the use of two-mode squeezed vacuum and show that it can achieve sub-shot noise limited measurement sensitivity. Using quantum estimation theory, we derived the quantum Fisher information and the quantum Cramér-Rao bound (QCRB) for stimulated ROA measurement to quantify the precision enhancement. This improvement comes from photon-number correlations which suppress the intensity fluctuation common to both modes. We further show that balanced detection of the output intensity difference is a practical measurement scheme that approaches the QCRB and becomes optimal in the small-chirality limit. This opens a promising path toward more sensitive Raman chiroptical spectroscopy of weak and photosensitive samples.

Current era quantum computers continue to grow in both capability and capacity. Despite these advancements, errors induced by environmental noise severely limit practical applicability. Current research into error mitigation and correction to bridge the gap between current-era quantum computers and the execution of noise-sensitive workloads. These methods have significant performance and resource overheads, thereby greatly limiting the real-world benefits of their use. Circuit replication, as a naive form of error mitigation, is not new and has largely been ignored given the resource constraints of current quantum hardware. However, its simplicity is attractive as a means to supplement modern methods, reducing the overall performance overhead while still preserving error-mitigation capabilities. In this paper, we profile the effects of simple circuit replication under real-world noise profiles to better establish replication's limits as a supplemental mitigation strategy. Quantum Approximate Optimization Algorithm (QAOA) for the Maxcut problem is explored for the analysis. For small graphs, we found that the average inference strength decreases by approximately 21.8% while the average standard deviation decreases by 108.8% compared to 6 replicates. For larger graphs, inference strength decreases by 35.4% while the average standard deviation decreased only 20.5%. Fewer replications did not affect smaller graphs, but degraded inference strength, with comparable benefits to standard deviation in larger graphs. These results show that replication has potential uses as a supplemental mitigation strategy for large-depth, highly variable workloads.

Successive interference cancellation (SIC) is an important technique for 5G/B5G wireless receivers to resolve interfering signals from multiple users. While SIC has been proven to approach the channel capacity limit in many settings of multiple access networks, it remains unknown if this limit can be surpassed by an advanced yet practically implementable quantum receiver technique. In this work, we answer this quest by proposing a full-stack quantum receiver that integrates front-end quantum sensing with back-end quantum signal processing. The proposed technique leverages simple qubit ensembles without using any complex entanglement resources to parallelly extract interfering multiuser signals, with a channel capacity beyond the limit of SIC in some operational corners. In performance evaluation, we report notable quantum advantage over the ultimate multiple-access channel capacity limit and practical SIC algorithms in low-SNR regimes in terms of spectral efficiency and detection efficiency due to the receiver's ability to exploit quantum correlated measurements and superposition-enabled parallel processing.

The interface between the quantum and the classical is an intriguing and, at times, hotly contested subject of ongoing research. The quantum regime is characterized by interference, made possible by the superposition principle, while such phenomena are absent in macroscopic, everyday experience. Here, we investigate the link of this absence (or, as we will argue, unobservability) to computational complexity. We show how the assumption that quantum systems cannot solve NP-complete problems efficiently implies that certain formally valid quantum measurements on finite-dimensional systems are unperformable. We study several consequences of this restriction. First, Pauli matrices in an inconveniently transformed basis are a simple example of unobservables. Furthermore, some quantum states are not connected by any physically realizable time evolution. Finally there are quantum states whose coherence cannot be observed, i.e. superpositions of pure quantum states which are indistinguishable from mixtures. We discuss the connection of this phenomenon to the presence of superselection sectors. Our results suggest that the apparent classicality of macroscopic systems may be partly due to limitations on measurements and time evolutions imposed by computational complexity.

