Papers

I present a short approach to discretizing continuous unitary evolution. It gives a correspondence in both directions between continuous unitary evolutions and products of unitaries in finite dimensions, and I use it to reduce discrete adiabatic theorems to continuous ones. At fine steps, holding truncated samples of a regulated Hamiltonian on a suitable finite partition gives an approximating product. Conversely, rounding the clock identifies a product of $T$ unit-step samples with a continuous evolution, up to two half-step phases. I bound its operator-norm distance from the original evolution by $O(1/T)$ through cancellation within each time step. This assumes bounded first and second derivatives, bounded spectral width, and eigenvalue differences bounded away from nonzero multiples of $2\pi$, uniformly in $T$. For a unitary walk with these derivative bounds, a fixed common free spectral arc supplies a Hermitian logarithm path satisfying the comparison hypotheses. Continuous simulation guarantees then transfer to the phase-corrected product, and continuous adiabatic bounds to the product itself, with an explicit additive $O(1/T)$ error and each adiabatic theorem's hypotheses retained. For positive definite quantum linear systems of condition number $\kappa$, this comparison and continuous adiabatic theory give a rescaled qubitized walk with $O(\kappa/\delta)$ steps for leakage $\delta$, matching the scaling previously obtained through a discrete adiabatic theorem. These products need no discrete adiabatic theorem.

Magic-state distillation is a major resource cost in fault-tolerant quantum computing. The cost of a magic-state factory depends strongly on its failure rate, which grows with the number of input magic states. Although symmetry-restricted methods have recently made distance two searches tractable, distance three and above have remained elusive at moderate input counts. We develop symmetry- and AI-assisted methods to search this regime. We present a unified binary-matrix formulation encompassing both triorthogonal-code and direct circuit searches. We show that distance at least three is equivalent to nonzero, pairwise distinct syndromes, separating the choice of syndromes from the search for compatible output gates. We restrict the syndrome search using group symmetry and language-model agents, followed by deterministic solving and independent verification. Our searches yield 699 factory classes, including 564 new ones. These include factories for pure-T states and factories with entangled outputs comprising combinations of T, CS, and CCZ magic states. The pure-T factories [[63, 11, 3]] and [[850, 128, 6]] achieve the lowest overhead exponents we know among protocols with at most 100 and 1000 inputs, respectively, with $\gamma = 1.589$ and $\gamma = 1.057$. Our [[1715, 287, 6]] factory, with $\gamma = 0.998$, is the smallest known pure-T factory with $\gamma < 1$. We also provide a context directory of search briefs and campaign notes with which readers can train their own agents and tailor the search to their requirements. With these results, we begin constructing an active, open-source repository of magic-state distillation protocols for the quantum community, supplemented by our methods and data, for the practical fault-tolerant quantum computing regime.

We present a generalization of the Mermin-Peres magic square game to $N$ players, in which the square is replaced by an $N$-dimensional hypercube. We show that the winning probability of the optimal classical strategy remains $8/9$ for all $N$, while for $N \ge 3$, a generalization of the quantum strategy for $N = 2$ achieves a winning probability between $1/3$ and $3/4$. This loss of quantum advantage for $N \ge 3$ is a consequence of monogamy.

We give a closed-form finite-dimensional construction of quantum channels with real algebraic entries exhibiting arbitrarily large violations of minimum-output Rényi entropy additivity uniformly above any prescribed positive Rényi order, using a different finite realization based on direct products of free groups and fixed-field high-girth graphs. More precisely, for every $p_0>0$ and $g>0$, we construct one channel and one Bell input for which the additivity gap is greater than $g$ simultaneously for all $p\in[p_0,\infty]$. With $r=\lceil2g\rceil$, the construction uses $15r$ output qubits and $O(r2^{30r}+r^2(1+p_0^{-1}))$ input qubits. Compared with the stated parameters of Shou and Gorshkov \cite{ShouGorshkov2026}, our construction uses fewer output qubits for every target gap and has a smaller asymptotic input-qubit bound as the gap grows with the positive cutoff fixed. At the von Neumann order, a separate specialization gives an explicit channel with gap greater than $1/1024$ using $37608898$ input qubits and $8$ output qubits.

