Papers

We implement the Hadamard test with Trotterized time-evolution operators on IBM quantum computers to simultaneously extract ground- and excited-state energies of the transverse field Ising model (TFIM) and transverse longitudinal field Ising model (TLFIM). The Trotterization circuits for the TFIM admit constant-depth circuits (CDCs) for arbitrary time, allowing us to locate a large number of eigen-energies above the background noise for up to six spins. Via circuit synthesis we show that the three-spin TLFIM has constant-depth structure although it does not meet the known CDC criteria. The CDCs enable the extraction of the ground and first-excited state energies of the three-site TLFIM via its dynamics. We also address complications from the noisy background and discrete Fourier transform to enhance the reliability of the extraction process and compare the results from different generations of IBM hardware to highlight the improvement.

The complex Sachdev-Ye-Kitaev (SYK) model, featuring fermions with all-to-all interactions, serves as a dual paradigm for understanding non-Fermi liquid behavior and the holographic nature of charged black holes. Two defining characteristics of the standard SYK model are its maximal chaos (Lyapunov exponent $\lambda_{\mathrm{L}}=2\pi T$ at temperature $T$), and its finite zero-temperature residual entropy. While previous studies have largely focused on couplings drawn from a zero-mean Gaussian distribution, we investigate a generalized model with a finite mean-to-standard-deviation ratio, $g\equiv J_{0}/\delta J$ of the coupling distribution in order to get deeper insight into the evolution of chaos. We find that increasing $g$ yields the following effects: (i) The system remains a fast scrambler with $\lambda_{\mathrm{L}}=A~T$, but with a suppressed coefficient $A<2\pi$. (ii) In the limit $g\to \infty$, out-of-time-ordered correlators (OTOCs) no longer exhibit exponential growth with $\lambda_{\mathrm{L}}\simeq 0$. (iii) The spectral correlations indicative of late-time chaos maintain Wigner-Dyson level spacing statistics for all values of $g$. (iv) The system preserves a finite residual entropy, albeit with reduced magnitude, for all $g$ values. We conclude that in this generalized SYK model, there is a chaotic to non-chaotic crossover. Moreover different measures of chaos decouple, demonstrating that the presence of finite residual entropy does not strictly imply maximal chaos.

Ferroelectric materials, with their strong nonlinearities, underpin key technologies across radio-frequency (RF) signal processing, optical communications, and emerging quantum systems. Barium titanate (BTO) is a notable example, combining strong piezoelectric and electro-optic responses. While bulk BTO has been studied for decades, the piezoelectric properties of its recently available thin films, and their behavior at the millikelvin temperatures relevant to quantum hardware, remain largely unexplored. Here, we fabricate and characterize surface acoustic wave (SAW) resonators on thin-film BTO. The measured devices exhibit high electromechanical coupling (k2eff 0.14 at 5.2 GHz) and operate up to 7.8 GHz. From these measurements, combined with finite-element modeling of the multi-domain microstructure, we extract an effective piezoelectric coefficient d33eff of 53 pC/N, comparable to bulk BTO. Exploiting the intrinsic ferroelectricity, we further demonstrate low-voltage switching with a fast (100 ns) response, attractive for reconfigurable RF front-ends and parametric amplifiers. Extending these measurements to millikelvin temperatures, we find that the piezoelectric response persists, with d33eff 19 pC/N, pointing to the potential of BTO for piezoelectric coupling in superconducting quantum circuits. These results position thin-film BTO as a promising piezoelectric platform for both classical and quantum information technologies.