Quantum low-density parity-check (QLDPC) codes are strong candidates for fault-tolerant quantum computation, but efficient decoding remains a major challenge due to short cycles, degeneracy, and the poor convergence of standard belief-propagation (BP) decoders. We propose a reinforcement learning-based list sequential (RL-LS) BP decoder for QLDPC codes by extending the reinforcement-learning-based sequential variable-node scheduling (RL-S) framework with list-based search. At each step, the learned policy selects the next variable node to update; the decoder then retains the ordinary RL-S trajectory while also exploring a competing branch obtained by softly biasing the post-update LLR pair toward the second-most likely Pauli symbol, recomputing the incident local BP messages, and setting the visited variable node to that second-best symbol. Candidate trajectories are ranked and pruned using our proposed cumulative path metric. The resulting decoder extends the learned decoder by combining the improved convergence of learned sequential scheduling with list exploration. Numerical results on representative QLDPC benchmark codes over the depolarizing channel show that our proposed method improves the decoding performance of the underlying decoder and compares favorably with existing BP-based decoding methods.

We investigate the dissipative dynamics of multilevel quantum systems strongly coupled either to a lossy cavity mode or directly to a bosonic environment. By deriving spectral localization bounds, we establish conditions under which strong system-bath coupling gives rise to a hierarchy of population relaxation timescales. Our approach builds on the reaction-coordinate polaron-transform framework. By mapping the original strong-coupling problem onto an effective weakly dissipative model, we analyze the spectrum of the resulting Liouvillian superoperator through localization bounds. For the generalized V model, we find that strong system-bath coupling gives rise to a bright-dark structure in the effective system-bath coupling operator: a single collective mode remains strongly coupled to the environment, while the remaining modes become progressively dark. Consequently, the dynamics separate into fast and slow sectors and, at finite coupling strengths, develop a hierarchy of population relaxation timescales. Numerical simulations based on both secular and non-secular quantum master equations corroborate the emergence of timescale separation and the pronounced slowing down of dissipative dynamics at strong coupling. Our results reveal a general mechanism underlying anomalously slow relaxation in strongly coupled open quantum systems and provide a route for engineering long-lived states through system-environment interactions.

The interplay between symmetry and thermalization governs the late-time dynamics of local quantum and classical many-body systems at nonzero temperature. Recently, two parallel frontiers have emerged: the search for robust anomalous hydrodynamics – such as superdiffusion – in generic, non-integrable models, and the formal effort to generalize the fundamental concept of global symmetry. In this paper, we bridge these frontiers by demonstrating that quantum group symmetry provides a novel mechanism for anomalous hydrodynamics in chaotic systems. We study the dynamics of local operators carrying $U(1)$ charge in non-integrable lattice models that also have quantum group symmetry. One example is transverse spin in the XXZ model with integrability breaking deformations. While such excitations are expected to decay very quickly at high temperature because their charge forbids overlap with conventional hydrodynamic densities, we find that protection by the quantum group symmetry makes these modes long-lived, despite the absence of local quantum group charge density or current. Furthermore, the dynamics is superdiffusive across Hamiltonian, Floquet, and classical realizations, and exhibits unusual finite size effects at very late times. We also revisit transverse spin dynamics in the integrable XXZ model.

We advocate an alternative paradigm to operate quantum computers that utilizes multipartite entanglement generated in dedicated auxiliary systems during idle times. This stored entanglement enhances the future capabilities of the quantum processor, as it can be flexibly used to assist and speed-up computations when needed. We identify classes of multipartite entangled resource states whose computational power are related to their entanglement features, and in turn to the complexity to generate them. During idle times, one can thus continuously work towards generating more and more powerful auxiliary multipartite entangled states. Idle times include both times prior to the start of a computation, but also any step during the execution of an algorithm where parts of the processor are not actively involved. To illustrate our approach, we consider architectures with limited connectivity, e.g. corresponding to a 1D geometry. We show that $d$-dimensional cluster states allow one to flexibly perform multiple long-distance two-qubit gates in parallel, where both the complexity to generate them, as well as the number of achievable gates increases with $d$.

