Papers

We study two bilinearly coupled harmonic oscillators driven by a common time-dependent spring. A fixed normal-mode transformation reduces the pair to two parametric oscillators, each solved exactly by its Lewis-Riesenfeld invariant and Ermakov-Pinney amplitude, including the ladder-operator construction and the Lewis-Riesenfeld phase. For invariant-vacuum inputs the physical two-mode covariance matrix is obtained in closed form, and the logarithmic negativity collapses to $E_{N}=\frac{1}{2} \operatorname{arcosh}(X/2)$, where a single dimensionless invariant $X \geq 2$ measures the relative phase-space deformation of the two normal modes. We give a normalization-explicit account of the Duan–Simon comparison: after local symplectic optimization the Duan test and the positive partial transpose share the entanglement threshold for this pure exchange-symmetric Gaussian family, but the optimized Duan quantity is a witness, not an independent measure, with $D_{\rm opt}/D_{\rm sep}=e^{-E_N}$. We carefully separate a genuinely separable product preparation from the already-entangled ground state of the coupled Hamiltonian, and use only the former for claims of entanglement generation. Under sinusoidal stiffness modulation a separable input shows bounded correlations away from resonance and sustained growth near parametric resonance, and we demonstrate numerically that the initial width and chirp act as two independent, experimentally accessible controls of the entanglement at a chosen target time. An $SU(1,1)$ formulation identifies $2 E_{N}$ with the hyperbolic separation of the two normal-mode squeezing trajectories on the $SU(1,1)/U(1)$ disk and shows that entanglement is governed by both the relative squeezing magnitude and the relative squeezing angle; ; we exhibit regimes in which nearly equal magnitudes still produce strong entanglement through the angle alone.

Near-term quantum optimizers accommodate roughly a hundred binary variables, requiring large Quadratic Unconstrained Binary Optimization problems to be decomposed into hardware-sized subproblems while other variables remain fixed. Variables are typically selected by ranking the objective changes from individual flips. We show that this rule is uninformative once the incumbent is optimal under single-variable flips: every score represents a cost, while remaining improvements depend on overlooked pairwise interactions. A second-order expansion instead yields a prize-collecting densest-subgraph selection problem, solvable greedily in time linear in the number of variables, and two solver-free bounds bracketing the improvement achievable within a selected subset. On transportation networks from Chicago and Philadelphia, our rule with 16-variable subproblems outperforms random selection with 64, demonstrating that quadrupling device capacity cannot compensate for weaker selection. Replacing geometric adjacency with road-network connectivity widens the margin by a factor of 1.6-1.9. With the selection trace fixed, varying the fraction of subproblems solved on a 120-qubit device from zero to one leaves the final objective unchanged to six significant figures. At tested hardware-accessible sizes, gains therefore arise from selection rather than the backend. Hardware feasibility is limited by coupling terms: 120-variable problems fail to compile with 7,260 terms but succeed with 5,118. Compilation scales almost quadratically with term count and dominates execution cost, reaching 1,752 seconds versus 469 seconds of quantum processing.

Quantum information enables many cryptographic primitives that are impossible in the classical world. A line of works has developed cryptographic protocol under the assumption that quantum adversaries are restricted to noisy intermediate-scale quantum (NISQ) computing power, enabling strong one-time functionalities. But the advent of early fault-tolerant quantum computers eras will allow deeper logical quantum circuits, calling into questions the applicability of these NISQ-based assumptions. In this work, we adapt the classically accessible random oracle model (CAROM) as in [BDF+11] and [AK22], in which adversaries are only allowed to classically query the random oracle. The restriction is well motivated for NISQ quantum adversaries and may remain plausible in the presence of early fault-tolerant quantum computers. Then, we show that an efficient simulation-secure one-time memory (OTM) is possible under CAROM. Our protocol uses only BB84 states and has quadratic communication: for a $\lambda$-bit message and integer-valued parameters $n=n(\lambda)$ and $\ell=\ell(\lambda)$, the construction uses $n\ell$ qubits and $(n+2)\lambda$ classical bits, and for any quantum adversary with at most $2^{\ell/2-1}-1$ classical queries to the random oracle, its simulation advantage is at most $(n+3)\left(\frac{3}{4}\right)^n.$ Hence exponentially small simulation advantage in $n$.