Barren plateaus are stated as an average-case phenomenon: pick an ansatz, initialize it naively, and concentration follows. This has led to the common view that a potential cure for barren plateaus is simply to initialize the parameters more carefully. Here we show that the situation is subtler. We introduce a first-moment framework that gives a simple operator-level diagnostic for when an initialization may escape the fully concentrated barren-plateau fixed point, and for comparing the biases induced by different initialization strategies. Our framework recovers several known initialization schemes such as identity and Gaussian initialization, but also shows that barren-plateau avoidance is highly non-unique. Indeed, many shifted, biased, and non-symmetric parameter distributions can avoid concentration, and these choices need not be equivalent. In fact, our results show that one can generate exponentially many families of inequivalent initialization strategies. Then, our numerics indicate that different first-moment-distinct initializations can lead to different attained minima, suggesting that avoiding barren plateaus via smart initializations can trade the exponential concentration problem for the challenge of selecting the right trainable pocket amongst many options.

A promising avenue for scaling quantum computing is to connect quantum processing units (QPUs) by generating entanglement between them. This requires circuit partitioning: partially rewriting quantum circuits to run on a distributed quantum system using quantum teleportation protocols, while preserving the unitary operation implemented by the circuit. The key metric to minimize when partitioning is the e-bit count, defined as the number of maximally entangled qubit pairs that must be generated between QPUs. We focus on partitioning the quantum Fourier transform (QFT) circuit, which is widely used as a subroutine in quantum algorithms such as quantum phase estimation and arithmetic circuits. Specifically, we present an optimal gate-packing-based partitioning scheme under bounded communication ancilla constraints, as well as a novel detached-gate-based partitioning scheme that achieves optimal e-bit consumption when ancilla availability is unrestricted. We compare these schemes against prior analytical partitioning approaches for the QFT and evaluate them against partitions produced by general-purpose circuit partitioning algorithms. We further validate our approach by implementing the bounded-ancilla circuits on quantum hardware.

We construct exact, positive-energy, normalizable wave-packet solutions of the Dirac equation in the axisymmetric potential $V=-\,v_0/\rho$ – to our knowledge, the first such solutions in any external potential. Remarkably, one family comprises only elementary functions whose longitudinal profiles reproduce the free-Schrödinger Hermite–Gauss wave packets in the nonrelativistic limit. All packets share two striking features: (i) a probability density that is pointwise decoupled from spin orientation – despite the inherent spin-orbit coupling of the Dirac equation – and (ii) a complete freezing of their time evolution at the critical coupling $v_0\to\hbar c/2$. We also present a simple scheme that maps solutions of the 2D Helmholtz equation to further exact Dirac wave packets.

In a standard two-level Ramsey interferometer, the accumulated signal phase is linearly mapped to the readout phase. Here, we introduce three-level Ramsey interferometry, in which projected interference between internal paths reshapes this mapping through a noncyclic geometric phase response. Near a geodesic-closure transition, a small accumulated signal phase produces a sharply amplified readout-phase shift. We quantify the accompanying gain–visibility tradeoff and identify a finite operating window in which the amplified response can yield a net signal-to-noise-ratio gain in the presence of additional technical phase noise. A controllable Ramsey phase offset further positions this high-slope response at a chosen operating point, making the local enhancement accessible without requiring a large signal-induced phase. More broadly, these results establish a multilevel Ramsey route to enhanced phase sensitivity in quantum platforms, in which two signal-collecting internal paths interfere to produce a controllable noncyclic geometric response.

There is growing interest in extensions of the standard model of gate-based quantum computation to include auxiliary degrees of freedom evolving according to a nonlinear Schrödinger equation. By reducing the Boolean satisfiability problem SAT to quantum state discrimination, Abrams and Lloyd argued that the right type of nonlinearity can be used to solve NP and #P problems in polynomial time, at least in an idealized noise-free limit. For practical implementation, however, we are restricted to simulated and emergent nonlinearities, such as that appearing in mean field models for ultracold atoms and similar ensembles. A prominent example is the torsion model, which arises in two-component Bose-Einstein condensates and spin models with all-to-all Ising interaction. But torsion-based state discrimination appears to fall short of solving SAT. Here we close this gap by constructing the filtered oracle of the Valiant-Vazirani theorem, providing a randomized polynomial-time reduction from SAT to UNIQUE SAT, a promise problem where there is at most 1 satisfying assignment. In the noise-free limit, the UNIQUE SAT problem can be solved in polynomial time using torsion nonlinearity. Quantum Valiant-Vazirani reduction is no faster than the efficient classical version, but a fault-tolerant implementation coupled to a nonlinear quantum coprocessor simulating torsion would enable polynomial time solution to NP (but not #P) problems.

