Papers

We study the problem of learning an unknown $n$-qubit Hamiltonian $H$ from $U = e^{-iHt}$ for a single time $t$, where $t$ may be arbitrarily large. For broad families of local Hamiltonians, we prove that, with high probability over $H$ and $t$, any sum of local observables $A$ that is normalized and orthogonal to $H$ satisfies $\tfrac{1}{2^n}\|[U(t),A]\|_F^2 \geq 1/\text{poly}(n)$. The Hamiltonian is therefore the unique approximately conserved local observable, and we can efficiently recover $H$, up to scale, as the approximate null vector of a data matrix built from random product-state inputs and classical shadows. As a corollary, we obtain a weak equilibration statement: the infinite-temperature autocorrelation of every sum of local observables orthogonal to $H$ decays by at least an inverse-polynomial amount.

In recent years, the spacetime code has arisen as a candidate for a unifying view of fault tolerance in space and time. On the other hand, the recent study of dynamical phases has increasingly turned its attention to fault tolerance as a notion of a dynamically stable process. In this work, I explore one pathway between the two, achieved by gauging the spacetime code. This gives rise to a lattice gauge theory that inherits the elements of fault tolerance associated with a circuit, with Gauss laws corresponding to equivalence relations between configurations of spacetime errors and Wilson loops corresponding to detectors. The obtained gauge theory finds a surprisingly wide array of applications, from quantum error correction to condensed matter physics, and even learning theory: (1) It contains in its description foliated computation, and hence gives rise to one version of a gauge theory for measurement-based quantum computation. (2) For a class of topologically ordered mixed states, it gives us a gauge-theoretic language to describe the classical memory associated with the state. (3) The gauge-invariant observables of the theory which describe detectors also coincide with the learnable degrees of freedom of circuit Pauli noise.

In compression-based quantum relaxations such as quantum random access optimization (QRAO), a quantum state is optimized on a reduced number of qubits and then decoded into a classical solution on which the objective function is evaluated. The Hermitian operator whose expectation value is optimized should therefore be consistent with the expected objective value after decoding. For a fixed single-shot POVM decoder, we define the decoder-consistent Hamiltonian as the pullback of the classical objective observable through the decoder. Its expectation value exactly equals the expected post-decoding objective value for every quantum state. We further show that any Hermitian operator inducing the same ordering over the full quantum state space must be a positive affine transformation of the decoder-consistent Hamiltonian. Using a Boolean Fourier expansion, the decoder-consistent Hamiltonian decomposes into pullbacks of individual Fourier components. This provides a common framework for comparing direct encoding, simultaneous-decoding POVMs for QRAC blocks, and the effective POVM induced by the magic rounding of Teramoto et al. in terms of which components they preserve and at what rates. For standard magic-state rounding in coloring-based QRAO for MaxCut, the framework recovers the known positive affine relation between the relaxed-Hamiltonian expectation and the expected rounded cut value. For the simultaneous-decoding POVMs analyzed here, we further show that the analogous relation generally fails for mixed-degree QUBO objectives because one- and two-body components are attenuated at different rates. We also present a systematic construction of POVM decoder blocks from prescribed Fourier components and derive corresponding lower bounds on the expected post-decoding objective value under explicit conditions.

We study two-photon entangled states for quantum radar cross section (QRCS), which is an extension of a single-photon QRCS formula. Since signal-idler entanglement does not provide any enhancement of the QRCS [Brandsema's PhD Thesis (2017)], we focus on signal-signal entanglement and derive the corresponding biphoton QRCS. We show that it can provide an enhancement over the single-photon QRCS and two-photon separable QRCS, where the performance is evaluated for various two-dimensional target geometries in monostatic/bistatic configurations. Furthermore, using the double-Gaussian approximation, we derive QRCS formula for biphoton states with arbitrary degree of entanglement and compute the resulting scattering patterns.