The waveguide-integrated architecture holds promise for scalable on-chip integration of a charger, a transmission channel, and a quantum battery in a modular, independently optimizable design. We investigate a minimal charging configuration consisting of two emitters coupled to a semi-infinite waveguide and identify the optimal charging mechanism, wherein non-Markovian dynamics driven by out-of-band bound states give rise to single-frequency oscillations of the stored energy. We show that near-unity charging efficiency is achievable at weak to moderate coupling strengths via detuning control, provided that the battery-to-boundary separation $n$ is less than three times the charger-to-boundary separation $m$ ($n<3m$)—a constraint imposed by the mirror-induced feedback—while the average charging power decays exponentially with the spatial separation $n-m$. These findings offer useful insights for monolithic solid-state quantum energy storage and transport.

We propose a paradigm for quantum enhanced axion dark matter search, which does not rely on power measurements. We propose to measure directly the axion amplitude and phase in an interferometric protocol at the quantum limit, using a non-linear cavity. In addition, we introduce gyromagnetic modes as wide mass range transducers for axion signals compatible with standard haloscope designs. We expect this scheme to offer an improvement of at least 4 orders of magnitude in figure of merit and at least 2 orders of magnitude in mass window with respect to standard haloscopes. Owing to its generality, our proposed protocol has the potential to speed up axion search but also the search for dark photons or other cosmological objects, such as galactic masers.

We prove an exponential strong converse for the unassisted private capacity of every finite-dimensional degradable quantum channel. We use a single error criterion: the infidelity between the actual message-estimate-environment state and an ideal state consisting of uniformly distributed, perfectly correlated messages that are independent of the environment. At every rate strictly above the channel's maximum coherent information, the optimized fidelity to this ideal state decays exponentially in the number of channel uses. The same bound holds when the ideal environment state is fixed to the actual environment marginal. The proof applies to arbitrary mixed-state encoders and arbitrary collective decoders. Its main operator ingredient is an overlap bound for privacy tests: two receiver placements with a common subsystem of dimension $d_C$ have overlap at most $d_C/M$, where $M$ is the key size, independently of both shield dimensions. We combine this bound with the signed averaging construction presented in arXiv:2608.01308 and a single-filter reduction to symmetric states. A Gaussian filter replaces the common receiver subsystem by a system of controlled dimension from which the original correlations can be approximately recovered using quantum side information. The filter preserves exact exchange symmetry, and a uniform smooth-entropy estimate bounds its output dimension for arbitrary correlated channel inputs. We also obtain an exponential strong converse at zero for antidegradable channels under the same joint criterion and, consequently, for the private capacity of the quantum erasure channel throughout its parameter range.

Feedback-based ALgorithm for Quantum OptimizatioN (FALQON) is a hybrid quantum-classical algorithm for solving combinatorial optimization problems, which circumvents classical parameter optimization but requires a deep quantum circuit. To reduce circuit depth, Arai et al. proposed second-order FALQON (SO-FALQON), achieving the best depth reduction among existing approaches. However, SO-FALQON brings a 2.3 times per-step measurement overhead, as it needs to calculate an additional second-order control coefficient. In this paper, inspired by the Backtracking Line Search (BLS) theory, we propose another method called BLS-FALQON, which not only reduces circuit depth to a comparable extent, but also achieves fewer measurements than SO-FALQON. Numerical simulations on max-cut problem with 8 to 20 vertices demonstrate that BLS-FALQON reduces the total measurement count by 37.7% compared to SO-FALQON, while maintaining a comparable circuit depth. Furthermore, we conduct real quantum hardware experiments on the Tianyan-176 quantum computer, which uses the zuchongzhi2 superconducting quantum processor, confirming that BLS-FALQON remains effective under real quantum hardware conditions.

