Papers

Quantum neural networks (QNNs) have shown promise in leveraging quantum computation for machine learning tasks. Utilizing multiple identical photons as input, multi-photon quantum neural networks (MPQNNs) have the potential to enhance the expressivity through increasing the photon number. However, how precisely the expressivity of an MPQNN is affected by an increase in photon number, and whether it can be infinitely enhanced by increasing the photon number, remains unexplored. In this work, we quantitatively estimate the expressivity of this model by deriving upper bounds on approximation error in two cases. In the case of a fixed observable, there exists a threshold that scales linearly with the mode number. Below the threshold, the expressivity of an MPQNN can be enhanced polynomially by increasing the photon number. Above the threshold, however, increasing the photon number does not affect the expressivity. In the case of a trainable observable, the expressivity can always be enhanced polynomially by increasing the photon number. These findings are then validated by numerical simulations. Our work elucidates the performance enhancement of multi-photon quantum feature in QNNs, as well as its limitations, offering guidance for leveraging multi-photon advantages in quantum machine learning.

Generalized measurements can be implemented projectively after enlarging the Hilbert space, but this dilation changes the available local dimension. We construct a Bell functional with rational coefficients that separates the two measurement models at local dimension two. An explicit three-outcome qubit positive-operator-valued measure with rational matrix entries attains $2\sqrt2+1/100$. On the other hand, all qubit-projective strategies are bounded by $2\sqrt2+\sqrt5/250+\sqrt2/32400$, giving a fully analytic certified gap greater than $1/1000$. To our knowledge, this is the first fully analytic Bell-functional separation between qubit POVMs and qubit projective measurements over arbitrary shared two-qubit states. Lean certificate for the separation theorem is provided for completeness. Separately, an exact level-3 noncommutative sum-of-squares certificate proves that the explicit qubit strategy attains the unrestricted finite-dimensional tensor-product quantum optimum.

Neutral-atom quantum computers can now arrange atoms in three-dimensional tweezer arrays, yet every existing compiler assumes a flat geometry. We present Piqasso, a compiler that exploits the vertical axis by stacking storage, entanglement, and readout into distinct layers. Its pipeline pairs an analytical placement respecting axial-clearance optics with a router that brings gate partners together via short vertical hops—bypassing in-plane crossing conflicts through out-of-plane detours—and a multi-AOD scheduler that parallelizes transport across focal planes. On 34 circuits, Piqasso reduces atom transport distance by 2.1$\times$ over a state-of-the-art planar compiler, yielding up to 7.3$\times$ faster execution, 2.2$\times$ higher movement fidelity, and 1.8$\times$ fewer serialized transport rounds, with all gains widening at scale.

The quantum capacity of a noisy channel quantifies the maximum rate at which quantum information can be transmitted reliably. For general channels, its evaluation requires an optimization over arbitrarily many channel uses. Degradable channels form a central exception: their capacity is given by the single-letter coherent information, while antidegradable channels have zero capacity. Nevertheless, even for these fundamental classes, it has remained open whether communication above capacity becomes possible when a fixed non-maximal error is tolerated. Here we resolve this problem by proving an exponential strong converse for every finite-dimensional degradable and antidegradable channel: at any rate above capacity, the fidelity of every coding scheme decays exponentially with the number of channel uses. As an immediate consequence, we establish the first all-code exponential strong converse for the quantum erasure channel throughout its full parameter range, strengthening previous results that applied only to almost all codes. We also show that exponential strong-converse bounds are preserved under receiver post-processing. This yields efficiently computable semidefinite-programming bounds for arbitrary finite-dimensional channels, improved bounds for Pauli channels, and an exact exponential strong converse for a nondegradable multilevel amplitude-damping family.