Motivated by the surge of interest in statistics of non-Hermitian random matrices as a framework for description of universal characteristics of dissipative chaotic quantum many-body systems, we address the problem of characterizing the parametric correlations of spectral densities. Considering parameter-dependent ensemble of complex Ginibre matrices we derive an explicit, closed-form expression for the parametric number covariance in the systems of symmetry class $\mathbf{A}$ for eigenvalues in a circular domain containing on average a finite number of eigenvalues in the spectral bulk. This behavior is expected to be universal, as further supported by numerical evidence for the real Ginibre ensemble, non-Hermitian Bernoulli Wigner matrices and bi-unitarily invariant ensembles. We also discuss a relation between parametric correlations of spectral densities and the distribution of the so-called eigenvector non-orthogonality factor, which attracted considerable interest in recent years.

Efficient simulation of strongly-interacting fermionic systems on quantum processing units (QPUs) is a challenging task due to nonlocal mode entanglement generation. However, it is not yet well understood how the structure of entanglement governs the hardness of large-scale quantum chemistry simulations or the scaling of distributing such workloads. Here, we introduce an algorithm for estimating the distribution complexity of hybrid quantum-classical simulation for electronic structure Hamiltonians over heterogeneous high-performance architectures. Our algorithm relies on efficient analytical evaluation of the low entanglement boundaries for the orbital rotations and dephasing-induced localization within tensor fragments, in a double-factorized representation. Our entanglement estimation scales as $O(N^3)$ for each fragment, where $N$ is the number of orbitals. When QPUs are communicating via a quantum network, the cost of distribution per fragment is reduced quadratically from $O(N^2)$ to $O(N)$. Similarly, for hybrid quantum-classical approaches, with access to only conventional HPC interconnects, the worst-case cost is reduced from $O(\exp(N^2))$ to $O(\exp(N))$. We show that emergent entanglement patterns are induced by the interplay between coherent Gaussian orbital rotations and disordered Coulomb interactions. We discuss the underlying physical mechanisms that govern distribution complexity and introduce model systems that are tunable based on the localizability of fragments and the overlap of interfragment rotations. We characterize three different regimes of hardness for distribution complexity and classical simulability. The framework introduced here enables novel and more efficient quantum-classical application workflows towards utility-scale quantum computing.

We present a variational approach to quantum field theory based on wavefunctions parameterized by neural networks. While variational methods have a celebrated history across many fields, their application to quantum field theory has been limited by well-known challenges. We show that neural-network wavefunctions, combined with modern machine-learning techniques, enable competitive variational calculations in nontrivial field theories. As a demonstration, we reproduce the essential features of the two-dimensional nonlinear $\sigma$-model: asymptotic freedom, dynamical mass generation and the model's step-scaling function.

Motivated by the role of the holographic entropy cone in constraining the entanglement structure of states with classical gravitational duals, we investigate combinations of subsystem complexities associated with reduced density matrices in multipartite quantum systems. Focusing on subsystems composed of three disjoint regions, we introduce two quantities: a tripartite complexity, inspired by the tripartite information, and a complexity gap, designed to characterize emergent complexity in the full quantum state beyond that of its constituents. We study the sign structure of these quantities in three selected approaches to subsystem complexity. In holography, we employ the complexity=volume proposal in AdS spacetimes; for Gaussian many-body states, we use Fisher-Rao subsystem complexity; and we further develop a Krylov-space inspired, effective framework for reduced density matrices, which we test in few-qubit systems and coherent-state dynamics. Across all three approaches, we find that the tripartite complexity is not sign-definite in general. By contrast, the complexity gap exhibits a definite sign in every example we analyze, although the sign itself depends on the underlying notion of subsystem complexity. Our results suggest that the complexity gap could be a natural candidate building block for a prospective hierarchy of subsystem complexity inequalities.