We introduce Transition states (T states), denoted by $\ket{T_k^n}$, as a class of multipartite entangled states characterized by a fixed number of state transitions between adjacent qubits. These states form equal-amplitude superpositions over all states with a specified transition count. Unlike Bell states based on two-qubit correlations, GHZ states characterized by global correlations among all qubits, and W and Dicke states based on fixed numbers of qubit excitations, T states are defined by transition counts along an ordered sequence of qubits. We prove that T states are unitarily equivalent to Dicke states through a chain of CX (controlled-X) operations, thereby establishing a direct correspondence between transition-based and excitation-based representations of multipartite entanglement.

We study the long-time dynamics of many-body bosonic lattice systems under translation-invariant Gaussian quantum cellular automata. We formulate two sets of conditions on GQCAs which separately guarantee thermalization of any state on the local Weyl algebra to the infinite temperature state, whenever the state is locally normal and has uniformly bounded particle density. Our main intermediate result is a quantum many-body generalization of the classic Riemann-Lebesgue lemma which is a bound on expectation values of local Weyl operators involving their support and the state's particle density.

Classically testing for the presence of anti-commuting operators on a quantum device is a critical tool underpinning recent progress in classical verification of quantum computation. While such tests can be based on cryptographic assumptions, known constructions rely on highly structured assumptions, e.g. trapdoor claw-free functions. In this work, we seek to explain this state of affairs by constructing strong cryptography from (certain forms of) classical tests of anti-commutation. In particular, we formulate the notion of a test of non-commutation (ToNC), an interactive protocol between a quantum prover and classical verifier in which the prover's final-round response is obtained by measuring one of two binary observables $P_0,P_1$ depending on the verifier's challenge bit $c$. We prove that, for a broad range of parameters, ToNC implies classical-communication key agreement (KA), and ToNC combined with one-way functions implies oblivious transfer (OT). Along the way, we develop tools for and provide the first known results on hardness amplification for post-quantum KA and OT, where communication is classical but adversaries may be quantum. In particular, we prove the following results of independent interest. - Post-quantum hard-core measure theorem: For any efficiently sampleable high-min-entropy distribution $D$ over pairs $(x,b)$ such that quantum circuits have advantage at most $\delta$ in predicting $b$ from $x$, there exists a sub-distribution $M\preceq D$ of density $(1-\delta)$ on which $b$ is nearly optimally quantum-hard to predict. - Post-quantum interactive XOR lemma: Given any classically-interactive protocol, if quantum adversaries have advantage at most $\delta$ in guessing a private challenger bit $b$, then two sequential repetitions reduce the advantage for predicting the XOR of the challenger bits $b_1\oplus b_2$ to at most $\delta^2+\rm{negl}(\lambda)$.

Succinct argument systems are of central importance to modern crytpography, enabling the efficient verification of computational claims. In the classical setting, Kilian (STOC 92) established that any probabilistically checkable proof for NP can be transformed into a succinct argument system for NP using only collision-resistant hash functions. In the quantum setting, recent works have established the feasibility of (classically-verifiable) succinct arguments for QMA, capturing statements that require *quantum* proofs. However, known constructions all rely on the highly structured assumption of learning with errors (LWE), which stands in stark contrast with the unstructured assumptions that suffice for NP. In this work, we develop a new framework that broadens the cryptographic foundations of succinct arguments for QMA. We assume the existence of (i) an oblivious state preparation (OSP) protocol, which in turn can be constructed from *plain* trapdoor claw-free functions, and (ii) collapsing hash functions, the quantum analogue of collision-resistance. In particular, we obtain the first succinct, classically-verifiable argument system for QMA which does not rely on the hardness of LWE. Our construction proceeds in two steps. First, we design a *round-efficient* classically-verifiable argument system for QMA based only on the assumption of OSP. Second, we introduce a *generalized communication compression compiler*, which, assuming collapsing hash functions, transforms any $T$-round interactive protocol into one in which the communication size is bounded by $T \cdot \poly(\secp)$ for some fixed $\poly$ independent of the original size of each message. Our compiler extends a quantum rigidity-based communication compression technique of Zhang (QCrypt 25), and may be of independent interest.