The pseudo-quantum representation re-encodes a finite, irreducible, reversible continuous-time Markov chain with $M$ states as a complex-orthogonal flow on a doubled space of dimension $2M$. After uniformisation, a square-root gauge, a doubling of the state space and a diagonal unitary twist, the chain generates an entire one-parameter group $W_z = e^{zK}$ with $z$ complex, and this single group is the object of the paper. Its real slice, $z$ real, reproduces the stochastic semigroup exactly through an explicit decoding whose probabilistic meaning is the parity of the number of ticks of the uniformised chain. Its imaginary slice, $z = i\theta$, is a finite-dimensional unitary quantum system. The chain and the quantum system are therefore not two analogous models but two restrictions of one entire representation. The setup also produces, with no further input, a pseudo-Schroedinger equation, a bilinear von Neumann equation for a complex-symmetric pseudo-density, and a pseudo-Bloch vector equation on a non-compact quadric. We develop the construction from first principles and work out one model completely, the usual symmetric Ehrenfest urn. Its gauged generator equals $(2/n) J_x$, the spin-$n/2$ operator, its relaxation modes are Lorentz boosts, and its imaginary slice is a depth-one quantum circuit whose Born distribution is the classical urn law under the clock $\theta(t) = \arccos(e^{-2t})$. The same clock identifies the Fisher-Rao lift of the urn trajectory with a rigid spin-coherent-state orbit. This is a preliminary simplified version of a longer paper. It treats only finite state spaces and only the symmetric Ehrenfest urn, and it previews without proofs the asymmetric urn, two queues, the symmetric simple exclusion process and the stochastic Ising model. Appendix primers make the quantum, geometric and information-theoretic language self-contained.

Sequential strategies in hypothesis testing use a variable number of measurement rounds, allowing a decision to be made as soon as the observed data provide a prescribed level of error tolerance. Although sequential testing is well established for a discrete set of hypotheses, extending this framework to a continuous parameter space poses additional challenges and has remained largely unexplored. In this article, we introduce sequential parameter testing, a framework for determining an unknown parameter up to a prescribed tolerance by ruling out sufficiently distant competing values with a target error tolerance. We clarify its operational distinction from conventional parameter estimation and develop sequential tests for continuous families of hypotheses, introducing the twin-peaks test as a natural and computationally efficient analog of sequential likelihood-ratio testing. We apply the framework to two paradigmatic quantum tasks: testing the phase and the purity of a qubit. For phase testing, we show numerically that adaptive projective measurements achieve the same average sample cost as collective covariant measurements with a fixed number of copies. For purity testing, local measurements are optimal, and sequential parameter testing yields significant average sample savings over fixed sample-size protocols. Our results establish parameter testing as an operationally meaningful framework for resource-efficient certification tasks involving continuous parameters.

Artificial intelligence has been transformed by deep neural networks, yet the search for new learning architectures continues. Quantum machine learning offers one such direction, and hybrid quantum neural networks, which combine classical neural-network components with quantum information processing units, have emerged as a practical framework for near-term quantum technologies. However, the rapid development of the field across diverse architectures, benchmarks and hardware assumptions makes it difficult to assess the utility of various proposals, identify where genuine advantages may arise, and determine how practitioners can use these models. While recent benchmarks caution that such gains have not yet been demonstrated at scale, theoretical work has identified tasks on which quantum models hold provable advantages, and hybrid approaches have delivered promising results on practical problems using deliberately compact quantum components and substantially fewer trainable parameters. Here, we review hybrid quantum neural networks for the machine-learning and quantum-machine-learning communities. We summarize their main theoretical and methodological foundations, survey some of the most promising architectures developed so far, and examine their implementation challenges and reported performance. By consolidating these perspectives, this review provides a structured view of the state of the field and helps identify promising paths for future research and application-driven development.

A set of pairwise non-orthogonal quantum states cannot be perfectly discriminated, and this remains true even when one bit of classical partial information is available prior to the measurement. Contrary to the usual intuition that earlier information is at least as valuable as later information, we show that the same bit can be more useful when it arrives after the measurement. We present a framework for state discrimination in which the sender provides classical information in response to a request from the receiver, which we refer to as a query. In some cases, pairwise non-orthogonal states can be perfectly discriminated when the query is allowed to depend on the measurement outcome. We give a general method for finding the optimal strategy in this setting, which turns out to be the standard minimum-error discrimination problem for an auxiliary ensemble.

