Papers

Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to encode PDEs into unitary time evolution and has potential for scalable electromagnetic analysis. We formulate Maxwell's equations in the potential representation and embed governing equations, boundary conditions, and observables consistently into Hamiltonian form. A key bottleneck is the exponential growth of Hamiltonian terms for complex geometries; we examine this issue and show that logical compression can substantially mitigate it, especially for periodic or symmetric structures. As a proof of concept, we simulate optical wave propagation through a metalens and illustrate that the method can capture wavefront shaping and focusing behavior, suggesting its applicability to design optimization tasks. This work highlights the feasibility of Hamiltonian-based quantum simulation for photonic systems and identifies structural conditions favorable for efficient execution.

A key challenge for quantum photonic technologies based on spin qubits is the creation of optically active defects in photonic resonators. Several of the most promising defects for quantum applications are hosted in diamond, and are commonly created through ion implantation and annealing at high temperatures and high vacuum. However, the impact of annealing on photonic resonator quality factor, a critical parameter governing their coupling to defects, has not been reported. In this work, we characterize the effect of annealing at temperatures >1200{\deg}C in high vacuum on the quality factors of diamond microdisk resonators. We investigate the optical losses associated with a non-diamond layer formed during annealing, and use Raman spectroscopy to analyze the resonator surface morphology and demonstrate that tri-acid cleaning can restore their optical quality factors. These results show the viability of creating defects in pre-fabricated diamond resonators without degrading their optical properties.

High-spin states hold significant promise for classical and quantum information storage and emerging magnetic memory technologies. Here, we present a systematic framework for engineering such high-spin magnetic states in dopant clusters formed from substitutional impurities in semiconductors. In single-valley materials such as gallium arsenide, impurity states are hydrogenic and exchange interactions generally favor low-spin configurations, except in special geometries. In contrast, multivalley semiconductors exhibit oscillatory form factors in their exchange couplings, enabling the controlled suppression of selected hopping processes and exchange couplings. Exploiting this feature, we demonstrate how carefully arranged impurities in aluminum arsenide, germanium, and silicon can stabilize ground states with a net spin that scale extensively with system size. Within effective mass theory and the tight-binding approximation for hopping, we construct explicit examples ranging from finite clusters to extended lattices and fractal-like tilings. In two dimensions, we identify several favorable dopant geometries supporting a net spin equal to around half of the fully polarized value in the thermodynamic limit, including one which achieves over $70\%$ polarization. Our results provide a general design principle for harnessing valley degeneracy in semiconductors to construct robust high-spin states and outline a pathway for their experimental realization via precision implantation of dopants.

The Beryllium Electron capture in Superconducting Tunnel junctions (BeEST) experiment uses superconducting tunnel junction (STJ) sensors to search for physics beyond the standard model (BSM) with recoil spectroscopy of the $\mathbf{^7}$Be EC decay into $\mathbf{^7}$Li. A pulsed UV laser is used to calibrate the STJs throughout the experiment with $\sim$20 meV precision. Phase-III of the BeEST experiment revealed a systematic calibration discrepancy between STJs. We found these artifacts to be caused by resistive crosstalk and by intensity variations of the calibration laser. For phase-IV of the BeEST experiment, we have removed the crosstalk by designing the STJ array so that each pixel has its own ground wire. We now also use a more stable UV laser for calibration. The new STJ arrays were fabricated at STAR Cryoelectronics and tested at LLNL and FRIB. They have the same high energy resolution of $\sim$1-2~eV in the energy range of interest below 100~eV as before, and they no longer exhibit the earlier calibration artifacts. We discuss the design changes and the STJ array performance for the next phase of the BeEST experiment.