As large language models (LLMs) become embedded in quantum simulation workflows (IDE copilots, notebook assistants, agentic pipelines), evaluation must move beyond functional correctness to anticipate and catch structured failures before they propagate through expensive pipelines. We present a layered evaluation framework for materials-informed Variational Quantum Eigensolver (VQE) circuit generation: (i) a gatekeeper screening rubric across seven physical and framework criteria; (ii) a circuit fidelity analysis comparing model outputs against analytical and reference-implementation values for H2/STO-3G/Jordan-Wigner/UCCSD, with ansatz classification and gate-composition breakdown; and (iii) design entropy, a run-to-run behavioral consistency metric. We surface a taxonomy of five distinct LLM failure modes (geometry hallucination, nonexistent API usage, runtime integration failures, constraint violations, and plausible-but-unverifiable output), each with distinct detectability profiles and structural to the task rather than to any one model. A forensic audit of the evaluation platform's own source code further establishes that two apparent model failures originated in the harness through silent fallback-template substitution, demonstrating that evaluation infrastructure belongs inside the same trust boundary as the models it tests. Applied across multiple foundation models on a Materials Project integrated pipeline, the framework shows that gatekeeper-style validation is necessary, not optional, for reliable deployment.

We investigate the response of entanglement to temperature variations in interacting two-qubit thermal states. For a general two-qubit interaction Hamiltonian, we derive exact expressions for the thermal concurrence, its first and second derivatives with respect to inverse temperature, and the thermal quantum Fisher information. We show that the rate of change of thermal entanglement is bounded by the thermal quantum Fisher information. We further derive a bound relating entanglement curvature and thermal quantum Fisher information, and show that temperature uncertainty induces a loss of entanglement bounded by the same quantity that determines thermometric sensitivity. These results establish thermal quantum Fisher information as a fundamental constraint on the response and robustness of entanglement in interacting two-qubit thermal states.

We characterize two nested Walsh parity-check filters implemented on Quandela's Belenos cloud photonic processor in a single-photon eight-mode spatial register. The modes are indexed by the vertices of the cube $Q_3$. The filters realize the classical $[8,7,2]$ single-parity-check code, the zero-sum neutral subspace $\mathcal{N}$ and the $[8,4,4]$ extended Hamming code, the parity-checked subspace $\mathcal{S}\subset\mathcal{N}$ with one DC and three face-parity syndrome channels. These are first-quantized path/mode encodings of classical codes: the experiment verifies leakage suppression and syndrome routing, not error correction or protection against photon loss, and all probabilities are conditional on postselected single-photon detections. Across more than 340,000 detections, neutral inputs show residual DC-port leakage of $0.02\%$-$1.1\%$ (mean $0.6\%$), corresponding to $\approx21\times$ suppression relative to the ideal $0.125$ DC-capture baseline and $31.6\times$ relative to the measured non-neutral control. Injected DC contamination gives a monotonic soft error signal, and the three face-parity syndrome channels route to their predicted ports with $94$-$99\%$ selectivity. A sector-preserving unitary core keeps leakage far below non-neutral controls over one to three applications, with differences dominated by calibration and compilation systematics rather than gate-cycle physics. We quantify these limits, including fixed-pattern separator bias, $\pm 0.02$ calibration offsets, and compilation scatter near the $10^{-3}$ leakage level, and report a Hong-Ou-Mandel degradation episode in which suppression vanished and recovered after recalibration.