Efficient preparation of Dicke states and, more generally, permutation-symmetric states is important for quantum metrology, quantum networking, and collective quantum information processing. Measurements and classical feedforward enable low-depth preparations of these states, with a cost of ancillary qubits. In this work, we introduce an exact constant-depth adaptive preparation protocol for arbitrary Dicke-$(n,k)$ states and further symmetric states. We first provide a protocol preparing the uniform subset superposition state, as a primitive, using constant-depth adaptive circuit with $O(k^2\log^2 n)$ ancillary qubits and success probability at least $1/k$. This yields an exact, probabilistic, constant-depth Dicke-state preparation protocol using $O\left(n^2+k^2\log^2 n+kn\log n\log\log n\right)$ ancillary qubits. Parallel repetition suppresses the failure probability exponentially without increasing the quantum depth. Moreover, the uniform subset superposition state is also of independent interest as the uniform vertex state of the Johnson graph and as the compact uniform subset state appearing in quantum-walk and topological-data-analysis algorithms. We further establish a general lifting framework that coherently combines clean unitary Dicke-state preparation circuits to prepare arbitrary symmetric states with only polynomial ancillary overhead. Combined with recent constant-depth unitary Dicke-state constructions, this gives an exact constant-depth preparation protocol for arbitrary $n$-qubit symmetric states using $O(n^3\sqrt{\log n})$ ancillary qubits.

Quantum relative entropies play a fundamental role in quantum information theory. In the classical setting, Rényi relative entropies constitute, up to linear combinations, the most general class of relative entropies, naturally motivating the search for their minimal and maximal quantum extensions. The minimal extension is known to be the reverse sandwiched Rényi relative entropy for $\alpha\in[0,1/2)$ and the sandwiched Rényi relative entropy for $\alpha\geq 1/2$. In contrast, the maximal extension had previously been identified only for $\alpha\in[0,2]$, where it is given by the geometric Rényi relative entropy. In this work, we complete this characterization by proving that for $\alpha>2$, the maximal extension is given by the $\alpha$-$z$ Rényi relative entropy with $z=\alpha-1$. As an application, we determine when an energy-incoherent state can be transformed into an energy-coherent state by a Gibbs-preserving operation assisted by an uncorrelated catalyst, thereby fully characterizing the coherence-generating power of this class of operations in the catalytic setting.

When does a noisy quantum sampler yield an end-to-end polynomial-time optimization algorithm with performance guarantees? Building on finite-depth and finite-shot guarantees for Constraint-Enhanced QAOA, we show that inverse-polynomial ideal probability on the optimal set, together with independent sampling, polynomial-time feasibility repair, and scoring, produces an exact-hit fully polynomial randomized approximation scheme, which we call an FPRASq. This guarantee survives device noise within an instance-dependent window. For effective circuit depth linear in the product of layer count and problem size, preserving an inverse-depth fraction of the ideal optimal mass increases the required shot complexity by one power of the problem size. Beyond this window, deterministic repair guarantees feasibility and provides an instance-dependent approximation guarantee whenever the induced objective inflation is controlled. The resulting NP-HQ algorithm fits the Chen-Cotler-Huang-Li oracle model. On any NP-hard kernel-admissible promise family, reproducing its inverse-polynomial optimal overlap with a polynomial-time classical sampler would imply that NP is contained in BPP, even with identical repair and perfect access to the constraint structure. Thus, the separation lies in generating the sampling distribution. We further introduce Heavy-Hitter QAOA, which preserves these conditional guarantees while reducing the retained candidate set and classical post-processing cost by one power of the problem size. Hardware experiments on IBM Eagle r3 processors cover instances with up to one hundred logical variables and match or improve every tested QOptlib reference tour.