Quantum data hiding is the existence of pairs of bipartite quantum states that are (almost) perfectly distinguishable with global measurements, yet close to indistinguishable when only measurements implementable with local operations and classical communication are allowed. Remarkably, data hiding states can also be chosen to be separable, meaning that secrets can be hidden using no entanglement that are almost irretrievable without entanglement – this is sometimes called `nonlocality without entanglement'. Essentially two families of data hiding states were known prior to this work: Werner states and random states. Hiding Werner states can be made either separable or globally perfectly orthogonal, but not both – separability comes at the price of orthogonality being only approximate. Random states can hide many more bits, but they are typically entangled and again only approximately orthogonal. In this paper, we present an explicit construction of novel group-symmetric data hiding states that are simultaneously separable, perfectly orthogonal, and even invariant under partial transpose, thus exhibiting the phenomenon of nonlocality without entanglement to the utmost extent. Our analysis leverages novel applications of numerical analysis tools to study convex optimisation problems in quantum information theory, potentially offering technical insights that extend beyond this work.

Bloch oscillations (BOs) describe the coherent oscillatory motion of electrons in a periodic lattice under a constant external electric field. Deviations from pure harmonic wave packet motion or irregular Bloch oscillations can occur due to Zener tunneling (Landau-Zener Transitions or LZTs), with oscillation frequencies closely tied to interband coupling strengths. Motivated by the interplay between flat-band physics and interband coupling in generating irregular BOs, here we investigate these oscillations in Lieb and Kagome lattices using two complementary approaches: coherent transport simulations and scattering matrix analysis. In the presence of unavoidable band touchings, half-fundamental and fundamental BO frequencies are observed in Lieb and Kagome lattices, respectively – a behavior directly linked to their distinct band structures. When avoided band touchings are introduced, distinct BO frequency responses to coupling parameters in each lattice are observed. Scattering matrix analysis reveals strong coupling and potential LZTs between dispersive bands and the flat band in Kagome lattices, with the quadratic band touching enhancing interband interactions and resulting in BO dynamics that is distinct from systems with linear crossings. In contrast, the Lieb lattice – a three level system – shows independent coupling between the flat band and two dispersive bands, without direct LZTs occurring between the two dispersive bands themselves. Finally, to obtain a unifying perspective on these results, we examine BOs during a strain-induced transition from Kagome to Lieb lattices, and link the evolution of irregular BO frequencies to changes in band connectivity and interband coupling.

Electronic voting systems face growing risks from cyberattacks and data breaches, which are expected to intensify with the advent of quantum computing. To address these challenges, we introduce a quantum-secure voting framework that integrates Quantum Key Distribution (QKD), Dual-Key Symmetric Encryption, and verifiable receipt mechanisms to strengthen the privacy, integrity, and reliability of the voting process. The framework enables voters to establish encryption keys securely, cast encrypted ballots, and verify their votes through receipt-based confirmation, all without exposing the vote contents. To evaluate performance, we simulate both quantum and classical communication channels using the Message Queuing Telemetry Transport (MQTT) protocol. Results demonstrate that the system can process large numbers of votes efficiently with low latency and minimal error rates. This approach offers a scalable and practical path toward secure, transparent, and verifiable electronic voting in the quantum era.

We show that the quantum smooth label cover problem is undecidable and RE-hard. This sharply contrasts the quantum unique label cover problem, which can be decided efficiently by a result of Kempe, Regev, and Toner (FOCS'08). On the other hand, our result aligns with the RE-hardness of the quantum label cover problem, which follows from the celebrated MIP* = RE result of Ji, Natarajan, Vidick, Wright, and Yuen (ACM'21). Additionally, we show that the quantum oracularized smooth label cover problem is RE-hard. Our second result fits with the alternative quantum unique games conjecture recently proposed by Mousavi and Spirig (ITCS'25) on the RE-hardness of the quantum oracularized unique label cover problem. Our proof techniques include a quantum version of Feige's reduction from 3SAT to 3SAT5 (STOC'96) for BCSMIP*-protocols, which may be of independent interest.

Precision sensing and imaging of weak static magnetic fields are crucial for a variety of emerging nanoscale applications. While nitrogen-vacancy (NV) centers in diamond provide exceptional AC magnetic field sensitivity with nanoscale spatial resolution, their sensitivity to static (DC) magnetic fields is fundamentally limited by the short dephasing time (T2*) due to spin-spin interactions. In this work, we present a novel hybrid sensing approach that integrates a soft ferromagnetic microwire with a single near-surface NV center to amplify its response to external static magnetic fields. This hybrid configuration achieves a DC magnetic field sensitivity of 63 nT/sqrt(Hz) for a single NV center - about 500 times greater than conventional inhomogeneous broadening- or T2*-limited magnetometry, with potential for further enhancement. The compact and highly sensitive nature of this sensor opens new opportunities for quantum sensing applications involving the detection of static or slowly varying magnetic fields across diverse scientific and technological domains.