The critical question after a correct driving veto is not only whether a maneuver is unsafe, but whether the blocked interaction admits a lawful, auditable, and responsibility-bounded repair. Prediction and game-theoretic planners can suggest plausible cooperation, yet they do not return a proof that the repair respects hard rules, right-of-way, cost allocation, and ego fallback. We introduce CARVE, Certified Affordable Repair of Vetoed maneuvers via Envelopes, a certificate architecture for prediction-free interactive repair. Given a vetoed maneuver, CARVE constructs a finite repair lattice and emits a structured certificate recording the binding rule, selected joint repair, right-of-way-scaled cooperation envelope, responsibility-weighted cost split, and ego-only fallback. This certificate view reveals the algorithmic bottleneck: multi-owner repair induces a product lattice $M = \prod_j |\mathcal{A}_j|$. We therefore introduce CARVE-Q, a verifier-shielded quantum-AI search layer that applies quantum minimum finding only to this black-box lattice while leaving all safety authority classical. In the conservative verifier-oracle model, exact classical minimum finding requires $\Theta(M)$ queries in the worst case, whereas Durr-Hoyer/Grover minimum finding uses $O(\sqrt{M})$ oracle queries with high probability. We prove verifier-shielded certificate soundness, priority non-elicitation, black-box query separation, and finite-precision reversible-oracle constructibility. We then demonstrate state-vector minimum finding on CARVE repair oracles up to 65,536 assignments and validate certificate preservation on Lanelet2-grounded INTERACTION replay with 100% right-of-way respect, 100% blame consistency, and zero priority false positives. The result is a trust-bounded quantum-AI pattern for certified autonomy: quantum proposes; CARVE certifies.

We present a universal framework to harness fermionic ultracold atom platforms for quantum simulation, showing how variational algorithms on existing hardware can simulate many-body systems well beyond the hardware's native Hamiltonian. Our analysis provides evidence that one can quantum simulate the ground-state properties of a broad class of gapless target Hamiltonians of local observables in a quantum evolution time that grows polynomially with the inverse relative error, $T\sim O(\mathrm{poly}(1/\epsilon))$ up to logarithmic corrections, offering an exponential speedup over naïve classical algorithms such as exact diagonalization. We provide numerical evidence and theoretical argument that this holds for energy density, density-density, and spin-spin correlations in three qualitatively distinct models – the repulsive Hubbard model; a Hubbard model augmented with nearest-neighbor attractive interactions, which introduces the phenomenon of pairing; and the Hofstadter-Hubbard model, which introduces a gauge field and fractional quantum Hall physics. This work demonstrates quantum simulation using current fermionic platforms far beyond the models natively implemented in the hardware.

The Fermi sea is a simple and common concept in physics. However, a related and equally simple concept – the Dyson orbital – is far less discussed in physics, especially in textbooks. Yet, Dyson orbitals offer a valuable tool for characterizing the complexity of a fermionic wave functions, particularly in distinguishing between Fermi-sea-like and non-Fermi-sea-like states. As a preliminary application, we examine the Laughlin wave function and find the fortunate fact that the Dyson orbitals can be determined analytically. Further numerical data provides quantitative evidence that the Laughlin wave function describes a strongly correlated, non-Fermi liquid state.