Graph coloring is a well-known NP-complete problem with applications in scheduling, register allocation, frequency assignment, and network optimization. Quantum computing offers the potential for polynomial or even super-polynomial speedups in certain problem instances, yet practical quantum graph coloring methods must carefully balance qubit resources, circuit depth, and constraint enforcement. We proposed a solver agnostic quantum framework for $K$-coloring. Along with a novel encoding and efficient constraint implementation for its exact coloring exploiting Grover search and almost optimal coloring by the Quantum Approximate Optimization Algorithm (QAOA), and Quantum Annealing. Unlike using $O(NK)$ qubits as in SOTA, we reduced the qubit requirements to $O(N \log_2 K)$, along with optimized comparator circuits enforcing adjacency constraints. Further symmetry-based graph reduction is incorporated as an optional preprocessing step to further reduce the instance size before quantum execution.

We prove a $\beta^{2}$ area law for the quantum mutual information of thermal states of local lattice Hamiltonians: for any bipartitioning $A|B$ and all inverse temperatures $\beta$ below a critical value $\beta^{*}$, we show $\mathcal{I}_{\beta}(A,B) \leqslant \tilde{f}(\beta)\, \beta^{2}\,|\partial_{AB}|$, where $|\partial_{AB}|$ denotes the size of the boundary region and $\tilde{f}(\beta)$ remains finite as $\beta \to 0$. This quadratic scaling improves the relationship between high-temperature correlations and macroscopic thermodynamics. While a linear area law implicitly permits a loose, temperature-independent upper bound on extractable work and binding energy, the quadratic scaling ensures that the nonequilibrium free energy available after decoupling regions and the total energy of the interface both are proportional to the area of the interface of $A|B$ and vanish as $\beta$ at high temperatures. These results show that the high-temperature mutual information and correlation are suppressed, respectively, quadratically and linearly in inverse temperature, which are consistent with the expected thermal decoupling in macroscopic thermodynamic quantities.

Carleman linearization represents nonlinear lattice Boltzmann collision dynamics in a form amenable to quantum block encoding, but low postselection probabilities in existing population-space encodings make coherent multi-step evolution exponentially unlikely to succeed. We present a quantum Carleman lattice Boltzmann scheme based on the multi-relaxation-time collision operator in a weighted Hermite moment basis. In this basis, the lifted collision operator separates into small coupled blocks whose norm exceeds unity because of the coupling between conserved and relaxing modes. This block structure enables a norm-attaining block encoding with a single-step success probability close to unity. Crucially, scaling the pair sector for a prescribed evolution horizon makes the combined encoding and sector-selection overhead grow polynomially rather than exponentially with the number of steps. For a hundred-step evolution, the resulting complete-run success probability exceeds that of population-space encodings by orders of magnitude. Over horizons of several tens of steps, the truncated dynamics reproduces the nonlinearly generated modes of a benchmark flow to within a few percent. We verify the combined preparation, evolution and readout protocol as a single unitary circuit and give a complete gate-level resource estimate for extracting a nonlinear observable of the benchmark flow from a coherent Carleman evolution. The block structure of conserved and relaxing modes holds equally on three-dimensional lattices and provides a constructive route to norm-attaining encodings for lattice Boltzmann models with quadratic equilibria.

1+1D symmetry-protected topological (SPT) phases with invertible symmetry can be characterized by the symmetric entanglers: globally symmetric finite-depth local unitary circuits that generate representative ground states from a product state. For non-invertible symmetries, however, distinct SPT phases, such as the three $\mathrm{Rep}(D_8)$ SPT phases, may not be connected by any symmetric entangler. We show that the three $\mathrm{Rep}(D_8)$ SPT phases can nevertheless be connected by symmetry-permuting finite-depth local unitary circuits, realizing dualities predicted by topological quantum field theory (TQFT). We construct an explicit matrix product unitary connecting two of the $\mathrm{Rep}(D_8)$ SPT phases, and show that its action on string order parameters reproduces the anyon permutation predicted by the TQFT duality.