The sign problem is a notorious obstacle for classically simulating quantum theories with fermions. We propose an effective field theory method for analyzing the sign problem. At high temperatures, a $d$+1 dimensional field theory reduces to a bosonic $d$-dimensional theory; the phase of the Pfaffian in the higher dimensional theory is encoded in an operator in the lower dimensional theory. We apply this framework to the D0-brane/BFSS matrix quantum mechanics, where the phase becomes an operator in a bosonic multi-matrix integral. Our results show that the continuum theory has a sign problem that persists in the large-$N$ 't Hooft regime. However, detecting the sign problem involves going to 10-loop order in the high-temperature expansion. This delayed onset follows from the fact that the Pfaffian phase transforms as an $O(9)$ pseudoscalar. Furthermore, the relevant diagrams give a numerically small prefactor. Consequently, ignoring the sign problem leads to a relatively small fractional error in thermodynamic quantities for temperatures $T \gtrsim \lambda^{1/3}$. However, at stronger coupling in the 't Hooft regime, the sign problem may become more severe. Finally, we initiate the application of this framework to higher-dimensional maximally supersymmetric Yang-Mills theories.

We consider the problem of identifying a topological order based on bulk entanglement of the ground-state wavefunction. Previous work showed that some universal information can be extracted from multi-entropy measures, a class of multipartite entanglement measures obtained by applying permutation operators exchanging the degrees of freedom between different replicas of the wavefunction. It remains an open question to what extent such entanglement measures can be used to extract any universal information from the ground state. Here we show that the topological partition function $Z(M)$ of a manifold $M$ can be extracted provided that $M$ satisfies a topological condition which we term “local achirality". We show that locally-achiral manifolds can be used to extract universal properties of 2+1d topological phases that go beyond the $S$ and $T$ matrices. As a first step towards classifying locally-achiral manifolds, we show that, in four dimensions, such manifolds have vanishing Pontryagin number. We relate this property to the existence of beyond-cohomology time-reversal symmetry protected topological order (T-SPT) in four dimensions. Finally, we present an entanglement measure that detects this nontrivial T-SPT.

Quantum systems governed by unitary and reversible microscopic dynamics may nevertheless exhibit equilibration, in the sense that some effective description becomes time-independent. Standard equilibration results usually consider two separate situations: system-environment structures, in which the composite system evolves unitarily while the system of interest equilibrates, and restricted measurements, such as coarse-grained POVMs and observables, in which the measurement statistics equilibrate. Here, we bring these descriptions into a common state-level framework using the concept of generalized subsystems, where the accessible effective state appears as the output of a quantum channel acting on the microscopic state. We derive bounds showing that generalized subsystems equilibrate when their dimension is small compared with the effective dimension of the discarded microscopic information. We further show that this condition is met for typical initial states in large subspaces and that the resulting equilibrium description is largely insensitive to microscopic initial details. The framework recovers the usual equilibration bounds for ordinary subsystems and finite families of POVMs. As an example, we also introduce a finite-resolution energy channel that maps unresolved microscopic energy levels into effective energy levels, thereby making residual effective coherences explicit and showing how spectral multiplicities constrain those coherences while strengthening equilibration. Our results provide a unified state-level formulation of quantum equilibration under general forms of limited accessible information.

Interference of time-bin encoded signals over free-space optical channels typically requires stringent mode filtering on receivers due to wavefront distortions from atmospheric turbulence, conventionally addressed with adaptive optics. Passive multimode receivers based on field-widened interferometers present a compelling alternative, enabling direct interference without the overhead of wavefront correction. We demonstrate a field-widened interferometer design that is implemented solely with reflective surfaces and achieves a high interference visibility (greater than 0.97) for spatially multimode beams. The interference of the multimode beams is enabled by two imaging systems that consist of a cavity configuration between a spherical concave mirror and a flat mirror. The configuration enables small form-factors, is inherently achromatic, and is based on standard spherical mirrors which reduces the complexity of the system. The interferometer is applicable for spatially multimode and turbulent optical channels, such as satellite communication, and is designed for quantum systems that use time-bin encoded qubits.