We compare the performance of representative cooling, adiabatic, and optimization algorithms for ground-state preparation in the presence of noise. Using an exactly solvable family of quadratic fermionic Hamiltonians subject to depolarizing noise, we derive the scaling of the achievable relative energy as a function of the noise rate and support these results with numerical simulations. The Hamiltonian exhibits two phases, separated by a quantum phase transition. As expected, the performance of the different algorithms depends on the phase: adiabatic evolution is favorable in the trivial phase, while a multi-frequency cooling algorithm, as proposed in [1], becomes competitive or superior in the topological phase, where gap-closing limits adiabatic protocols. We further present numerical results for the quantum approximate optimization algorithm [2], showing that it performs competitively with cooling in the trivial phase but is typically outperformed in the topological regime. Finally, we show that for this model the cooling protocol exhibits enhanced robustness to parameter imperfections, highlighting its potential advantage for realistic implementations of noisy quantum state preparation. The analytical approach developed here, in conjunction with numerical validation, establishes an extendable approach to benchmarking ground-state preparation algorithms.

Translation invariance underlies all algebraic constructions of topological codes with geometrical locality. It has remained an open question whether codes that generically break this invariance can still be topological and simultaneously possess geometrical locality. Resolving this question is important both fundamentally—deepening our understanding of topological phases—and practically, as relaxing translation invariance could vastly expand the design space and potentially reduce resource overhead in fault-tolerant architectures. Here we introduce space-group codes, in which crystallographic point-group operations enter the bulk stabilizer algebra; bivariate bicycle (BB) codes arise as the translation-only limit. The key insight is that the point-group orbit resolves topology and locality together: it yields a computable algebraic criterion for topological order and a folded geometry in which point-group operations become local. We identify space-group codes whose code parameters exceed the reported same-blocklength, same-check-weight BB benchmarks. In five parameter-matched neutral-atom comparisons, reflection codes reduce the optimized movement cost in every case, by up to $60\%$, while folded placements also enable lower-overhead multilayer superconducting layouts. Treating spatial operations as a code-design variable therefore opens a route to topological codes jointly optimized for information protection and hardware geometry.

We study the problem of learning local Lindbladians from black-box access to the physical evolution, where the goal is to estimate all Hamiltonian and dissipative coefficients. For local Lindbladians with low-intersection dissipators and local dynamical strength at most $\Lambda$, we design an algorithm that learns the coefficients to target accuracy $\varepsilon$, whose number of channel uses and total evolution time scale as $\widetilde{O}(\Lambda^2/\varepsilon^2)$ and $\widetilde{O}(\Lambda/\varepsilon^2)$, respectively, with only logarithmic dependence on the number of qubits. The algorithm is built directly from finite-time channel probes. It runs the unknown evolution for short times, estimates the corresponding Pauli transfer matrices from classical shadows, and converts these estimates into Lindbladian coefficients by stable local Fourier inversions. The algorithm is non-adaptive, uses no ancillas, and requires only random product states as inputs followed by random Pauli measurements. The method does not require knowing the structure of the Lindbladian in advance. We prove matching lower bounds that establish the near-optimality of the algorithm in both resources. By constructing a family of single-qubit dephasing Lindbladians, we show that any algorithm, even an adaptive one with arbitrary ancillas and measurements, requires $\Omega(\Lambda^2/\varepsilon^2)$ channel uses and $\Omega(\Lambda/\varepsilon^2)$ total evolution time. In particular, the lower bounds imply that the Heisenberg-limited scaling achievable for Hamiltonian learning is information-theoretically impossible once dissipative coefficients must be estimated.