We study the problem of implementing multivariable matrix-valued functions on a quantum computer and propose two quantum algorithms for multivariable matrix eigenvalue transformations acting on tuples of pairwise commuting matrices. The first algorithm is based on multivariable contour integrals and applies to arbitrary holomorphic functions on $\mathbb{C}^n$. The second algorithm is based on high-dimensional Fourier transforms and designed for smooth functions of commuting Hermitian matrices. For both algorithms, we discuss and analyze the complexity of their quantum implementation leveraging quantum singular value transformation, compression gadgets, and linear combination of unitaries. We additionally study their hybrid quantum–classical variants that reduce the number of required ancilla qubits to logarithmic dependence on the number of variables, at the cost of increased query complexity. As an application, we show that multivariable matrix polynomials can be implemented with no additional explicit degree dependence, depending only on global properties of the polynomials.

The sudden removal of a potential barrier from a Bose-Einstein condensate (BEC) gives rise to a quantum version of a hydrodynamic dam break and leads to rich wave dynamics that have similarities to other localized defect problems such as domain wall dynamics in spin systems. Denoting $\Delta n$ as the initial difference in density between the upper $n_{1}$ and lower $n_{0}$ reservoirs on either side of the dam, we use the Gross-Pitaevskii equation to study the quasi-one dimensional case in both perturbative ($\Delta n \ll n_{0}$) and non-perturbative ($\Delta n \sim n_{1}$) regimes. In the perturbative regime a pair of outwardly propagating dispersive wavepackets forms which can be viewed as quantum versions of undular tidal bores that have analytic forms at long times in terms of the integrals of Airy functions with a wavelength that grows as $(\hbar^2 t)^{1/3}$. Airy functions are the universal wave functions that dress structurally stable fold caustics where pairs of rays coalesce, and, indeed, we show that the quantum dam break problem has the same ray structure as the naturally occurring caustic phenomenon of a double rainbow, including Alexander's dark band between the two bows where no light is scattered: we identify the intermediate density plateau in the dam break as an analogous `silent band' where only evanescent sound waves can exist. In the opposite regime of a non-perturbative dam break we show that a self-induced sonic horizon occurs when $\Delta n \geq (8/9)n_{1}$. A discussion of possible experimental schemes for amplification of quantum undulations is included as well as an alternative scheme for dispersive wave generation where a constant flow is imprinted on a BEC in box trap.

Telecom-band spin defects in silicon offer a compelling platform for integrated quantum networks by combining scalable silicon photonics with spin-based quantum memories and multiqubit registers. The T center and recently demonstrated Al1 center are particularly promising, but their limited coherent zero-phonon emission requires strong cavity enhancement for efficient spin-photon interfaces. Here, we inverse-design silicon nanobeam cavities for both centers using a unified adjoint-optimization framework targeting Purcell enhancement, resonance alignment, and photon extraction. For each emitter, symmetric cavities maximize Purcell enhancement, while asymmetric cavities provide directional coupling to an integrated waveguide. Three-dimensional finite-difference time-domain simulations yield loaded quality factors up to 3.25 x 10^6, Purcell factors up to 1.43 x 10^5, and cooperativities of approximately 280-5000, corresponding to cavity-coupled emission fractions exceeding 99.6%. The asymmetric cavities direct approximately 90% of emitted power into a single on-chip waveguide while maintaining cooperativity above 280. Under nanometer-scale fabrication perturbations, all four designs remain within the high-cooperativity regime, and high cooperativity persists when the cavity quality factor is constrained to a realistic absorption-limited value of 10^5. This unified, fabrication-compatible framework establishes a scalable cavity-design route for silicon telecom spin-photon interfaces and, to our knowledge, the first cavity designs for the Al1 center.