Photon loss makes Gaussian boson sampling easier to simulate classically. A standard approach replaces the lossy input by classical light, and it stays accurate while the mean number of surviving photons grows no faster than the square root of the number $N$ of squeezed inputs at fixed squeezing and accuracy. We prove that this scale is a limit of replacement by classical light. For explicit interferometers, no state with a nonnegative Glauber–Sudarshan $P$ representation, Gaussian or not and however correlated, keeps the error in the photon count distribution small beyond this scale. We then surpass this limit by approximating the detection instead of the input. The sampler evolves the state exactly between detections and, after each detection, replaces the conditional state by a Gaussian with the same covariance. For every interferometer its total variation error is $O(N\eta^3)$ at polynomial expected cost, where $\eta$ is the photon survival probability. The mean surviving photon number can therefore grow as $N^{2/3}$ at fixed accuracy. A separate pair construction reaches $N^{3/4}$ when every input mode is equally squeezed.

What makes one quantum process more complex than another? We adopt an operational approach inspired by classical complexity science, which characterises structure through the memory required for causal generation. We develop a fully-quantum extension of computational mechanics for quantum space series: Correlated sequences of quantum outputs that do not return to interact with their generator. For stationary, memoryful quantum space series admitting finite-dimensional, primitive causal models, we show that any memory-minimal causal generator can be chosen to produce outputs isometrically, without a discarded environment. The resulting canonical matrix product state representation uniquely determines the irreducible memory required for generation. In particular, the minimum memory entropy is exactly the entanglement entropy across the past-future bipartition, giving entanglement a direct operational interpretation as irreducible memory for causal generation. The same structure determines the minimum memory dimension through the corresponding Schmidt rank. Within this class, we further show that the fundamental entropy rate vanishes, that causal generation is symmetric under time reversal, and that all memoryful processes possess infinite quantum Markov order with respect to arbitrary sharp measurements. These results establish an operational framework for quantifying intrinsic quantum structure, revealing deep connections between causal generation, complexity, memory, entropy, and entanglement.

We identify a structural mechanism by which perfect play in a nonlocal game requires and self-tests a specific non-maximally entangled state. To this end, we construct a Flagged Magic-Square game by extending the standard Magic-Square game with an additional “flag” outcome and two additional questions for each player. The game admits a perfect strategy using a state with Schmidt coefficients proportional to $(1,\sqrt{2},\sqrt{2},\sqrt{2},\sqrt{2})$. We give a direct algebraic proof that maximally entangled strategies have winning probability bounded away from one, independently of dimension. Moreover, the game self-tests this state, providing an example of a two-party pseudo-telepathy game that certifies a specific non-maximally entangled state. Our construction illustrates how adding suitable constraints to a rigid measurement geometry can enforce specific Schmidt ratios and provides a modular route to further self-tests based on other rigid pseudo-telepathy games. We establish a general game-to-channel reduction that transfers separations in the game model to one-shot zero-error communication over classical channels. Applied to the Flagged Magic-Square game, it yields a classical channel for which entanglement permits the zero-error transmission of ten messages in a single use, whereas any finite-dimensional maximally entangled resource permits at most nine. Thus, maximally entangled states are not a universally optimal entanglement resource for zero-error communication over classical noisy channels.

Photonic quantum technologies require the integration of high-quality quantum light sources with programmable photonic circuitry to enable on-chip quantum information processing. Semiconductor quantum dots have emerged as a leading platform for quantum light generation, yet their monolithic integration with cryogenic-compatible, programmable photonic circuitry remains challenging. Here we demonstrate a programmable quantum photonic platform that enables simultaneous control of highly coherent quantum dot-based single photon emitters and reconfigurable optical elements at cryogenic temperatures. System-level integration enables individual electrical and optical addressing of active components on a single chip, allowing their concurrent operation while preserving coherent non-classical light emission. We demonstrate multiple quantum-photonic functionalities, including pure single-photon generation, two-photon interference, and resonant transmission and reflection measurements of integrated emitters. These results mark a step from isolated quantum-optical devices towards programmable quantum-photonic hardware platforms capable of combining coherent quantum emitters with large-scale photonic functionality.