Variational infinite matrix product state (iMPS) calculations usually make Hamiltonians with algebraically decaying interactions compatible with standard MPO algorithms by first replacing the target Hamiltonian with a finite-pole sum-of-exponentials surrogate, thereby introducing a Hamiltonian-representation residual. We formulate the fixed-$D$ variational energy without introducing such a surrogate. For a fixed finite-$D$ MPS, the algebraic tail can be summed directly through the connected transfer matrix: the tail $e^{\mathrm{i} Qr}/r^\alpha$ is represented by the matrix function $F_{\alpha,Q}(\widetilde{T}_A)$, with $F_{\alpha,Q}(z)=\operatorname{Li}_\alpha(e^{\mathrm{i} Q}\,z)/z$. We evaluate the resulting matrix-function action using a Krylov method and obtain stable gradients by combining a Fréchet adjoint with implicit fixed-point differentiation. Benchmarks on long-range free fermions and the inverse-square Heisenberg family, including the Haldane–Shastry point, validate the transfer-matrix-function formulation. A long-range Ising-chain calculation illustrates a practical consequence of avoiding a finite-pole Hamiltonian representation. At a fixed, independently known critical field, finite-pole surrogate Hamiltonians can bias a critical diagnostic away from criticality, whereas the matrix-function calculation retains the expected critical signatures of the target algebraic Hamiltonian.

The process matrix formalism describes quantum correlations in scenarios without a fixed causal order between local laboratories. Operational signatures of such correlations can be investigated through causal games. A paradigmatic example is the Guess-Your-Neighbour's-Input game, in which two parties attempt to guess each other's inputs. Correlations compatible with any definite, or probabilistically mixed, causal order cannot achieve a winning probability exceeding $1/2$. The best process-matrix strategy currently known attains a value of approximately $0.6218$ using local dimension $d=5$, while the strongest known dimension-independent upper bound is $0.7592$. In this work, we investigate whether increasing the local dimension beyond $d = 5$ can narrow this gap. To this end, we employ a see-saw optimization scheme in which each step is formulated as a semidefinite program. For scalability, we develop a custom implementation of the SCS solver in which the dominant computational cost, the projection onto the positive-semidefinite cone, is offloaded to a GPU, yielding a six-fold speedup. Using this implementation, we explore local dimensions up to $d = 8$, and we do not find significant improvements over the value at $d=5$. Our results suggest that either qualitatively different strategies are required to approach the known upper bound, or that the bound itself is not tight.

We introduce the Frontier decoder, a pruned dynamic-programming decoder for sparse quantum decoding problems. Frontier processes error variables in a chosen order, merges prefixes with the same residual syndrome and logical label, and approximates logical-coset posterior masses by retaining only a narrow scored frontier. Without pruning, the recursion is exact ordered inference with exponential complexity. In the code-capacity setting, the decoder reaches thresholds close to optimal for the surface code and the color code. In the circuit-level noise model, it achieves state-of-the-art performance with a very small average retained list size: less than 100 for the gross code $[[144,12,12]]$ at a physical error rate of $0.001$. When the list size is constant, the decoder has linear complexity, suggesting the possibility of low-latency implementations.

We consider protocols for control of dipolar Bose-Einstein condensates where the critical role is played by the long-range anisotropic interatomic magnetic dipole-dipole interaction. The phase diagram of such a condensate has been explored theoretically and experimentally with certain values of the interatomic scattering length corresponding to superfluid and supersolid phases, where supersolidity appears as a modulation in the ground state density. Preparation of this modulated ground state is challenging, since excitations appear as a result of a finite-time evolution required to produce qualitative changes in the wavefunction density. To solve this problem we consider the time-dependent control of a dipolar Bose-Einstein condensate using shortcuts to adiabaticity techniques, concentrating on design of the time-dependent scattering length, a parameter of the system easily tunable by contemporary experiments. The first technique is the variational approach based on the Euler-Lagrange equations for a separable ansatz describing the evolution of the superfluid state. Secondly, we study the transition from superfluid to supersolid using a direct optimization protocol. We discuss the fidelity of the developed protocols in terms of the evolution time.