Evaluating the permanent of a matrix is a fundamental computation that emerges in many domains, including traditional fields like computational complexity theory, graph theory, many-body quantum theory and emerging disciplines like machine learning and quantum computing. While conceptually simple, evaluating the permanent is extremely challenging: no polynomial-time algorithm is available (unless $\textsc{P} = \textsc{NP}$). To the best of our knowledge there is no publicly available software that automatically uses the most efficient algorithm for computing the permanent. In this work we designed, developed, and investigated the performance of our software package which evaluates the permanent of an arbitrary rectangular matrix, supporting three algorithms generally regarded as the fastest while giving the exact solution (the straightforward combinatoric algorithm, the Ryser algorithm, and the Glynn algorithm) and, optionally, automatically switching to the optimal algorithm based on the type and dimensionality of the input matrix. To do this, we developed an extension of the Glynn algorithm to rectangular matrices. Our free and open-source software package is distributed via Github, at https://github.com/theochem/matrix-permanent.

The atomtronic matter-wave triple-well transistor is theoretically predicted to exhibit current gain and act as a coherent matter-wave emitter. In this work, we investigate the dynamics of an atomtronic transistor composed of a triple-well potential – source, gate, and drain – modeled by the time-dependent Gross-Pitaevskii equation. We systematically explore the dependence of the drain population and the current on the source bias potential and the strength of the interatomic interaction. Our simulations reveal signatures of resonant tunneling when the source chemical potential aligns with discrete energy levels in the gate well, leading to coherent matter-wave emission in the drain. Contrary to previous many-body studies that predicted interaction-induced current gain via coupling to gate well modes, our results suggest that coherence in the drain is primarily governed by single-particle resonances, with no evident broadening from nonlinear coupling.

Current quantum computers require algorithms that use limited resources economically. In quantum machine learning, success hinges on quantum feature-maps, which embed classical data into the state space of qubits. We introduce Quantum Feature-Map Learning via Analytic Iterative Reconstructions (Q-FLAIR), an algorithm that reduces quantum resource overhead in iterative feature-map circuit construction. It shifts workloads to a classical computer via partial analytic reconstructions of the quantum model, using only a few evaluations. For each probed gate addition to the ansatz, the simultaneous selection and optimization of the data feature and weight parameter is then entirely classical. Integrated into quantum neural network and quantum kernel support vector classifiers, Q-FLAIR shows state-of-the-art benchmark performance. Since resource overhead decouples from feature dimension, we train a quantum model on a real IBM device in only four hours, surpassing 90% accuracy on the full-resolution MNIST dataset (784 features, digits 3 vs 5). Such results were previously unattainable, as the feature dimension prohibitively drives hardware demands for fixed and search costs for adaptive ansätze. Furthermore, Q-FLAIR demonstrates de-quantization robustness against direct classical modeling, satisfying a benchmark rare in the literature and a necessary condition for potential quantum advantage. By rethinking feature-map learning beyond black-box optimization, this work takes a concrete step toward enabling quantum machine learning for real-world problems and near-term quantum computers.