With the advance of generative artificial intelligence (AI) synthetic texts and images have become commonplace. These capabilities offer clear benefits, but have also raised a number of ethical concerns that often have to do with misrepresenting AI outputs as genuine material. A lesser known capability of generative AI is to perform the basic analysis, processing and even synthesis of numerical data. This raises the question of whether AI can be used to imitate experimental data that an expert would consider scientifically meaningful and on par with data in the figures of peer-reviewed manuscripts? In this paper, we focus on synthesizing data inspired by well-known experiments done frequently on quantum electronic devices. This field is related to information technologies such as spintronics and quantum computing, and is considered data-rich and data-driven. We demonstrate that it is possible to generate dramatic signals associated with iconic effects such as quantum bit control, Majorana fermions, Josephson effects, quantum dots and wires using widely available ChatGPT. We find that because some of the clearest data from quantum devices can be expressed in terms of relatively basic mathematical models, AI does not need to learn on the specialized body of data. Instead, knowledge of the physics equations and of the basic features of experimental signals can go a long way towards building a realistic dataset. We also demonstrate that real data can be augmented by AI, and that AI can mimic the noise of common scientific instruments. To help assure that published data come from experiments and are not synthesized by AI, we recommend sharing large volumes of the primary data. While it is straightforward for AI to mimic a few sets of data, consistently generating long measured sequences poses sufficient barriers to the proliferation of undisclosed synthetic data.

Quantum entanglement assistance is known to improve the Shannon capacity of classical communication networks but the largest gains noted thus far are rather modest (less than 6%), motivating the question: are large capacity gains ever possible? It is shown in this work that in the presence of causal channel state information at the transmitters (CSIT), quantum entanglement assistance provides a multiplicative capacity advantage that grows exponentially with the number of users K for certain classical K-user multiple access channels with fixed size (binary) alphabet for inputs, outputs and states. Similarly, in the presence of causal channel state information at the transmitters, quantum entanglement assistance is shown to provide a multiplicative capacity advantage that is unbounded as the size of the state alphabet grows, while the number of users (K=3) and the input and output alphabet (binary) are held fixed. Even with only a few users and small alphabet sizes, substantial multiplicative gains in capacity are found, e.g., with binary inputs, outputs and states, multiplicative gains by factors exceeding 21 and 88 are noted with K=5 and K=7 users, respectively. The gains are robust in the sense that they persist even with noisy quantum resources, e.g., an exponential (in K) capacity advantage from quantum entanglement assistance remains available even if each entangled qubit independently depolarizes completely with probability $\approx$ 30%. The gains are based on quantum entanglement assistance provided only to the transmitters.

Fault-tolerant quantum computing requires translating application-level quantum circuits into the Clifford+$T$ gate set, where the $T$ gate is the dominant resource cost. Phase kickback is an ancilla-based technique that can dramatically reduce $T$-count for rotations with dyadic angles, but has previously been limited to highly structured circuit families. We present Dyadic Phase Fixing (DPF), a general multi-qubit synthesis tool that extends phase kickback to general quantum circuits. DPF uses numerical unitary synthesis to greedily extract dyadic angle rotations from any input circuit. Combined with a decision matrix to automatically size the final phase gradient register, our end-to-end workflow achieves up to 70% reduction in $T$-count compared to gridsynth and up to 60% compared to Repeat-Until-Success synthesis on a diverse set of benchmarks. We map these compiled circuits to a surface-code architecture to evaluate space-time volume, demonstrating up to a 60% reduction in this metric as well. However, for some circuits and mapping strategies the two metrics diverge significantly, demonstrating that $T$-count alone is a useful but incomplete proxy for fault-tolerant program costs.

The encoding of classical data into quantum states constitutes the primary performance bottleneck in Quantum Machine Learning (qml) on Noisy Intermediate-Scale Quantum (nisq) devices. No existing framework jointly characterises resource cost, expressivity, and noise robustness, nor provides actionable selection guidelines for practitioners. This survey addresses that gap through a systematic review of 66 primary works (2017-2026) assembled via a PRISMA-adapted protocol across five academic databases. Four principal contributions are made. First, a three-axis cost-expressivity-robustness taxonomy classifies all major encoding families - basis, angle, dense-angle, amplitude, data re-uploading, and IQP - along independently measurable axes. Second, closed-form depth-fidelity bounds under nisq decoherence channels identify the critical gate-error rate p* ~ 10^-3 below which amplitude encoding is viable. Third, a unified treatment of Fourier expressivity, barren-plateau onset, and quantum kernel concentration as functions of the encoding circuit provides the first joint trainability analysis. Fourth, a five-regime decision framework maps (D, n, p, tau) - feature dimension, qubit budget, error rate, and task type - to a hardware-grounded encoding recommendation. The central finding is that for p >= 10^-3, shallow angle-based encodings consistently outperform amplitude encoding in practice, despite the latter's exponential qubit advantage.