Estimating multiple unknown parameters simultaneously is essential for practical quantum sensing. However, it faces a fundamental challenge: the optimal strategy for estimating one parameter is often incompatible with that for another, making it impossible to simultaneously achieve the ultimate precision limits for all parameters. Here we develop a general and efficient computational framework that jointly optimizes probe states, control operations, and measurements across different strategy families, including parallel, sequential, and those with indefinite causal order. Our approach provides exact semidefinite-program formulations for several precision bounds, including the Holevo, Nagaoka-Hayashi, and quantum Cramér-Rao bounds. We demonstrate the capabilities of the framework in multiparameter magnetometry and frequency estimation, identifying optimal protocols within each class and revealing a strict hierarchy among the achievable performances of different classes in the multiparameter regime. The framework also directly incorporates resource constraints, such as energy budgets, enabling systematic investigation of experimentally realistic sensing scenarios. Furthermore, we develop a finite-memory optimization method for sequential strategies with restricted ancillary-memory dimension. By decomposing the protocol into initial probe preparation and intermediate control operations, this method provides a practical route to designing resource-constrained sequential sensing schemes. Our work establishes a versatile computational tool for determining fundamental precision limits and designing optimal quantum-sensing protocols in complex multiparameter settings.

The scalability of fault-tolerant neutral-atom quantum computers is constrained by the latency of shuttling with optical tweezers, imposing a stringent trade-off between qubit overhead and circuit depth in quantum algorithm compilation. Here we propose a hardware-efficient, shuttling-free architecture that achieves all-to-all connectivity. Remote Rydberg atoms are resonantly entangled through a microwave “Cat Bus”—a cavity mode autonomously stabilized in a bosonic cat state. The Cat Bus natively supports the highly parallelized execution of one-to-many $\mathrm{CZ}^n$ gates with exponentially suppressed crosstalk. We derive the resulting cat–atom error channel from the underlying interactions and physical constraints. For fault-tolerant operation, we develop a hardware-aware scheduling scheme that exploits the native cat–atom $\mathrm{CZ}^{n}$ gate to construct a syndrome-extraction circuit with minimum depth. We benchmark the architecture using hypergraph-product (HGP) codes and estimate a 180-fold reduction in syndrome-extraction cycle time at $N=10^5$ data qubits compared with an atom-rearrangement-based architecture. Under matched two-qubit depolarizing noise, the corresponding error threshold increases from $0.55\%$ to $0.72\%$. Under the hardware-derived error model, we obtain a threshold of $0.80\%$, corresponding to a threshold cooperativity of $C_{\mathrm{th}}=7.8 \times 10^4$, compatible with experimentally accessible parameters for Rydberg-coupled microwave-cavity systems. By avoiding atom transport, the Cat Bus provides a route towards high-speed, fault-tolerant neutral-atom quantum computation.

Reversible quantum channels play a fundamental role in quantum dynamics and quantum information processing. A quantum channel is reversible if there exists another quantum channel acting as its left inverse. Due to their intrinsic significance and wide applications, it is desirable to characterize reversible quantum channels from diverse perspectives. In this work, we study reversible quantum channels on finite-dimensional Hilbert spaces, with particular emphasis on the case of different input and output dimensions. We systematically present twenty-one equivalent characterizations of reversible quantum channels from algebraic, geometrical, and information-theoretical perspectives. Among these characterizations, some are well known, while others, implicit in the literature or formulated in other contexts, are clarified here; the Choi-state characterization is derived in this work. Specifically, we prove that the Choi states of reversible quantum channels admit three equivalent forms: the spectral, direct-sum, and tensor-product representations. These twenty-one equivalent characterizations establish a comprehensive framework for reversible quantum channels, provide diverse insights into the structural and information-theoretic properties of quantum channels, and facilitate applications of reversibility in quantum information processing such as quantum error correction, quantum teleportation, and quantum thermodynamics.