The Variational Quantum Eigensolver (VQE) has become a central hybrid quantum-classical method for addressing electronic structure and materials science problems on near-term quantum hardware. As researchers across physics, chemistry, and quantum information engage with VQE, they encounter a wide range of algorithmic choices, including problem encoding, ansatz construction, classical optimization, and measurement strategies to choose from. This article provides a structured overview of these components and discusses practical factors that influence VQE performance in real settings, such as noise characteristics, available error-mitigation techniques, and hardware-dependent circuit considerations. Drawing partly on our early experiences, we highlight aspects that may be especially relevant for newcomers and outline common challenges observed in practical workflows. Our aim is to offer an accessible entry point for researchers approaching VQE-based quantum simulation and to support informed decision-making as the method and underlying hardware continue to evolve, which we support by discussion of examples from physics and quantum chemistry.

We derive a quantum master equation in Lindblad form for the open quantum Rabi model in the perturbative deep strong coupling regime, where the spectrum is close to degenerate and harmonic. The Lindblad form is obtained by combining secular and singular-coupling approximations, working in a Schrieffer-Wolff transformed frame. We benchmark our equation against a Bloch-Redfield one, analyzing the time-evolution and steady state properties of several observables and find excellent agreement. Analytical results are obtained in limiting cases.

We study semi-Clifford and generalized semi-Clifford structures in the Clifford hierarchy as a function of hierarchy level $k$ and qubit number $n$. We show that $\mathcal{C}_k(n)$ is semi-Clifford if and only if $k\le2$, $n\le2$, or $k=3$ and $n\le6$. We also establish that $\mathcal{C}_k(n)$ is generalized semi-Clifford when $k\le4$ or $n\le3$ and construct counterexamples when $k,n \geq 5$. For $n=4$ and $k\ge5$, we show that every gate defined over $\mathbb{Q}(i)$ up to a scalar is generalized semi-Clifford, reduce the general case to a single level, and propose a strategy to prove our conjecture that $\mathcal{C}_k(n)$ is generalized semi-Clifford if and only if $k\le4$ or $n\le4$. Lastly, we go beyond this structure by introducing $n_c$-generalized semi-Clifford gates, which we show are exactly the gates of the form $\sum_x|\pi(x)\rangle\langle x|\otimes V_x$ up to Clifford gates on both sides, where $\pi$ permutes the computational basis states of $n_c$ control qubits. We conjecture that for $k\ge3$ every gate in $\mathcal{C}_k(n)$ has this form for some $n_c\ge1$ with every $V_x\in\mathcal{C}_{k-3}(n-n_c)$, refining the conjecture of Zeng, Chen, and Chuang.

We develop a combinatorial and Bayesian framework to quantify the information gained by increasing the local photon-number resolution of multiplexed detection systems based on superconducting nanowire single-photon detectors (SNSPDs). Motivated by recent studies that attribute photon-number resolving capabilities to a single SNSPD overcoming the typical on/off detection mechanism, we generalize the existing formulation for the binary devices by deriving the probability response tensor of multiplexed systems based on SNSPDs with an arbitrary number of resolvable states. We include finite efficiency through binomial loss convolution and, separately, assess the impact of dark counts. From this response tensor we derive a generalized N-photon detector fidelity, a Bayesian photon-number reconstruction, and the corresponding reconstruction fidelity. We particularize this formulation to study 2-, 3- and 4-state multiplexed systems with different numbers of detectors and show that increasing local photon-number resolution systematically improves both detector fidelity and Bayesian photon-number reconstruction. This substantially relaxes the quadratic scaling between detector number and resolvable photon-number required by purely binary multiplexed arrays. These results provide a quantitative value-of-information assessment for multi-state photon-number-resolving detector arrays.