We present new theoretical mechanisms for quantum speedup in the global optimization of nonconvex functions, expanding the scope of quantum advantage beyond traditional tunneling-based explanations. As our main building-block, we demonstrate a rigorous correspondence between the spectral properties of Schrödinger operators and the mixing times of classical Langevin diffusion. This correspondence motivates a mechanism for separation on functions with unique global minimum: while quantum algorithms operate on the original potential, classical diffusions correspond to a Schrödinger operators with a WKB potential having nearly degenerate global minima. We formalize these ideas by proving that a real-space adiabatic quantum algorithm (RsAA) achieves provably polynomial-time optimization for broad families of nonconvex functions. First, for block-separable functions, we show that RsAA maintains polynomial runtime while known off-the-shelf algorithms require exponential time and structure-aware algorithms exhibit arbitrarily large polynomial runtimes. These results leverage novel non-asymptotic results in semiclassical analysis. Second, we use recent advances in the theory of intrinsic hypercontractivity to demonstrate polynomial runtimes for RsAA on appropriately perturbed strongly convex functions that lack global structure, while off-the-shelf algorithms remain exponentially bottlenecked. In contrast to prior works based on quantum tunneling, these separations do not depend on the geometry of barriers between local minima. Our theoretical claims about classical algorithm runtimes are supported by rigorous analysis and comprehensive numerical benchmarking. These findings establish a rigorous theoretical foundation for quantum advantage in continuous optimization and open new research directions connecting quantum algorithms, stochastic processes, and semiclassical analysis.

With the advent of quantum cloud computing, the security of delegated quantum computation has become of utmost importance. While multiple statistically secure blind verification schemes in the prepare-and-send model have been proposed, none of them achieves full quantum fault-tolerance, a prerequisite for useful verification on scalable quantum computers. In this paper, we present the first fault-tolerant blind verification scheme for universal quantum computations able to handle secret-dependent noise on the verifier's quantum device. Composable security of the proposed protocol is proven in the Abstract Cryptography framework. Our main tools are two novel distillation protocols that turn secret-dependent noise into secret-independent noise. The first one is run by the verifier and acts on its noisy gates, while the second and more complex one is run entirely on the prover's device and acts on states provided by the verifier. Both are required to overcome the leakage induced by secret-dependent noise. We use these protocols to prepare states in the X-Y-plane whose noise is overwhelmingly secret-independent, which then allows us to verify with exponential confidence arbitrary fault-tolerant BQP computations.

Concordant quantum computations, in which circuits whose register carries zero quantum discord with respect to every subsystem at every step, contain neither entanglement nor any other form of quantum correlation, yet no efficient classical simulation of them is known beyond restricted gate sets. We argue that the obstruction is not a shortage of correlations but the absence of a uniquely identifiable local product basis, and we develop this basis ambiguity on two fronts. Quantitatively, we introduce the Basis Ambiguity Measure $\beta\in[0,1]$, the normalized dimension of the manifold of admissible diagonalizing bases on a gate support, and prove a sharp equivalence: a concordance-preserving gate that defeats the Local Basis Finder of Cable and Browne exists if and only if $\beta>0$. Both directions are constructive. Physically, we identify the resource whose absence the obstruction is: basis objectivity, a redundant and independently accessible record of the local basis. We show that an environment in spectrum broadcast form, together with the system–environment interaction map, replaces the NP-hard degeneracy test of Eastin by a fixed number of pairwise fragment comparisons per gate, at a cost independent of register size and circuit depth; the two ingredients live on different axes (state and dynamics), and neither alone suffices. We further prove that a theory in which every state has a strictly unique decomposition into perfectly distinguishable pure states has a simplex state space and lacks the continuity content of Hardy's fifth axiom, so that $\beta$ is a computational witness of that axiom.

Coin-flipping is a fundamental task in two-party cryptography where two remote mistrustful parties wish to generate a shared uniformly random bit. While quantum protocols promising near-perfect security exist for weak coin-flipping – when the parties want opposing outcomes – it has been shown that they must be inefficient in terms of their round complexity, and it is an open question of how space efficient they can be. In this work, we consider a variant called cheat-penalised weak coin-flipping in which if a party gets caught cheating, they lose $\Lambda$ points (compared to $0$ in the standard definition). We find that already for a small cheating penalty, the landscape of coin-flipping changes dramatically. For example, with $\Lambda=0.01$, we exhibit a protocol where neither Alice nor Bob can bias the result in their favour beyond $1/2 + 10^{-8}$, which uses $24$ qubits and $10^{16}$ rounds of communication (provably $10^{7}$ times better than any weak coin-flipping protocol with matching security). For the same space requirements, we demonstrate how one can choose between lowering how much a malicious party can bias the result (down to $1/2 + 10^{-10}$) and reducing the rounds of communication (down to $25,180$), depending on what is preferred. To find these protocols, we make two technical contributions. First, we extend the point game-protocol correspondence introduced by Kitaev and Mochon, to incorporate: (i) approximate point games, (ii) the cheat-penalised setting, and (iii) round and space complexity. Second, we give the first (to the best of our knowledge) numerical algorithm for constructing (approximate) point games that correspond to high security and low complexity. Our results open up the possibility of having secure and practical quantum protocols for multiparty computation.