We study signatures of quantum chaos in finite-loop truncations of the planar dilatation operator in the $\mathfrak{su}(2)$ sector of $\mathcal N=4$ super Yang-Mills and its $\beta$-deformation. These truncations define holographically motivated long-range deformations of the nearest-neighbour XXX spin chain. At one-loop the model is integrable, while the all-loop planar theory is expected to again be integrable. Finite-loop truncations therefore provide a natural setting for investigating how chaotic behaviour emerges between these two integrable limits. We analyse this question using spectral statistics, eigenvector diagnostics and spread complexity. We find that the two- and four-loop truncations develop GOE-like level statistics at sufficiently large coupling but with features characteristic of weak integrability breaking. The integrability breaking at four-loops is weaker than at two-loops and the critical coupling at which chaos occurs is larger, at least for long spin chains. The three-loop truncation does not show the same onset of chaos in the range studied. Eigenvector diagnostics show that the corresponding eigenstates remain less random than GOE vectors, indicating weak ergodicity and multifractality. Finally, we can identify signatures of the eigenvalue and eigenvector chaos in the Krylov-space data. Namely, we demonstrate a correlation of the level spacing statistics with the peak of spread complexity and disorder on the Krylov chain. The delocalisation of the initial state in the Hamiltonian eigenbasis is shown to strongly affect the saturation of complexity. Our results suggest that finite-loop dilatation operators are not generic long-range spin chain Hamiltonians, but already display patterns consistent with the restoration of integrability in the all-loop planar theory.

We elucidate the physical nature of ghosts above the multi-particle threshold by contrasting them with unstable particles in quantum field theory. We first consider the asymptotic formulation, where ordinary positive-norm one-particle states can be unstable and decay, whereas ghosts survive asymptotically without decaying, yet admit no particle interpretation due to interference with the multi-particle component which masks the negative-norm one-particle state. This distinction originates from two different analytic structures of the dressed propagator, whose complex conjugate poles lie on the first or second Riemann sheet in the ghost or ordinary case, respectively. Ghost resonances are, in principle, phenomenologically distinguishable from ordinary ones, being narrower and exhibiting weaker interference between positive- and negative-energy peaks. We then formulate the quantum field theory in a finite interval of time and, working within a suitable approximation for the dressed propagator, find that finite-time effects amplify differences in the resonant behavior and give rise to new features, such as higher peaks in ghost resonances. Distinct temporal regimes are also identified: for times shorter than the inverse width, an approximate free-particle description is valid; at later times interactions and interference dominate, leading to decay or multi-particle masking. This study supports the absence of freely propagating ghost particles in the asymptotic limit.

Spectral kissing, recently realized in a Kerr parametric oscillator (KPO), refers to the merging of pairs of energy levels and arises as a manifestation of an excited-state quantum phase transition (ESQPT). Here, we show that this phenomenon has a dissipative counterpart encoded in the spectrum of the steady-state density matrix. Using a dissipative KPO as a representative example, we demonstrate that, in the weak-dissipation regime, the eigenvalues of the steady-state density matrix organize into quasi-degenerate pairs that mirror the spectral kissing of the corresponding closed system. As the dissipation strength increases, this pairing gradually disappears. By analyzing the classical limit of the system, we derive analytical expressions for the critical lines governing both the onset of steady-state spectral kissing and its disappearance at a dissipative phase transition.

The effect of a large environment on a finite-size quantum mechanical system is two-fold: It brings dissipation, but also fluctuations of thermal and quantum origin. While dissipation tends to stabilize the dynamics, we question if and how environmental quantum fluctuations can generate chaos in an otherwise classically non-chaotic system. We work out a paradigmatic model of quantum optics: the dissipative Dicke model, where a large spin interacts with a dissipative harmonic mode. We dial in the classical/quantum correspondence by working in the semiclassical regime at large but finite spin. We demonstrate that, starting from a classically regular phase space in the superradiant regime, quantum noise can generate a strange attractor with fractal dimension and a positive Lyapunov exponent. We unveil the deep connection with shear-induced chaos that was recently developed in the mathematical community.