Unstructured database search is a fundamental problem that requires finding one or more elements satisfying a specific property within a set of candidates. While Grover's algorithm provides a quadratic speedup for finding a marked element when the number of solutions is known, finding all solutions when their number is unknown presents additional challenges. In this paper, we thoroughly analyze this problem by considering all the different regimes of combinations of classical, Grover and generalized fixed-point quantum search instances. We unify these into an adaptive Bayesian approach that maximizes the expected success probability per unit execution time at each searching instance. For a problem with a known number of solutions, much lower than the database size, we prove that our proposed approach is asymptotically optimal within the considered search model. Furthermore, we prove that for any probability distribution characterizing the likely number of solutions, in regimes where the classical verification time is at most 25% of the quantum amplitude amplification time, hybrid classical and Grover approaches are preferred to generalized fixed-point. Outside of this regime, we derive an upper bound on the maximal improvement achievable by fixed-point search compared to the best Grover-based score. Additionally, we determine the optimal transition point between classical sampling and quantum searching using an integral approximation of the probability distribution of the number of solutions. The analytical results are also supported by numerical simulations of the proposed algorithm and by comparisons between the generalized fixed-point and Grover-based search policies.

We study leakage from Shamir secret sharing when each device uses its share to produce one qubit from an initial quantum resource independent of the secret and sharing randomness. We prove exponentially small trace distance between the leakage states of any two secrets, when reconstruction requires a sufficiently large fraction of the shares, for fixed stationary chains satisfying an upper operator mixing condition and for resources generated by fixed finite quantum memories with primitive transfer channels. These guarantees permit arbitrary extensions of the device marginal as adversary side information and hold uniformly over prime fields larger than the number of shares. For independent device–reference pairs, which provide the quantitative input to the argument, we determine the optimal exponential base when reconstruction requires all shares: $2\sqrt2/\pi$ for a qubit and $2/\pi$ for a classical bit, in both cases allowing arbitrary finite references. A comparison of selected marginals with product states converts the bounds for independent device–reference pairs into security guarantees for the correlated resources.

The concept of subspace designs was introduced by Guruswami and Xing (STOC'13), and explicit constructions were given by Guruswami and Kopparty (FOCS'13). These are families of subspaces that have small intersection with any given subspace of a fixed dimension. We introduce robust subspace designs. Informally, these are a quantitative extension in which we demand that not too many subspaces of the family contain directions that lie close to any given subspace of a fixed dimension. We give a probabilistic construction of such a robust subspace design of polynomial size, as well as a non-trivial explicit construction of superpolynomial size. Our main application of this new concept is a quantum space-bounded variant of the Valiant-Vazirani theorem (Theor.Comput.Sci.'86), which shows that restricting $\mathsf{NP}$-complete problems to instances with at most one accepting witness preserves hardness under randomized reductions. For quantum witnesses, the analogous quantity is the dimension of an accepting witness subspace. We use our probabilistic construction of robust subspace designs to isolate a unique witness for space-bounded quantum Merlin-Arthur protocols with perfect completeness and an acceptance gap outside their perfectly accepting subspace. As further applications, we give a randomized reduction of well-conditioned nullity testing to space-bounded quantum Merlin-Arthur protocols with perfect completeness. Using a similar idea, we find that ordinary subspace designs allow us to recover the classical $\mathsf{C_= L}$ containment of Allender, Beals, and Ogihara (STOC'96) for general nullity testing through a simpler proof.