The quantum approximate optimization algorithm (QAOA) is a powerful heuristic that seeks to solve combinatorial optimization problems using quantum hardware and classical optimization in tandem. Various methods exist to train the parameterized quantum circuits that serve as an ansatz in QAOA. However, which method works best to identify optimal angles for a given problem instance remains poorly understood, especially at utility-scale, i.e., $100$ qubits or more. In this work, we address this challenge through utility-scale benchmarks from which we distill operational guidance for QAOA practitioners. First, we investigate approximation techniques, such as matrix product states and Pauli propagation, to find optimal angles. Second, we train QAOA on small-scale representative problems and transfer the angles to larger ones. We then validate the results on quantum hardware for utility-scale problem instances that can be meaningfully executed. In this way, we identify insights for QAOA angle setting strategies that work best for problems at the utility scale, including as a function of resource cost for the search. Crucially, the operational implications we draw from our benchmarks will help quantum optimization practitioners execute QAOA end-to-end pipelines efficiently on current and future hardware.

Systems with flat band structures, when written in the language of Compact Localised States (CLS), have been shown to be explicitly invariant under supertranslation symmetries, making Carrollian symmetries inherently important for such systems. In this work, we explore the state dynamics of these systems, focusing on quenches induced by Carroll breaking perturbations, through the probe of Krylov (spread) Complexity. We specialise to Fermionic ladder Hamiltonians with all bands flat (ABF) scenario, augmented by a supertranslation preserving interaction, and discuss Krylov state complexity for quenches across critical lines. We further discuss how the growth of Krylov complexity sharply resolves the phase-dependent resilience of Carrollian sectors against delocalising perturbations. This is augmented by a complementary mechanism for Krylov growth in a continuum Carroll scalar field theory with a gradient deformation, which exhibits strong ultraviolet sensitivity (UV/IR mixing).

We present a continuous-variable adaptive variational quantum eigensolver (CV-ADAPT-VQE). As concrete examples, we consider the ground-state preparation for (i) the Bose-Hubbard model and (ii) the bosonic Kitaev chain, including its extension with an on-site Kerr interaction. The former conserves the total boson number, while the latter conserves global parity. We construct symmetry-preserving operator pools tailored to each case and show, using GPU-based classical simulations, that CV-ADAPT-VQE results in significantly shallower circuits compared to Hamiltonian-based VQE approaches. Our results point toward direct applications in quantum simulations of condensed-matter systems, quantum chemistry, and high-energy physics.

We study a pair of exactly solvable, isospectral fermion chains, one strongly interacting and one quadratic, that nevertheless display remarkably different phase structures and operator dynamics. A nonlocal nonlinear unitary transformation maps one onto the other while preserving the entire many-body spectrum and converting local fermion operators into extended many-body strings. Thus, operators that evolve within a closed linear subspace in the quadratic model become interacting operators that generate increasingly higher-body terms and exhibit asymptotic Lanczos growth $b_n\propto\sqrt n$. Despite their identical spectra, the two models realize distinct phases and sharply different notions of operator complexity. Our results demonstrate that free many-body spectra and interacting operator dynamics are fundamentally compatible.

Thermalization in strongly correlated fermionic systems remains a central open problem in quantum many-body physics. In this work, we investigate the real-time dynamics and the approach to thermalization in the two-dimensional Hubbard model, a paradigmatic framework for correlated electrons, relevant to high-temperature superconductivity and ultracold quantum simulation. Focusing on the half-filled square lattice, we monitor the time evolution of the double occupancy following a quench in the on-site interaction $U$, and assess whether its long-time value is captured by a canonical thermal ensemble. We employ time-dependent variational Monte Carlo methods combined with transformer-based Neural-Network Quantum States to accurately describe the nonequilibrium dynamics of fermions, especially for the behavior at long times, thereby accessing regimes that were previously inaccessible to numerical simulations. Our results reveal two dynamical behaviors: for weak to intermediate interactions, the double occupancy rapidly approaches the thermal prediction, consistent with ergodic evolution; beyond a critical interaction $U_{C}$, the dynamics remains distinct from the thermal expectation on the timescales investigated, revealing signatures of a prethermal plateau delaying fast relaxation. These results establish numerical simulation as a powerful tool to probe nonequilibrium quantum phenomena in correlated fermionic matter.