Compact and efficient frequency conversion within optical fibers is highly desirable for nonlinear and quantum photonic technologies, yet it remains challenging due to weak nonlinear interactions and limited coupling efficiencies onto optical fibers. Here, we demonstrate resonantly enhanced second-harmonic generation (SHG) through the all-fiber integration of a gallium nitride (GaN) hole-type circular Bragg grating (h-CBG) cavity, directly transferred onto a standard optical fiber. Together with the large second-order nonlinear susceptibility and wide optical transparency window of GaN, the fabricated h-CBG membrane cavity on GaN enables strong field confinement and vertically directional out-coupling of the generated SHG signal. As a result, we observe drastically enhanced SHG signals from the h-CBG device compared with the bulk GaN and the unpatterned freestanding GaN membrane. Using a deterministic pick-and-place transfer technique, we demonstrate robust and precise fiber integration of the GaN cavity device, enabling in-line SHG generation from a conventional fiber platform. This work establishes a compact and scalable approach for incorporating optical nonlinearity into fiber-based photonic systems.

We prove that an absolutely maximally entangled state of seven qudits exists if and only if the local dimension satisfies $d\geq 3$. Prior to this work, to the best of our knowledge, $\text{AME}(7,d)$ states were known to exist only when $d$ is a prime power other than $2$, or when $d$ can be expressed as a product of dimensions for which existence was already known. Since it has been proved that no $\text{AME}(7,2)$ state exists, it remains to establish existence for all $d\geq 3$. We construct cyclic quadratic-phase states for every odd local dimension and develop a coupled binary–odd-dimensional construction for every dimension congruent to $2$ modulo $4$. Together with the known power-of-two cases and the product property of AME states, these constructions cover every local dimension $d\geq 3$.

How we identify heat and work is a fundamental question in modern quantum thermodynamics. Usually, heat and work are attributed to changes in the density matrix and the Hamiltonian, respectively, during time-evolution processes in quantum systems. Recently, it has been recognized that this identification is ambiguous. Furthermore, quantum thermodynamics involving quantum measurement is still under development. Motivated by these on-going works, we consider a quantum many-body system from which we extract energy by local operations and classical communication (LOCC) according to the quantum energy teleportation (QET) protocol. The central idea to define heat and work unambiguously is based on a sharp insight into the optimization condition of LOCC. When LOCC is optimized, the extractable energy by QET becomes a daemonic ergotropy; thus, it can be attributed as work. On the other hand, when LOCC is not optimized, we have not squeezed out all the energy with the unitary operation. It means there is uncontrollable energy left in the system. The uncontrollable energy can be attributed as heat after careful treatment of many-body interactions. The heat term consists of nonlocal correlation due to communication between remote participants, and the correlation cannot be directly observed for the participant in the subsystem. Thus, this feature is consistent with the traditional perspective of heat as an uncontrollable energy. To deeply understand the nature of heat, we derive two types of generalized Clausius inequality in our effective quantum thermodynamics, and discuss the direction of the inequality. To justify our perspective, we examine a one-dimensional Kitaev-like model and discuss the physical meaning of effective temperature in our thermodynamics.

The readout amplification chain imposes a critical thermal scalability bottleneck in large-scale superconducting quantum systems. This happens through three mechanisms: amplifier dissipation, passive conduction through bias wiring and Joule heating within that same wiring. These terms are absent or only partially represented in several prior system-level thermal-scalability models, leading to bottleneck misidentification and scalability overestimation. In this work, we improve upon previous system-level heat estimation models by fully accounting for the major heat sources in modern cryogenic quantum systems including the active dissipation, passive conduction, and Joule heating in the readout amplifier module. Our analysis demonstrates that amplifier-associated heat emerges as the dominant thermal bottleneck that fundamentally alters the thermal landscape of modern large-scale cryogenic systems. We explore various technology options and their tradeoffs to identify configurations that reduce this critical heat load and improve scalability. Finally, we evaluate forward-looking system configurations, including larger refrigeration platforms and optical approaches, and analyze forward-looking pathways toward single-fridge 10k-qubit cryogenic systems.