Since its discovery at the Tevatron in 1995, the top quark has been extensively studied due to its unique properties. We discuss how the remarkable progress in top-quark physics has opened the possibility of using the top quark as a tool to test quantum mechanics at the energy frontier. After reviewing the motivations for exploring beyond quantum mechanics, we present an example: probing post-quantum correlations at the energy frontier with boosted top quarks.

We identify the mechanism of slow heterogeneous relaxation in quantum kinetically constrained models (KCMs) in which the potential energy strength is controlled by a coupling parameter. The regime of slow relaxation includes the large-coupling limit. By expanding around that limit, we reveal a nested hierarchy of states that remain frozen on time scales determined by powers of the coupling. The classification of such states, together with the evolution of their Krylov complexity, reveals that these time scales are related to the distance between the sites where facilitated dynamics is allowed by the kinetic constraint. While correlations within frozen states relax slowly and exhibit metastable plateaus that persist on time scales set by powers of the coupling parameter, the correlations in the rest of the states decay rapidly. We compute the plateau heights of correlations across all frozen states up to second-order corrections in the inverse coupling. Our results explain slow relaxation in quantum KCMs and elucidate dynamical heterogeneity by relating the relaxation times to the spatial separations between the active regions.

Holes in Ge/SiGe heterostructures are now a leading platform for semiconductor spin qubits, thanks to the high confinement quality, two-dimensional arrays, high tunability, and larger gate structure dimensions. One limiting factor for the operation of large arrays of qubits is the considerable variation in qubit frequencies or properties resulting from the strongly anisotropic $g$-tensor. We study the $g$-tensors of six and seven qubits in an array with a Y geometry across two devices. We report a mean distribution of the tilts of the $g$-tensor's out-of-plane principal axis of around $1.1 \deg$, where nearby quantum dots are more likely to have a similar tilt. Independently of this tilt, and unlike simple theoretical predictions, we find a strong in-plane $g$-tensor anisotropy with strong correlations between neighboring quantum dots. Additionally, in one device where the principal axes of all g-tensors are aligned along the [100] crystal direction, we extract the spin-flip tunneling vector from adjacent dot pairs and find a pattern that is consistent with a uniform Dresselhaus-like spin-orbit field. The Y arrangement of the gate layout and quantum dots allows us to rule out local factors like electrostatic confinement shape or local strain as the origin of the preferential direction. Our results reveal long-range correlations in the spin-orbit interaction and $g$-tensors that were not previously predicted or observed, and could prove critical to reliably understand $g$-tensors in germanium quantum dots.

Electron spin shuttling, the gate-controlled, coherent transport of electrons between qubit registers, increases qubit connectivity and enables efficient quantum-error-correction schemes. It is emerging as a key enabler of scalable silicon spin-qubit quantum computing. As an electron travels over micrometers, it encounters angstrom-scale disorder, causing fluctuations in its confinement potential, valley splitting, and valley phase. These lead to leakage into the valley-excited state, limiting high-fidelity shuttling speeds. Accurate predictions of shuttling fidelities thus require modeling tools that link atomistic and mesoscopic physics. We develop a multiscale simulation workflow to quantify these effects in the experimentally-realized Si/SiGe "QuBus" conveyor-belt architecture. First, we resolve the time-dependent, gate-controlled device electrostatics by solving the Poisson equation using the finite-element method. Second, we construct conveyor belt atomic structures with realistic atomistic disorder (random alloying and interface roughness); we resolve strain atomistically using the Keating valence force-field model. Third, we perform position-tracked atomistic tight-binding simulations of the shuttled electrons to obtain their time-dependent valley splittings and phases. Finally, these time traces parametrize a time-dependent Schrödinger equation, which we solve to predict valley dynamics. We find that interface roughness strongly suppresses shuttling fidelities, with a sharp anomaly near the atomic-layer scale. Overall, our predictions set practical, quantitative guidelines to realize scalable, high-fidelity shuttling in silicon spin-qubit architectures.