Advanced levitation optomechanics in the quantum regime requires sophisticated quantumengineered protocols operating at shorter length and time scales, demanding an increasing control over both optical and electrical potentials. Integrated chip-scale platforms offer a natural route toward such control. Here, we demonstrate optical levitation in vacuum using a miniaturized hybrid electro-optical metalens. Motion control is achieved using a high numerical aperture metalens combined with electrical active feedback using planar electrodes, enabling cooling to low phonon occupations. Reheating measurements enable us to rule out any significant influence from electric field noise; an encouraging result for the future development of on-chip levitation platforms operating close to surfaces. This compact integrated platform facilitates the precise manipulation and control of levitated nanoparticles while laying the ground toward exploiting the full capacity of metaoptics to engineer complex optical potentials, marking a significant step forward in technologies for quantum levitation optomechanics.

Gauge theories describe fundamental interactions in the standard model of particle physics and build effective theories in condensed matter physics. Being notoriously hard to simulate, these theories are commonly regularized as lattice gauge theories which can be evaluated with high precision through Monte Carlo algorithms or variational methods. However, Monte Carlo algorithms are not applicable in all regimes due to the sign problem; while variational methods, quantum and classical alike, only give upper-bounds on the ground-state energy. Their precision crucially depends on the chosen ansatz. Here, we present a framework based on a hierarchy of semidefinite programs to yield increasingly good lower-bounds on the ground-state energy and propagate these bounds to extended observables like Wilson loops and mesonic strings. We demonstrate the numerical capabilities by applying the algorithm to a (1+1)-dimensional $\mathbb{Z}_2$ theory with dynamic fermionic matter and its pure-gauge version in (2+1)-dimensions. In both cases, we obtain certified intervals for the ground-state energy. For a one-dimensional system with 129 sites, the certified interval has a relative spread of $0.04\%$. For a two-dimensional system with 97 sites (corresponding to a $7 \times 8$ lattice), the relative spread is $2.08\%$. Beyond energy estimates, the proposed method provides rigorous bounds on both short- and long-range observables such as Wilson loops over multiple plaquettes and the magnitude of the mesonic string. The method can be both used as a computational microscope into many-body physics and a way to certify results of quantum simulators.

We develop a discrete adiabatic framework for Gibbs-state preparation in classical and quantum optimisation algorithms. For finite time-inhomogeneous reversible Markov chains, we derive a tracking theorem that bounds the distance from the evolving distribution to the instantaneous stationary state by combining two effects: contraction of previously accumulated error by the Markov dynamics and the new error generated as the stationary distribution changes from one step to the next. For Gibbs paths, this leads to explicit step-complexity bounds and to gap- and fluctuation-adapted schedules controlled by the Markov-chain spectral gap and the energy-fluctuation scale $V(\beta)=\sqrt{\operatorname{Var}_{\pi_\beta}(E)}$. In the weak-damping regime, the resulting schedule takes the form $\dot{\beta}\propto\delta(\beta)/V(\beta)$. We then apply the discrete quantum adiabatic theorem to temperature-dependent Szegedy quantum walks. The quantum-walk eigenphase gap satisfies $\Delta_w=\Theta(\sqrt{\delta})$, where $\delta$ is the spectral gap of the underlying Markov chain. By analysing the finite-difference terms entering the theorem, we show that this square-root spectral amplification translates into a quadratic improvement in the gap dependence only for suitably gap-adapted schedules. Under the corresponding regularity conditions, the quantum adiabatic cost scales as $O(\delta_{\min}^{-1/2})$, compared with the classical $O(\delta_{\min}^{-1})$ relaxation scale.

Frequency crowding, the close spacing of qubit transitions, limits superconducting quantum processors through crosstalk, leakage, and spectator dependent errors. We introduce a Hamiltonian based framework that maps two- and three-body collision mechanisms onto a Max-k-Cut problem on qubit frequency allocation. In order to make larger lattices tractable, we introduce a cluster-stitching protocol that decomposes larger lattices into overlapping subgraphs and reconciles their local frequency assignments into globally consistent configurations. We tested our proposed framework across multiple qubit architectures to suppress dominant collision penalties by revealing a hardware residual crosstalk. We benchmark digitized counterdiabatic QAOA (DC-QAOA), standard QAOA, and simulated annealing. Counterdiabatic terms improve QAOA optimization near steep collision penalties, while simulated annealing achieves the lowest costs on the tested instances. These results indicate that our hardware-aware optimization connects microscopic interaction physics to processor-level frequency planning. These results enable a systematic solver for benchmarking of scalable software hardware co design.