The threat of quantum computers to classical public-key cryptography has created an urgent need to evolve secure communication protocols with post-quantum cryptographic (PQC) primitives. The Noise Protocol Framework, widely used in systems such as WireGuard and WhatsApp, traditionally relies on the Elliptic Curve Diffie-Hellman (ECDH) public-key exchange scheme, which is vulnerable to quantum threats. In this paper, we present NoisePQC++, a unified C++23 implementation of the Noise Protocol framework augmented with post-quantum Key Encapsulation Mechanisms and Hybrid Forward Secrecy. Our design integrates the National Institute of Standards and Technology (NIST) standardized ML-KEM algorithm alongside classical ECDH, enabling full PQC, hybrid ECDH+PQC handshakes, and unified support for all 57 classical Noise handshake pattern variants, 13 post-quantum Noise handshakes, and their hybrid variants. Compared with prior work, NoisePQC++ offers broader protocol coverage, more complete implementation support, and greater flexibility. Our evaluation shows minimal overhead under normal network conditions and acceptable overhead in adverse cases, while significantly improving resistance against quantum adversaries. These results indicate that NIST-standardized post-quantum and hybrid Noise handshakes are practical and provide a credible basis for future deployment.

We study parallel repetition in the two-player quantum cloning game, a monogamy-of-entanglement game motivated by quantum position verification. Colisson Palais, Escolà-Farràs, and Speelman bounded the value of $n$ copies between $(3/4)^n$ and $\cos^{2n}(\pi/8)$. For two copies, we prove that neither bound is tight. An explicit challenge-dependent strategy achieves value $(5+\sqrt{17})/16>9/16$, so strong parallel repetition fails for the unrestricted game. A block Gram matrix argument gives the upper bound $(11+\sqrt{65})/32<\cos^4(\pi/8)$ and strictly improves the previous parallel-repetition upper bound for every $n$. For every $n$, challenge-independent strategies have optimal value $(3/4)^n$.

High-precision laser interferometers are commonly used to search for signatures of random spacetime fluctuations, in an attempt to understand the fundamental nature of gravity. Conventionally, $SU(2)$ interferometers have been used in such experimental investigations. Motivated by [K. Zheng et al., Photon. Res. 8, 1653 (2020)], I assess if there is any advantage to be gained by using an $SU(1,1)$ interferometer instead of the $SU(2)$ interferometer. To this end, I compute the quantum Fisher information for estimating the strength and the correlation length of the spacetime fluctuations, and the corresponding classical Fisher information considering different experimentally relevant measurement schemes, in both types of interferometers. I compare the information metrics corresponding to different parameter regimes that are relevant to both current and possible future experimental setups. This helps me assess if and when the $SU(1,1)$ interferometer offers any advantage over the $SU(2)$ interferometer for estimating either the fluctuation strength or correlation length of the spacetime fluctuations.

We study the dynamics and localization of two oppositely charged particles constrained to a helicoidal manifold in a uniform magnetic field. The embedding-induced metric and the pullback of the ambient electromagnetic gauge potential, together with restriction to the reflection-symmetric longitudinal rest frame, lead to an exact reduction of the relative dynamics to a one-dimensional Hamiltonian with a coordinate-dependent kinetic term and a gauge-shifted momentum. We analyze the corresponding effective potential, turning points, and classically allowed regions, and determine how the geometric and magnetic parameters modify the bounded relative motion. For a regularized attractive interaction, we derive the zero-energy condition for localization around the symmetric configuration and obtain the local stiffness governing its stability. When this stiffness changes sign while the quartic coefficient remains positive, the symmetric minimum undergoes a pitchfork-type bifurcation to two symmetry-related finite-separation minima of the relative coordinate. Canonical quantization of the reduced Hamiltonian then gives the low-energy spectrum in the harmonic approximation and the associated zero-energy localization thresholds. At the critical stiffness, the quadratic term vanishes and the quartic term provides the leading contribution to the local low-energy scaling. These results establish how helicoidal geometry and magnetic coupling modify the relative localization and low-energy spectral properties of the two-particle system.