We provide an exact analytical solution of the single-particle Schrödinger equation for a chain of non-interacting fermions subject to a time-dependent linear potential, with its slope varied as an arbitrary function of time. The resulting dynamics exhibit self-similar behavior, with a structure reminiscent of the domain wall melting problem, albeit characterized by a nontrivial time-dependent length scale and phase. Building on this solution, we derive hydrodynamic predictions for the evolution of particle density, current, and entanglement entropy along the chain. In the special case of a sudden quench, the system develops a breathing interface region, which may be interpreted as a realization of Wannier-Stark localization, as previously suggested on the basis of hydrodynamic arguments.

Quasi-optical experiments are emerging as a powerful technique to probe magnetic transitions in molecular spin systems. However, the simultaneous presence of the electric- and magnetic-dipole induced transitions poses the challenge of discriminating between these two contributions. Besides, the identification of the spin-electric transitions can hardly rely on the peak intensity, because of the current uncertainties on the value of the spin-electric coupling in most molecular compounds. Here, we compute the polarizations required for electric- and magnetic-dipole induced transitions through spin-Hamiltonian models of molecular spin triangles. We show that the polarization allows a clear discrimination between the two kinds of transitions. In addition, it allows one to identify the physical origin of the zero-field splitting in the ground multiplet, a debated issue with significant implications on the coherence properties of the spin qubit implemented in molecular spin triangles.

We consider the class of Davies quantum semigroups modelling thermalization for translation-invariant Calderbank-Shor-Steane (CSS) codes in D dimensions. We prove that conditions of Dobrushin-Shlosman-type on the quantum Gibbs state imply a modified logarithmic Sobolev inequality with a constant that is uniform in the system's size. This is accomplished by generalizing parts of the classical results on thermalization by Stroock, Zegarlinski, Martinelli, and Olivieri to the CSS quantum setting. The results in particular imply the rapid thermalization at any positive temperature of the toric code in 2D and the star part of the toric code in 3D, implying a rapid loss of stored quantum information for these models.

We investigate the role of symmetries in constructing resource-efficient operator pools for adaptive variational quantum eigensolvers. In particular, we focus on the lattice Schwinger model, a discretized model of $1+1$ dimensional electrodynamics, which we use as a proxy for spin chains with a continuum limit. We present an extensive set of simulations comprising a total of $11$ different operator pools, which all systematically and independently break or preserve a combination of discrete translations, the conservation of charge (magnetization) and the fermionic locality of the excitations. Circuit depths are the primary bottleneck in current quantum hardware, and we find that the most efficient ansätze in the near-term are obtained by pools that $\textit{break}$ translation invariance, conserve charge, and lead to shallow circuits. On the other hand, we anticipate the shot counts to be the limiting factor in future, error-corrected quantum devices; our findings suggest that pools $\textit{preserving}$ translation invariance could be preferable for such platforms.

Recently, BCFT and ICFT have been generalized to the CFT on networks (NCFT). A key aspect of NCFT is how we connect the CFTs across different edges at the network nodes. Previous research has primarily concentrated on a specific junction condition (JC) that requires the field to be continuous at the nodes. In this paper, we investigate the most general junction conditions for $(1+1)$-dimensional free scalars that are consistent with the variational principle and energy conservation. These general junction conditions are characterized by an $O(p)$ group, where $p$ represents the number of edges connected at a node. We provide exact realizations of two typical JCs in real physical systems. Additionally, we derive both the lower and upper bounds on the network Casimir energy for $(1+1)$-dimensional free scalar fields and extend the lower bound to encompass general NCFTs. Finally, we analyze the Casimir effect in networks composed of regular polyhedra and examine the binding energy required to construct such networks from individual components.