The ground state of random Hamiltonians with all-to-all interactions such as the quantum Sherrington-Kirkpatrick (SK) model and the Sachdev-Ye-Kitaev (SYK) model follow volume-law entanglement and are expected to be hard to model using tensor networks. In recent years, some progress has been made to push the limit of classical methods using neural quantum states. However, it remains an open question whether there exist quantum algorithms that could offer a quantum advantage over the state-of-the-art classical methods in simulating random Hamiltonians. In this work, we show that one such algorithm, TETRIS-ADAPT-VQE, can construct accurate ground states for dense and sparse SYK models containing up to $N=20$ Majorana fermions achieving fidelities $\geq 99.3\%$ and for the quantum SK model with up to $L=18$ sites achieving fidelities $\geq 99.9998\%$. We find that while the preparation of ground states is efficient (in terms of operator pool size and circuit depth) for the SK model, it is not efficient for either dense or moderately sparse SYK models.

Quantum error correction is essential for building scalable quantum computers. Within the stabilizer formalism, the Calderbank-Shor-Steane framework constructs quantum codes from pairs of classical linear codes. A distinctive feature in this setting is degeneracy, where multiple equivalent error estimates exist-a phenomenon that has no classical counterpart, and the lack of a meaningful classical coding-theoretic interpretation of which has remained a gap in the literature. In this paper, we demonstrate that degeneracy is closely related to the classical operation of shortening of a linear block code. Interestingly, the shortening here takes place at the decoder rather than at the encoder. Leveraging this insight, we present a parallel decoding scheme for quantum low-density parity-check codes, which we term impulse decoding, that significantly outperforms belief propagation with ordered statistics decoding, as well as several other existing techniques, under both code-capacity and circuit-level noise, with significantly lesser complexity. We then present another algorithm based on decoding of residual errors, which when combined with impulse decoding achieves further performance improvement under circuit-level noise.

Quantum correlations are essential for achieving quantum advantage in computing, communication and sensing. Moreover, their observation challenges and constrains our fundamental understanding of nature. Mechanical oscillators in the quantum regime provide an appealing platform for preparing and investigating quantum correlations at macroscopic scales. Despite substantial progress, however, continuous-variable quantum correlations stronger than entanglement have not yet been observed in this macroscopic regime. Here, we report the experimental observation of continuous-variable Einstein-Podolsky-Rosen correlations between two spatially-separated mechanical oscillators with an effective mass of $\sim 16 \,\mu g$ each. This is achieved by coupling them to a superconducting qubit which allows for engineering a two-mode squeezing interaction when parametrically driven. Crucially, we show that this interaction can be used to witness quantum correlations through the realization of a mechanical SU(1,1) interferometer. Our results expand the toolbox of operations in circuit quantum acoustodynamics and demonstrate that quantum correlations stronger than entanglement can also be observed in macroscopic systems, thereby shedding light on the boundary between quantum and classical regimes.