Bound states in the continuum (BICs) provide a mechanism for preserving entanglement in waveguide quantum electrodynamics. Here, using quantum control techniques in a configuration of two braided giant atoms, we propose a robust approach to create high-fidelity entangled BICs. The protocol combines quasi-Floquet modulation of the effective atom–waveguide couplings with an independent phase-controlled atomic exchange, which provides restricted counterdiabatic assistance for preparing the complete dressed BIC. In the lossless effective model, we obtain a full-state BIC fidelity of $0.99992$ and an unconditional atomic Bell fidelity of $0.99588$ using a fast control protocol. Microscopic finite-mode simulations validate the central-sideband description during the passage, while static calibration-error scans quantify its control tolerances. A separate microscopic study with relaxation and dephasing, using experimentally motivated component scales, identifies a finite useful entanglement window and a benefit from shaping the coupling envelopes. These results support controlled preparation, retention, and retrieval of dressed entanglement within the stated control and noise assumptions.

Hegerfeldt's theorem shows that the localization of a particle (or field) is not possible under very general assumptions of quantum mechanics and special relativity. This theorem, and further developments and associated theorems force penetrating questions on the proper understanding of the theory and its use. In particular, the use of the collapse postulate is called into question. The existence of particles and even localized fields are called into question. And, this in turn challenges local measurements. It generally forces one to consider the profound problems and even wrong results that arise from the collapse postulate. We give a qualitatively new example of such a wrong result. Researchers and students alike are bothered by these fundamental issues. Students' ability to learn the material, and even their interest in physics, can be compromised by such disturbing conundra that seem to make physics, or at least QFT and its QM limit, seem incomprehensible and even inconsistent. This article resolves these issues in a way accessible to undergraduates, by applying the natural (minimal) interpretation of quantum mechanics (QM) (the ensemble interpretation) and explicating and clarifying the basic principles and premises used in QM and the Hegerfeldt theorem and its application to measurements.

We study braid representations obtained from character-twisted Burau inputs by the Katz-Long-Moody (KLM) construction, which corresponds to multiplicative middle convolution for KZ-type equations. For $n\ge2$, let $q=e^{2\pi ia}$, $\tau=e^{2\pi ic}$, where $a,c>0$ and $nc+(n+1)a<1$. Known form and signature results give a positive-definite invariant form for $\lambda=e^{2\pi il}$, $0<l<1-nc-(n+1)a$. For fixed input, unitary realizations are unique up to simultaneous unitary conjugation. We address two questions. First, we determine spectra and invariant summands of the $M=n(n+1)$-dimensional output. The generator spectrum recovers $(q,\tau)$. The output decomposes into two trivial and two reduced Burau summands, and an $n(n-1)$-dimensional summand isomorphic to Long's reduced construction, generically irreducible for $n=3,4$. If $a$ or $c$ is irrational, every generator is non-Clifford in every finite-dimensional Weyl-Heisenberg frame; if $1,a,c$ are linearly independent over $\mathbb{Q}$, every generator is entangling for every nontrivial bipartition. The full braid image is not projectively dense. For general positive-definite unitary inputs, irreducibility of the full braid output at a nonexceptional parameter forces the free-group input operators to commute. Second, we construct one orthonormal basis giving each generator one block of size $2(n+1)$, $n-2$ blocks of size two, and identity elsewhere. Each generator is a product of $2n$ rank-one phase reflections and, in a fixed binary encoding, an $O(M)$-length word in one-qubit unitaries and CNOTs, without auxiliary qubits and including direction preparation and its inverse. We give finite-alphabet approximation, conditioning and error bounds, and a matched-resource comparison with a Quantum Shannon reference compiler. The gate bound is exponential in the encoded qubit count and excludes classical preprocessing.