We uncover a distinct form of nonequilibrium temporal order: self-similar quantum revivals in a many-body system driven by quasiperiodic spiral kicks, where the system recurrently returns close to its initial state at a hierarchically nested sequence of times. We demonstrate that both the fidelity and entanglement entropy exhibit this self-similar temporal structure. It originates from an emergent dynamical attractor, which we identify, such that all momentum modes eventually fall into the same closed orbits at self-similar times. We analytically justify this behavior and show that, for special momentum modes, this attractor arises as a consequence of a generalized spin echo process, and more generally we prove its existence using quasiperiodic SU(2) cocycles. Interestingly, the dynamics between consecutive revivals supports either volume- or area-law entanglement scaling, tunable via the driving parameters. In the presence of integrability-breaking perturbations, the system eventually heats up, but a long-lived prethermal regime with algebraically tunable lifetime occurs before heating sets in. Our results establish self-similar quantum revivals as a new paradigm for nonequilibrium quantum matter and provide a realistic route for its observation in current quantum simulators.

The symmetric double-well potential is one of the simplest quantum-mechanical systems in which perturbative and non-perturbative physics are deeply entangled. Its energy levels have non-analytic expansions in inverse powers of the inter-well separation, with factorially growing coefficients, while the parity splitting is exponentially small and invisible to perturbation theory. Resurgence ties the two features together, organizing the exact spectrum into a single tightly-constrained trans-series. This paper gives a self-contained account of this trans-series from two complementary approaches: exact WKB and the Euclidean path integral, developed in a common notation with explicit calculations through the four-instanton level and three-loop order. In exact WKB, Stokes phenomena encoded in the Delabaere–Dillinger–Pham relations control the analytic continuation of the wavefunction past turning points. The quantization condition expressed in terms of Voros symbols then determines the full trans-series. The DDP relations are local and do not require knowing the global topology of the energy surface, but that surface is an elliptic curve. In the path integral, elliptic curves enter differently: the classical saddle points are doubly-periodic elliptic functions of Euclidean time, and Stokes phenomena play out within the finite-dimensional manifold of quasi-zero modes rather than through analytic continuation of the wavefunction. A Lefschetz thimble decomposition determines which saddles contribute, and the resulting partition function trans-series is much simpler than the energy trans-series: at each instanton order the $T$-dependence is a polynomial fixed by the quasi-zero-mode thimble integrals. Together, the two approaches deploy a shared mathematical infrastructure in complementary ways, showing that the double well is an ideal setting to explore resurgence.

Understanding how frustration and symmetry breaking shape collective behavior is a central problem in quantum many-body systems. In this work, we investigate this problem in large one- and two-dimensional arrays of coupled Dicke models on a periodic lattice, where strong light-matter coupling gives rise to a superradiant phase and competition between neighboring order parameters induces spontaneous translational symmetry breaking. Such Dicke lattice models constitute a fundamentally new class of quantum many-body systems, as they simultaneously realize the thermodynamic limit associated with the lattice size and an intrinsic thermodynamic limit arising from collective on-site interactions with quantum emitters. We show that frustration drives photonic density-wave ordering, and that the resulting broken periodicity can be predicted from the excitation spectrum of the symmetric phase, without requiring computationally prohibitive thermodynamic energy minimization. Furthermore, we demonstrate that an emergent Nambu-Goldstone mode arises near the critical point in a one-dimensional chain despite the presence of only discrete symmetry, and uncover the mechanism that enables this otherwise forbidden gapless excitation. We also find quasi-periodic ordering in the superradiant phase, reminiscent of quasicrystals, and demonstrate that synthetic magnetic flux provides a powerful knob to control the nature of translational symmetry breaking. Our results establish a new direction in quantum many-body physics where the coexistence of local and global thermodynamic limits gives rise to unconventional symmetry breaking and emergent collective behavior.