Measurement-based quantum computation (MBQC) relies on entangled graph states, yet existing remote state preparation (RSP) protocols prepare only separable states, requiring subsequent entangling gates on the remote server. Here, we introduce Remote Graph State Preparation (RGSP), a framework that prepares arbitrary graph states directly from a single high-dimensional photonic qudit. By encoding multiple qubits and their graph connectivity into the photon's structured phase profile, RGSP can reduce or, for small computations, completely eliminate the need for server-side entangling operations among qubits. We show that under a reasonable noise model the resulting state fidelity is independent of the graph topology. Under cumulative fiber phase drift, we demonstrate that this fidelity is significantly enhanced by a “highest-weight-first” mode reordering strategy. Finally, we show that RGSP enables reduced-SWAP universal blind quantum computing on arbitrary topologies, reducing qubit overhead e.g., for a six-qubit Quantum Fourier Transform from $420$ RSP qubits with a standard brickwork topology to $48$ RSP qubits. These results establish RGSP as a resource-efficient, topology-invariant primitive for quantum-secured cloud computing.

Edge magnetoplasmons (EMPs) provide a platform for probing chiral charge dynamics and nonreciprocal microwave transport in topological quantum materials. However, detecting small perturbations to EMP propagation remains challenging because their signatures in conventional microwave scattering measurements can be weak. Here, we investigate microwave-photon-induced perturbations of EMP transport using a quantum anomalous Hall topological circulator. Pump–probe measurements reveal a strongly frequency-selective response: while microwave irradiation substantially modifies the EMP transmission at several pump frequencies, the transmission remains nearly unchanged at selected frequencies, including 4 and 7 GHz. We further exploit the non-Hermitian mode hybridization of the coupled EMP-resonator system to probe the response near an exceptional point (EP). The pump-induced change in transmission magnitude near the EP is approximately twice that observed away from the EP, demonstrating an enhanced microwave response to perturbations. These results reveal the interplay among chiral EMP transport, microwave-photon-induced perturbations, and non-Hermitian dynamics, and demonstrate the potential of topological circulators as a promising platform for enhanced microwave spectroscopy and sensing.

Intermediate measurements let quantum computations discard information and reuse their workspace. Deferring all measurements can require storing their entire history, which need not preserve logarithmic space. Fefferman and Remscrim proved that measurements can nevertheless be eliminated with two-sided bounded error, and asked whether the same holds with one-sided error [FR21]. We prove RQL{\Gamma} = RQUL{\Gamma} for the standard gate set {\Gamma} = {H, T, CNOT}, preserving polynomial time, logarithmic space, and exactly zero acceptance on no-instances. Our proof extends the density-matrix doubling method of Girish, Raz and Zhan [ GRZ21 ] to general channels, including resets and classical memory. We also prove measurement elimination for broader finite gate sets with exact inverses, including suitable gates with transcendental entries, and establish gate-set independence for a specified family of algebraic gate sets. A separate history-checking construction proves QMAL1,G = QUMAL1,G under explicit gate assumptions: measurements can also be eliminated from logarithmic-space quantum verification while preserving perfect completeness

The mean Hawking flux does not determine how quantum stress fluctuations perturb a black-hole geometry. That information resides in field correlations, including vacuum contributions absent from the outgoing luminosity. Here we connect the complete exterior Unruh Wightman function to a finite-band stochastic reconstruction of Schwarzschild geometry. We retain the incoming vacuum and both outgoing frequency branches, form the connected stress covariance before angular projection, and propagate its monopole through a density-driven radial response. A shared Gaussian reconstruction then resolves how the value and derivative of the lapse control different geometric observables. For the specified covariance and noise amplitude, 2,200 realizations give relative widths of 0.0185 for the local horizon radius and 0.0483 for the surface-gravity temperature parameter, consistently across histograms and reconstruction checks. Covariance derivatives explain this unequal sensitivity. The construction separates the quantum-state input from the gravitational closure and spatial sampling assumptions, providing a reproducible finite-resolution description of how Hawking-field correlations affect horizon positions and surface-gravity statistics.