We present a systematic study of von Neumann entropy estimation in multi-qutrit quantum systems using two complementary approaches: variational quantum algorithms (VQAs) and classical convolutional neural networks (CNNs), evaluated using an ideal (noise-free) quantum simulator. For systems up to three qutrits, we construct and evaluate 11 hardware-efficient SU(3)-inspired ansatzes. A parameter sweep shows that estimation accuracy is primarily determined by the number of trainable parameters, provided sufficient entanglement is present. Based on this study, we fix the parameter count to approximately 120 for subsequent experiments, observing that increasing entangling-gate counts beyond a threshold yields only marginal improvements. For larger systems (two to five qutrits), we use a CNN trained on measurement outcomes from tensor-product mutually unbiased bases. The model achieves accurate and stable predictions and exhibits a systematic improvement in performance with system size, with the highest errors for two-qutrit systems and the lowest for five-qutrit systems. Notably, using only 12.5% of the measurements required for full state tomography is sufficient to reach 90th-percentile absolute errors of approximately 0.13-0.16 nats for both four- and five-qutrit systems. The CNN model is also robust to shot noise and generalizes well to out-of-distribution states. Overall, within the simulated settings studied here, our results indicate a transition in practical methods: VQAs are effective for small systems, while CNN-based estimators offer improved scalability and robustness for larger qutrit systems.

Neutral atom quantum computers (NAQC) are emerging as a promising, scalable quantum computing platform because of their long qubit coherence, flexible qubit arrangement, and multiqubit gate capabilities. However, circuit execution often requires physically moving qubits, making compilation a critical optimization challenge. We propose a circuit independent mathematical framework built on graph-theoretic combinatorial optimization that determines the minimal number of required qubit transfers. This model captures spatial constraints specific to NAQC platforms with zone-limited gate operations and multi-qubit gates. From this framework, we encode the qubit mapping problem as a nonlinear integer program and solve it using a genetic algorithm, enabling trade-offs between minimizing the total traveled distance and the number of parallel transfer operations. Compared to the state-of-the-art scalable compiler for zoned architectures, our approach consistently finds fewer transfers. Depending on the optimization focus, our method produces shorter traveled distances or fewer parallel transfer operations. This work provides both theoretical guaranties and a practical tool for efficient, architecture-aware quantum circuit compilation. As a result, practitioners can generate hardware-aware mappings that reduce movement-induced errors and better exploit atom transfer parallelism, directly improving execution efficiency on NAQC devices.

As quantum-computing platforms are susceptible to noise, the fidelity of quantum operations is limited by decoherence. Understanding this limitation is crucial for building utility-scale quantum processors. In previous works [Phys. Rev. Lett. 129, 150504 (2022); Quantum 9, 1684 (2025)], we presented analytical formulae for the average gate fidelity of multi-qubit operations under static Markovian noise processes, including operations that temporarily leave the computational subspace. However, some quantum-computing architectures dynamically modulate qubit or coupler frequencies to implement two-qubit gates, e.g., baseband flux gates; such modulation can lead to dissipation rates varying in time. In this Letter, we therefore generalize the fidelity-reduction formulae to encompass time-dependent dissipation. Applying our generalized formula, we obtain a fidelity bound for adiabatic operations and demonstrate that flux-dependent noise sensitivity, combined with qubit-coupler hybridization, significantly reduces the fidelity of adiabatic controlled-Z (CZ) gates in superconducting quantum computers. Our work thus provides essential theoretical tools for evaluating error budgets and optimizing the design of quantum operations in tunable quantum-computing architectures, and may also find applications in quantum-sensing and quantum-communication protocols that are affected by time-dependent dissipation.

In PRL 129, 110401 it was shown that it is theoretically possible to have operationally detectable causal loops without violating the principle of no superluminal signalling (NSS) in (1+1)-Minkowski spacetime. Whether or not such causal loops are also possible in $d > 1$ spatial dimensions, has remained a key open question. We resolve this question by showing that in a wide class of "conical" spacetimes, including Minkowski with d > 1, NSS does rule out all operationally detectable causal loops, in classical, quantum and post-quantum theories. This establishes that the relationship between the relativistic principles of NSS and no causal loops depends inherently on the geometry of spacetime.