Graph codes offer multiple physical representatives of logical observables, while Gottesman-Kitaev-Preskill (GKP) codes retain analog information about bosonic displacement noise. We develop a causal framework that unifies these mechanisms for measurement-based loss tolerance under pure loss followed by quantum-limited amplification. In this framework, each local GKP recovery produces a refreshed logical block, a continuous syndrome record, and a confidence score for the inferred Pauli class. Low-confidence outcomes are deliberately converted into located erasures, so the availability pattern is generated directly from the bosonic data rather than sampled independently. Both accepted and rejected syndromes contribute to a syndrome-resolved posterior over the graph branch, which determines accessible logical representatives and the outgoing logical Pauli frame. We derive decoder-conditioned branch restriction, signed-outcome reconstruction, Pauli-frame updating, recursive concatenation of graph-GKP modules, and syndrome-resolved logical fusion. Numerical simulations across several squeezing levels identify task-dependent loss-tolerance behavior and finite-depth pseudothresholds for square and hexagonal GKP lattices. The resulting graph-GKP interface provides a unified causal control layer for fault-tolerant MBQC, fusion-based computation, and all-photonic repeaters.

The reconstruction of unknown quantum states via minimal informationally complete measurements (MICs) is a cornerstone of quantum tomography. Although the statistical properties of these measurements are well-understood, their geometric structure has remained elusive. In this work, we establish a correspondence between the class of minimal $s$-tight informationally complete measurements, encompassing, among others, tight IC and morphophoric measurements, and the classical geometry of orthocentric simplices. In particular, we prove a three-way equivalence: a MIC is $s$-tight if and only if its measurement vectors, upon suitable rescaling, form the vertices of an acute orthocentric simplex with the orthocentre at the origin, and such simplices are precisely the homothetically self-dual ones. This geometric manifestation of operational ”tightness” provides a bridge between the physical world and Euclidean geometry. Furthermore, the $s$-tight class is fully characterised by its measurement directions: the angles between them must be obtuse and satisfy a cross-ratio condition. We determine the space of admissible direction configurations: modulo rotations, every such configuration is encoded by a single probability vector, the ”skeleton” of the measurement, together with an orientation class, so that the moduli space of $s$-tight MIC directions is $\Delta^{\circ}_{d+1}\times\{\pm 1\}$. Conversely, every acute orthocentric simplex with the orthocentre at the origin can be anchored in the state space, generating a class of minimal $s$-tight IC measurements that contains exactly one tight IC measurement up to overall rescaling.

We develop a symplectic formulation of the Lagrangian Radon transform based on the transitive action of the symplectic group on the Lagrangian Grassmannian. This geometric framework naturally extends the classical notion of the marginals of the Wigner transform, viewed as elementary tomograms, to arbitrary Lagrangian subspaces. The resulting generalized tomography provides a unified treatment of position and momentum measurements related by symplectic rotations. As applications, we revisit the Pauli reconstruction problem and establish reconstruction formulas for density operators from generalized Lagrangian tomograms.

Property testing of distributions is a central topic in information theory, learning theory, and statistics. While quantum algorithms are known to offer significant speedups for property testing of a single distribution or a pair of distributions, it is unclear whether quantum algorithms provide speedups for property testing of $m$ ($m\geq 3$) distributions. This work focuses on quantum algorithms for testing whether $m$ distributions have similar means or are $\epsilon$-far from mean similarity under two models. In the query model, the algorithm can choose which distribution to sample from, whereas in the sampling model, the distributions are selected uniformly. We design quantum algorithms with complexities $\tilde{O}(1/\epsilon)$ (the $\tilde{O}$ notation hides poly-logarithmic factors) and $\tilde{O}(\sqrt{m}/\epsilon)$ in the query and sampling models, respectively, achieving quadratic speedups over the classical counterparts. We further establish quantum lower bounds of $\Omega\left(1/\epsilon\right)$ and $\Omega\rbra{m^{1/3}+\frac{m^{1/4}}{\epsilon}}$ for the query model and the sampling model, demonstrating the optimality of our quantum algorithms in terms of the dependence on $\epsilon$ up to logarithmic factors.