Trapped particles in hollow-core fibers enable long-range sensing, though advanced control of their in-fiber motion, such as multimodal cooling and squeezing, remains challenging. Here, we present optical interference-based adaptive techniques for controlling the motion of a fringe-trapped silica nanoparticle inside a fiber. After feedback-cooling its axial and radial motion, we induce axial delocalization (position anti-squeezing) via two complementary approaches. First, non-adiabatic fringe suppression expands the position variance by 11.83 ($\pm$0.7) dB to that of the initial cold-state while retaining Gaussian statistics. Second, multi-pass particle positioning at dark fringes increases the delocalization to 13.23 ($\pm$0.5) dB relative to the cold-state's variance via dark inverted optical potentials, in agreement with our Wiener stochastic model. Stronger delocalization produces non-Gaussian states of motion. Unlike prior inverted-trap implementations, our method requires neither auxiliary optical traps nor charged particles in Paul traps. Our results demonstrate fringe-trapped particles in hollow-core fibers as a versatile platform for long-range sensing and macroscopic quantum physics.

The manipulation of non-Abelian anyons is a foundational ingredient for topological quantum computing and underlies topologically protected quantum memories. Here we analyze a quantum-impurity-based protocol for braiding non-Abelian anyons. Exploiting mobile impurities with addressable internal spin states, we provide a concrete protocol to experimentally measure the matrix elements of the $R$ and $F$ matrices that characterize the non-Abelian statistics of anyons. In particular, focusing on the case of Ising and Fibonacci anyons, we illustrate how the anyonic nature of the excitations emerges directly in the Ramsey interferometer we propose. Building on this framework, we further introduce a conventional-to-topological qubit encoder to transfer quantum information from conventional flying qubits into a topologically protected quantum memory.

We develop a finite-temperature field-theoretical description of the Casimir interaction between two perfectly conducting boundaries with the intervening gap filled by a two-component quantum Boltzmann plasma embedded in a homogeneous dielectric background. The quantum motion of the charged particles is represented by imaginary-time worldlines, while the electromagnetic field is treated in the Gaussian approximation. The resulting partition function contains distinct longitudinal and transverse response contributions and an additional quantum-induced source term with no classical counterpart. In the classical limit the theory reduces to the usual Casimir-screening picture: the static longitudinal mode is Debye screened, whereas the transverse electromagnetic sector is unaffected by classical mobile charges. Finite thermal de Broglie wavelengths modify the nonzero Matsubara response and produce the leading quantum correction to the force. In the static long-wavelength limit, the longitudinal dielectric function has, through the leading quantum correction, the same expansion structure as the Lindhard response of a degenerate electron gas under the correspondence $k_{TF}\leftrightarrow\kappa_D$ and $k_F\leftrightarrow\lambda_{dB}^{-1}$, while the static transverse response reproduces the leading high-temperature Landau orbital diamagnetic susceptibility.