Significant efforts are being spent on building a quantum computer. At the same time, developments in quantum software are rapidly progressing. Insufficient quantum resources often are the problem when running quantum algorithms. New techniques can aid in using smaller quantum computers to run larger quantum algorithms. One of these techniques is circuit cutting. With this method, a circuit is broken into multiple pieces, each of which is run on quantum hardware independently and then recombined to obtain the overall answer. These circuit cutting techniques require additional circuit evaluations, which can form a bottleneck for algorithms requiring many interactions. This work explores the potential of circuit cutting techniques precisely in this regime of many interactions. We consider two different models, a standard method based on expectation values, and a novel method based on probability distribution reconstruction. Next, we compare two different training methods we call train-then-cut and cut-then-train and show that in practice, cut-then-train still produces good results. This observation brings closer the practical applicability of circuit cutting techniques, as a train-then-cut strategy is often infeasible. We conclude by implementing a cut and uncut circuit and find that circuit cutting helps achieve higher fidelity results.

Dating back to the seminal work of von Neumann [von Neumann, Automata Studies, 1956], it is known that error correcting codes can overcome faulty circuit components to enable robust computation. Choosing an appropriate code is non-trivial as it must balance several requirements. Increasing the rate of the code reduces the relative number of redundant bits used in the fault-tolerant circuit, while increasing the distance of the code ensures robustness against faults. If the rate and distance were the only concerns, we could use asymptotically optimal codes as is done in communication settings. However, choosing a code for computation is challenging due to an additional requirement: The code needs to facilitate accessibility of encoded information to enable computation on encoded data. This seems to conflict with having large rate and distance. We prove that this is indeed the case, namely that a code family cannot simultaneously have constant rate, growing distance and short-depth gadgets to perform encoded CNOT gates. As a consequence, achieving good rate and distance may necessarily entail accepting very deep circuits, an undesirable trade-off in certain architectures and applications.

Boundary time crystals are a class of exotic dissipative quantum phases that spontaneously break continuous time-translation symmetry in the thermodynamic limit of open quantum systems. In finite-size systems, the long-time evolution of boundary time crystals exhibits decaying oscillations that cannot be captured by widely used mean-field theory. To address this issue, we develop an effective approach called the stroboscopic rotating wave approximation, which provides a well-approximated state for the long-time evolution of boundary time crystals in the strongly driven regime. In this approach, the order parameter exhibits both a long-time decaying envelope governed by an effective Lindblad superoperator and short-time oscillations dominated by a reduced quantum dynamical semigroup. Our results reveal that the competition among dephasing processes along three directions induces persistent oscillations, marking the emergence of the boundary-time-crystal phase. We obtain the analytical expressions for the steady-state density operator, the oscillation period, and the decay rate of the order parameter when the coherent energy splitting exceeds the dissipation rate. Our work provides a beyond-mean-field tool for studying the dynamics of periodically driven open quantum systems and understanding the formation of time crystals.

Optical non-reciprocity is a fundamental phenomenon in photonics. It is crucial for developing devices that rely on directional signal control, such as optical isolators and circulators. However, most research in this field has focused on systems in equilibrium or steady states. In this work, we demonstrate a room-temperature Rydberg atomic platform where the unidirectional propagation of light acts as a switch to mediate time-crystalline-like collective oscillations through atomic synchronization. We find that thermal-motion-induced coupling asymmetry, enabled by counterpropagating probe and control fields, generates persistent oscillations; conversely, co-propagation quenches this effect. We identify, through both numerical and analytical approaches, the criteria for realizing optical non-reciprocity within a synchronization regime. These results provide key insights for chiral quantum optics and promote the on-chip integration of non-reciprocal devices in nonequilibrium many-body systems.

This work presents an alternative methodology for computing potentials matrix elements within the Lagrange-mesh method in momentum space. The proposed approach extends the range of treatable potentials to include previously inaccessible cases, such as the Coulomb and linear interactions. It enables, in particular, an efficient and accurate treatment of the Cornell potential, which plays an important role in potential models for hadronic physics. The method is validated across a variety of systems, with special attention given to the representation of both momentum and position probability densities.