We study ansatz-free Lindbladian learning, the problem of reconstructing the generator of an open quantum system without prior knowledge of its Hamiltonian or dissipator structures. This problem exhibits two fundamental precision limits. Hamiltonian components not obscured by dissipation are Heisenberg-limited, while full Lindbladian reconstruction is subject to the quadratically worse standard quantum limit. This creates an apparent algorithmic impasse: achieving the Heisenberg-limited Hamiltonian learning requires suppressing unknown dissipation, which seemingly demands prior reconstruction of the noise and thereby incurs the standard-quantum-limit cost. In this work, we resolve this obstruction by giving an algorithm that learns the Hamiltonian disjoint from dissipator (HDD) at the Heisenberg limit without prior knowledge of either the Hamiltonian or dissipator supports. Our main technical ingredient is a randomized recursive stabilizer-code construction that progressively identifies and suppresses the dominant dissipative terms without reconstructing the full dissipator. Building on this framework, we also introduce an efficient end-to-end algorithm that learns the entire sparse Lindbladian at the standard quantum limit. Finally, we prove that in the ansatz-free setting, the HDD terms constitute the maximal set of Hamiltonian coefficients uniformly learnable at the Heisenberg limit. We show that every term outside HDD is fundamentally standard-quantum limited, extending prior no-go results to the ansatz-free setting. Together, our protocols provide a scalable framework for characterizing open quantum systems, with quantum error correction serving as a key learning primitive.

We study the optimization of input states for phase estimation under covariant measurements. Building on Holevo's framework, which provides the optimal covariant measurement for a fixed input state, we further optimize over the input state itself. For a general even $2\pi$-periodic cost function with non-negative Fourier coefficients, we derive a necessary and sufficient condition for the optimal input state: Its Fock coefficients are determined, up to arbitrary phases, by the eigenvector corresponding to the largest eigenvalue of a Toeplitz matrix defined by the cost function. This characterization yields an explicit expression for the attainable lower bound of the average cost under optimal covariant measurements and shows that this bound asymptotically approaches zero in the infinite-energy limit. For the specific cost function $W(\theta,\tilde{\theta})=4\sin^2[(\theta-\tilde{\theta})/2]$, we obtain the optimal input state and the corresponding minimum average cost in closed form, demonstrating Heisenberg scaling with respect to the mean photon number.

The reliable distribution of entanglement is essential for the effective operation of quantum networks. Due to fundamental differences between quantum and classical communication systems, it is necessary to develop specialised algorithms and protocols that also account for quantum-specific constraints. In this work, we focus on the issue of recalibration. As suggested by recent experimental studies, the process of local entanglement generation in a quantum link degrades over time due to environmental changes that have to be estimated and compensated via a fixed-duration calibration operation, during which the link is not available. Therefore, in such a quantum network, every link alternates between an activation period, during which it operates normally, and a calibration period, during which it cannot participate in the end-to-end entanglement distribution, thereby creating a trade-off between link quality (the initial fidelity of generated pairs, which decays during activation) and availability (the fraction of time the link is usable, which calibration reduces). We develop analytically a protocol for optimally assigning activation periods to each link in linear quantum repeater chains, subject to any general end-to-end fidelity requirements and local initial fidelity thresholds. Building on this foundation, we extend to general quantum networks, where multiple paths may cross at common links. To this, we propose a heuristic approach, evaluate it through simulations, and compare its performance with a benchmark, a numerical approach and theoretical bounds, confirming the analytical ordering of their performance.

We introduce a framework for analysing the spectrum of Hamiltonian interpolations without heavily relying on discretising the interpolation parameter. The method is based on the concept of accessible symmetries: a problem-class-dependent family of certifiable reflections that induce bipartitions of the Hilbert space. At each step, the interpolation Hamiltonian is projected onto the sectors of the accessible symmetry that is closest to being satisfied, yielding a hierarchy of weakly coupled pseudo-eigenspaces together with explicit residual couplings between them. We show that this representation captures qualitative signatures of quantum phase transitions, provides estimates of their location, and offers insights into their nature. The quality of the approximation is controlled by the compatibility between the accessible symmetry family and the problem instance. Although motivated in spirit by adiabatic quantum computation, our approach applies more broadly to the study of Hamiltonian phase diagrams, providing a new perspective on the spectral reorganisation of many-body quantum systems.