We give quantum algorithms that estimate the log partition function of an $n$-qubit quantum Hamiltonian to additive error $\epsilon$ with Heisenberg scaling, while minimizing calls to thermal-state purification preparation. The input is a block encoding of $H$, unitaries preparing thermofield-double states at chosen inverse temperatures, with their inverses and controlled versions, and an adaptive slowly-varying cooling schedule. The system-size bounds below assume $0\preceq H\preceq hI$ with $h=O(n)$ and block-encoding normalization $\alpha=\Theta(h)$. For constant inverse temperature, we show that such a schedule of length $O(\sqrt n)$ always exists and can be generated from overlap estimates with $\widetilde O(\sqrt n)$ further preparations. Given such a schedule and classically chosen temperatures, we estimate the log partition function with $\widetilde O(n^{5/4}/\epsilon)$ expected calls to state preparation and to the block encoding, improving by $n^{1/4}$ on non-adaptive strategies. To achieve our result, we use a recursive-doubling identity that expresses each schedule increment as a weighted sum of logarithms of thermofield-double overlaps and of short imaginary-time steps implemented by quantum singular value transformation combined with previously developed variance reduction techniques. If thermofield doubles can be prepared controlled on a temperature register, a quantum inverse-binomial log estimator combined with quantum mean estimation reduces both query counts to $\widetilde O(n/\epsilon)$. We show that the latter scaling is optimal in block-encoding queries up to polylogarithmic factors and discuss end-to-end complexities for one-dimensional partition-function estimation.

Reliable verification of squeezed-light sources is essential for photonic quantum technologies. High-dimensional quantum optical networks demand single-mode, pure squeezed states which, in principle, can be generated through careful engineering of parametric down-conversion-based (PDC) sources. However, due to the imperfections of optical components, the generated state is never pure and commonly contains internal mode structure. Existing characterisation techniques, based on either joint spectral intensity or normalized second-order correlation functions, work under the assumption that the probed state is pure, and therefore can result in incomplete or misleading assessment of the source quality. Here, we develop a device-agnostic characterisation framework for PDC-based sources with distinguishable signal and idler fields. Treating the source as a black box producing a mixed multimode Gaussian state, we find a lower bound for the state purity, which can be experimentally determined via mode-unresolved measurements. Our approach enables a holistic assessment of realistic squeezed-light source quality without requiring a detailed model of the nonlinear device and its surrounding optical network, providing practical benchmarks for optimizing sources for state-of-the-art quantum applications.

Multipartite systems of high-dimensional particles can host forms of quantum entanglement inaccessible to qubit systems. A particularly fascinating class is formed by the fully antisymmetric states, also known as supersinglets, which possess a remarkable symmetry: they are invariant under arbitrary collective local unitaries. Here, we explore their entanglement properties and establish their quantum information applications. Using convex optimisation, we show that central entanglement features of supersinglets are remarkably robust to noise, substantially surpassing the robustness of several paradigmatic entangled states under certain relaxations. We then develop witness methods, based on collective-spin or randomised measurements, that certify both the depth and dimensionality of their entanglement. Finally, we identify supersinglets as a natural resource for high-dimensional gradient sensing and prove that they enable Heisenberg scaling. Together, these results reveal supersinglets as an exceptionally robust and versatile class of multipartite entangled states, combining striking symmetry and strong entanglement with concrete potential for quantum sensing.

Near-term quantum natural language processing (QNLP) experiments often run on classical simulators, so simulator cost is part of the field's practical compute burden, yet accuracy tables do not show it. We measure that cost for a variational quantum classifier (VQC) on binary SST-2 sentiment classification, using PennyLane's state-vector simulator over a controlled grid of 27 configurations: three balanced training-set sizes (N = 200, 500, 1000), three qubit counts (4, 6, 8), and three circuit depths. Each VQC is compared with logistic regression on the same PCA-reduced input; full TF-IDF logistic regression gives an uncompressed reference. The VQC beats its matched baseline in 6 of 27 single-seed comparisons. After reruns at two further seeds, only 1 of these 6 keeps a positive mean advantage larger than its paired seed-to-seed variability, and paired tests on the fixed validation set do not establish it. VQC training is 886-21,127 times slower in measured wall-clock time than the matched classical fit (median 3,158 times); going from 4 to 8 qubits roughly doubles simulator time, and within the tested range per-step cost is well approximated by a linear function of the parameter count. CodeCarbon energy and CO2 estimates are secondary: they imply an almost constant power of about 41 W, so they add little beyond runtime, and we do not build an energy ratio from them. The study is narrow (one dataset, representation, ansatz, simulator, and CPU environment) and is a reproducible feasibility measurement, not a general verdict on QNLP.