The quantum Rabi model captures fundamental aspects of light–matter interaction, where symmetry dictates both spectra and dynamics. Over the past years, experiments have explored many of its nonperturbative properties, but have mostly focused on the isotropic limit, where rotating and counterrotating processes are locked together, leaving the broader symmetry landscape largely unexplored. Here we realize a programmable anisotropic quantum Rabi model in a superconducting processor, with independent control of the rotating and counterrotating couplings $(g_1,g_2)$ and of a transverse bias $\varepsilon$. Continuous anisotropy tuning, combined with a duality mapping, gives access to the full parameter space from the Jaynes-Cummings to the anti-Jaynes-Cummings limits. In the deep-strong-coupling regime, we show that anisotropy reconstructs the spectrum and turns complete collapse-revival dynamics into incomplete revivals even near degeneracy. With adiabatic state preparation and joint tomography, we resolve an anisotropy-induced ground-state parity switch, a crossing that has no analogue in the isotropic model. We further observe selective tunnelling associated with hidden symmetry in biased Rabi models and track its anisotropic displacement within the same device. These results establish a controllable route to engineering nonperturbative light–matter Hamiltonians, where symmetry, spectrum, and dynamics can be programmed independently.

We propose a Floquet-engineered cold atom realization of a parity anomaly inspired anomalous Hall staircase in a two dimensional $\pi$-flux lattice. The effective model hosts massive Dirac fermions generated by the combined action of a time reversal symmetry breaking Floquet mass and a static inversion breaking mass offset. An additional momentum dependent scalar displacement term shifts different Dirac sectors in opposite energy directions without modifying their Bloch eigenvectors. As a result, the Berry curvature contribution associated with individual massive Dirac sectors can be selectively occupied, allowing the anomalous Hall response to evolve stepwise as a function of chemical potential or scalar displacement term. Evaluating the full lattice Berry curvature integral, we find plateau-like responses near $0$, $e^2/2h$, and $e^2/h$, corresponding respectively to the activation of zero, one, and two effective massive Dirac sector contributions. We analyze the associated low energy Dirac theory, band topology, Berry curvature structure, and two parameter response maps, and discuss a possible realization using Raman-assisted tunneling, off-resonant Floquet driving, and auxiliary AC-Stark dressing in ultracold atomic optical lattices.

Accurate electronic excited states are essential for photochemistry, spectroscopy and non-adiabatic molecular dynamics, but high-level calculations often scale steeply and require prior knowledge of the target state's character or symmetry. Here we show that variational excited-state optimization can be reformulated as an iterated ground-state-like problem for a low-energy subspace of the electronic Hamiltonian. Applying this variational principle to non-orthogonal Slater determinants leads to EXIDOS, an automatic method for excited state calculations controlled only by the number of states and determinants per state. EXIDOS optimizes multiple excited states simultaneously, without explicit orthogonality constraints or imposed spin and point-group symmetries. Benchmarks against FCI and state-of-the-art quantum chemistry methods show chemical accuracy for a multitude of states in N$_2$ and CO, charge-transfer states in HCl, Rydberg states in NH$_3$, double excitations and extended potential-energy curves in C$_2$, and avoided crossings and conical intersections in ethylene. These results establish EXIDOS as a low-scaling, fully variational route to chemically accurate excited states.