Two-dimensional topological translationally invariant (2D TTI) stabilizer codes lie at the heart of fault-tolerant quantum computation, but using them requires solving the decoding problem. Minimum-weight decoding of these codes was recently shown to be NP-hard, even in basic settings, such as the color code with Pauli $Z$ errors and the toric code with Pauli $X$, $Y$ and $Z$ errors. Here, we prove that minimum-weight decoding of 2D TTI codes nonetheless admits a polynomial-time approximation scheme (PTAS), i.e., for any constant $\varepsilon>0$, a recovery operator of weight within a multiplicative factor of $1+\varepsilon$ of the minimum can be found in polynomial time. Our approach builds on Arora's PTAS for Euclidean problems, such as the traveling salesman problem, and applies when decoding can be cast in terms of point-like excitations connected by string-like errors. It therefore extends beyond two dimensions, covering certain higher-dimensional topological codes and quantum memories, including the toric code with phenomenological or circuit-level noise.

Electromagnetic finite element method (FEM) implementations using traditional basis functions struggle to accurately represent field behavior near singular features such as conducting wedges. To combat this, specialized singular basis functions have been introduced to directly model the singular fields in these regions, leading to substantially improved performance. While these efforts have been pursued extensively in 2D, few functions have been developed for 3D elements. In this work, we develop basis functions for this in tetrahedra. Unlike prior functions, these basis functions are additive, meaning they are included alongside the standard vector basis functions to achieve more robust performance. Further, these functions are designed to be adaptable to tetrahedra touching several unique singular features by using combinations of basis functions singular with respect to each node and edge in the element, making them applicable to highly complex geometries. Higher-order interpolatory versions of the basis functions for modeling singular behavior with greater accuracy are also provided. These basis functions lead to substantial improvements in accuracy relative to the standard basis functions, and allow otherwise expensive simulations to be performed at far lower costs. As an application example, we perform simulations to extract critical quantities for designing superconducting qubits that significantly depend on the behavior of singular fields. In Ansys HFSS, this took 21.27 hours and a peak memory usage of 6.23 TB with 800 processors available, while using our singular basis functions achieved comparable results in 196 seconds while using 27.24 GB of memory and only 16 processors. Due to these benefits, our singular basis functions could be applied to enable design optimization of electromagnetic geometries with dominantly singular behavior, such as superconducting qubits.

State preparation, measurement, and reset operations take finite time and use finite energy in realistic experiments, yet the impact of this on optimal quantum metrological protocols is not properly understood. We study the effect on sensing a stochastic signal, relevant for the detection of ultralight dark matter and other searches for fundamental physics. We prove that two-mode squeezed vacuum is the optimal probe state given a finite mean-energy constraint for a family of incoherent sensing problems, including noise sensing and quantum illumination. For estimating a gain independent of a loss, we show that entanglement is a required resource to achieve the fundamental quantum limit and observe a non-Gaussian to Gaussian transition in the optimal unentangled state as the dead time increases. We apply our results to bulk acoustic wave resonators.

Collective behaviour such as flocking (the collective motion of a spontaneously formed group along a common direction) or aster formation (the binding of opposing flocks, inhibiting each others motion) are intriguing emergent phenomena in active systems with local alignment rules. Until recently, their occurrence was mainly studied for classical systems, a prime example being the active Ising model (AIM), which translates the main ingredients of flocking and aster formation (i.e., alignment and self-propulsion) to a lattice framework. Here we introduce and study a one-dimensional (1D) quantum lattice variant of the AIM, based on ideal bosons with a spin degree of freedom. We find that both the collective behaviours of the 1D classical model, flocking and aster formation, are markedly enhanced by the bosonic quantum statistics. This contrasts with a recent quantum generalization of the AIM based onto hard-core bosons [Khasseh et al., Phys. Rev. Lett. 135, 248302 (2025)], where flocking, but neither its quantum-statistical stabilization nor aster states were observed as a consequence of interactions. Moreover, we investigate the competition of this quantum statistical stabilization of collective phases with their suppression by the quantum fluctuations induced by a transverse external magnetic field.