Universal quantum computation requires single-qubit control together with at least one entangling two-qubit gate. CNOT and CROT gates are two famous examples of such gates, wherein the state of one qubit (control) dictates the transformation applied to the other (target). By using a simple derivation motivated by symmetry, we show that current device architectures of semiconductor-based quantum dot devices prevent efficient implementation of a CNOT and other asymmetric control-target gates via Heisenberg exchange, Coulomb repulsion, or other interaction that is invariant under spin exchange. Guided by this general principle, we propose a heterogeneous blueprint of double quantum dot devices that enables efficient implementation of the CNOT by breaking the spin exchange symmetry. Crucially, our numerical simulations predict that this novel device blueprint can enable a single-pulse fault-tolerant 100-ns CNOT gate in isotopically purified silicon.

Pure quantum states, as described in quantum mechanics textbooks, are ideal representations inevitably deteriorated in real systems by any dissipative connection to the environment. In this work we derive a unified theoretical frame to study the non-Hermitian dynamics of a driven-dissipative quantum system and validate it by comparison to experimental data of matter-wave diffraction. To highlight the role of dissipation, we perform the comparison in a near-resonant regime of light-matter interaction, where perturbative approaches fail. Here, we show that the developed formalism enables both exact simulations and an intuitive interpretation based on modal analysis. The theoretical analysis is based on the general master equation description of driven-dissipative systems, from which we derive an effective complex potential $V_\mathrm{eff}(\Omega,\Delta)$ that depends on control parameters such as the amplitude and detuning of the light matter interaction. Experimentally, we drive a $^{87}$Rb BEC near resonance using periodic excited-state engineering, mapping the spatially modulated $V_{\rm eff}[\Omega,\Delta(x)]$ into momentum space for precise quantification. The experimental results agree with numerical simulations of the master equation and demonstrate the interplay between coherent drive and dissipation, with an exceptional signature: a reduced decay rate with increasing drive. Such dynamics is then interpreted by a modal analysis of the non-Hermitian Hamiltonian $H_\mathrm{eff}=p^2/2m+V_\mathrm{eff}$ which provide an intuitive and qualitative explanation for such driven-dissipative system.

Quantum computing provides a promising framework for the simulation of quantum field theories, where the computational cost depends both on the quantum algorithm employed and on the representation of the Hamiltonian. We investigate a formulation of the $\phi^4$ model based on the harmonic-oscillator basis in coordinate space. We derive the lattice $\phi^4$ Hamiltonian in this representation and analyze the structure of the resulting one-body matrix and interaction tensor. We show that both exhibit an effective band-diagonal structure, allowing controlled truncations of the Hamiltonian while preserving the low-energy spectrum. We validate this formulation by comparing low-energy observables obtained from numerical diagonalization with those computed in the standard harmonic-oscillator momentum-space representation. Finally, we estimate the resources required to encode the Hamiltonian on a quantum computer using both binary and unary boson-to-qubit mappings. By exploiting effective locality, the coordinate-space representation reduces the resources required for quantum simulation over a broad range of parameters.

We develop a terminal-resolved theory of work statistics for autonomous quantum energy pumps. By modeling the systems that supply and receive energy as explicit quantum terminals, the energy exchanged with each terminal is defined directly from its Hamiltonian change. When the terminals are modeled by ideal clocks, these full-space observables admit exact representations on the pump Hilbert space and recover the conventional phase-derivative currents of periodically and quasiperiodically driven systems. The framework resolves transported work from energy accumulated in the pump. It also incorporates arbitrary initial pump–terminal correlations and identifies when correlations can enhance directional energy transfer under uncertain driving phases. For periodic pumps, we derive finite-cycle work statistics in Floquet eigenstates, relate their fluctuations to Floquet quantum geometry, and show that the long-time terminal currents become mutually compatible. An exactly solvable two-terminal qubit exhibits noise matching, in which transport becomes sharp through cancellation of common-mode terminal fluctuations even though the individual terminal energies remain noisy. Finally, for physical terminals beyond the ideal-clock limit, we introduce a positive work-variance gap that quantifies the fluctuations missed by a pump-only description. A coherent-cavity benchmark shows systematic convergence toward the ideal-clock regime with increasing occupation while demonstrating that agreement of the mean current alone does not guarantee accurate work statistics.