When a quantum system passes through an unstable fixed point the local dynamics reduces to the inverted harmonic oscillator (IHO). It exponentially amplifies along one quadrature while squeezing the other, producing macroscopically extended quantum states from microscopic zero-point fluctuations. We realize this dynamics with a Bose-Einstein condensate on an AtomChip. Radio-frequency dressing flips the transverse harmonic confinement into an IHO. Through phase-space tomography we follow the full Wigner function of the evolving quantum state, observe sub-vacuum squeezing of 10.6(1.3) dB, and test coherent reversibility by time-reversing the IHO evolution. Matter-wave interference between the two daughter clouds confirms quantum coherence over timescales far beyond the initial expansion. Our experiment establishes ultra-cold atoms as a clean, controlled, many-body platform for unstable quantum dynamics opening a route to force sensing with time-reversal-based coherence certification and to analog studies of the amplification of quantum fluctuations in inflationary field dynamics.

Tight bounds on quantum sample complexity and quantum query complexity have been known for various computational problems in the literature, whereas tight bounds on quantum time complexity (i.e., the size of quantum circuits) remain unresolved. In this paper, we provide a framework to establish lower bounds on the quantum time complexity for testing permutation-invariant properties of quantum states, via a reduction from quantum sample complexity. As an application, we obtain a series of matching lower bounds when given sample access to the input quantum states, including: 1. The SWAP test due to Buhrman, Cleve, Watrous, and de Wolf (Phys. Rev. Lett. 2001) is time-optimal to estimate the purity $\operatorname{tr}(\rho^2)$ and the inner product $\operatorname{tr}(\rho\sigma)$. 2. The Shift test due to Ekert, Alves, Oi, Horodecki, Horodecki, and Kwek (Phys. Rev. Lett. 2002) is time-optimal to estimate the high-order functionals $\operatorname{tr}(\rho^k)$. 3. The productness tester for multipartite pure states due to Harrow and Montanaro (J. ACM 2013) is time-optimal. 4. The LMR protocol due to Lloyd, Mohseni, and Rebentrost (Nat. Phys. 2014) is time-optimal to implement the reflection operator about a pure state. 5. The samplizer due to Wang and Zhang (IEEE Trans. Inf. Theory 2025) is time-optimal for pure states. 6. The estimator for pure-state trace distance and fidelity due to Wang and Zhang (ICALP 2026) is time-optimal. To the best of our knowledge, this is the first method that allows us to systematically establish tight lower bounds on quantum time complexity.

Photon loss in optical channels fundamentally limits long-range reliable quantum communication. A standard approach to overcoming this limitation is the use of quantum repeater nodes, which typically perform experimentally demanding non-Gaussian operations. However, whether Gaussian repeater protocols can enhance quantum communication rates over bosonic attenuation channels has remained open. In this work, we prove a no-go theorem for Gaussian quantum repeaters in a quantum network. Specifically, we show that any repeater chain composed of Gaussian operations, homodyne measurements, and arbitrary classical communication cannot enhance the quantum capacity of a pure-loss attenuation channel beyond that achievable by direct transmission. Our proof introduces a generalisation of $k$-extendibility to a notion of fractional extendibility for Gaussian states and establishes some of its useful properties, thereby providing a powerful framework for analysing Gaussian quantum networks.

A strongly interacting chain of Majorana fermions realizes the supersymmetric tricritical Ising phase, with supersymmetry (SUSY) extending into a symmetry-broken ordered phase adjacent to the tricritical point. Although the signatures of SUSY at the tricritical point are well understood, their behavior in the gapped phase remains less clear. Here, we address two key questions: how SUSY manifests in the gapped phase and what is the nature of the excitations in this phase. We show that, in the thermodynamic limit, a conventional SUSY diagnostic that remains finite at the tricritical point diverges immediately on the Ising side, yet decays continuously to zero deeper in the gapped phase, signaling the persistence of SUSY. Focusing on the lowest excited states in the supersymmetric gapped regime, we find that the excitations consist of soliton-antisoliton pairs separating distinct ordered regions. Each soliton binds an emergent localized Majorana mode, and together the pair forms a nonlocal Dirac fermion. The occupation of this Dirac mode distinguishes eigenstates with even and odd fermion parity.