Collective spin systems in solid-state materials are promising platforms for quantum-enhanced sensing. In systems such as nitrogen-vacancy centers in diamond, donor spins in silicon, and magnetic materials, interactions among many spins can generate collective quantum correlations that improve measurement precision beyond the standard quantum limit. This tutorial develops an intuitive, materials-oriented framework for understanding these effects through nonlinear collective-spin dynamics. We show how nonlinear interactions reshape collective spin states in phase space, redistribute quantum fluctuations, and generate metrologically useful states such as spin-squeezed and entangled states. We then connect these ideal collective dynamics to microscopic interactions and realistic solid-state systems, discussing how interaction strength, disorder, decoherence, and experimental control affect sensing performance. Different platforms and experiments are compared to highlight key material properties, advantages, and limitations. The tutorial focuses on a materials-oriented understanding of nonlinear collective-spin sensing, rather than a comprehensive comparison of experimental platforms or a practical guide to sensing experiments.

The entangling layer of a quantum circuit Born machine can supply both entanglement and nonstabilizerness. In this work we show that the entangling layer can be a Clifford circuit, which supplies no nonstabilizerness. We use an architecture in which a fixed, non-trainable entangler is reused in every layer and only single-qubit rotations are optimized. There, a Clifford entangler reaches the same Kullback–Leibler divergence as a near-Haar one at sufficient circuit depth, and entanglers spanning zero to Haar-typical nonstabilizerness reach the same loss, up to a small offset for a free-fermion matchgate entangler. A doping control that raises the entangler's nonstabilizerness while leaving the entangling power of every gate unchanged leaves the loss flat. With a Clifford entangler the nonstabilizerness of the trained state comes entirely from the rotations, which take the trained circuit outside the stabilizer formalism. We also show that, among all pure states whose Born distribution is a given target, the one whose amplitudes are the positive square roots of the probabilities has the smallest stabilizer Rényi entropy, so this minimum can be computed without training.

Practical tests for witnessing entanglement in the presence of noise are needed to verify and apply entanglement-based applications in real-world communication networks. Quantum dense network coding is a communication protocol that uses an entangled state preparation together with quantum communication to halve the amount of communication needed to evaluate certain bijective functions in networks having multiple senders and one receiver. In this work, we consider a dense network coding protocol that uses graph state entanglement to implement a family of affine transformations, we derive a bound on the success probability that can be achieved by classical networks, and we show that the noise robustness exponentially amplifies with the number of senders. We apply our results in a semi-device-independent protocol for robustly estimating the effective visibility of graph states and measurement bases. Overall, our approaches are robust to noise, can support the usage of uncharacterized state preparations or measurements, and can be applied to any graph state.

Trotterization approximates quantum time evolution by sequentially applying Hamiltonian terms. Because noncommuting terms introduce ordering-dependent errors, selecting an optimal term ordering is a combinatorial problem over a factorial search space. Prior approaches rely on fixed heuristics or on selection among predefined structured orderings, both of which require simulating candidates before choosing among them. For 1D and 2D Heisenberg-style Hamiltonians, we instead learn the ordering directly with a physics-aware ranking transformer that assigns a scalar score to each Hamiltonian term and predicts an ordering by sorting these scores. Physical structure enters through commutator-biased attention and an anticommutation-weighted ranking loss, and the models are trained on simulated-annealing (SA) reference orderings. We train separate models for first- and second-order Trotterization, each jointly on chains up to 14 qubits and lattices up to 12 qubits, and evaluate them on unseen chains with 16-20 qubits and lattices with 16 and 20 qubits. Predicted orderings are evaluated by the median gap in simulation fidelity to the SA reference. At first order, the model reaches a pooled gap below 10^-4 on chains, 0.0144 and 0.0088 on triangular lattices, and 0.0948 and 0.0823 on rectangular lattices at 16 and 20 qubits; at second order, the gaps are 0.0114, 0.0364 and 0.0244, and 0.1348 and 0.1239. The prediction exceeds the SA reference on 34% of first-order and 8% of second-order chain instances and can match its fidelity even when the two sequences differ because commuting terms may be rearranged without changing the Trotter unitary. The learned models generalize to larger systems across all three geometries, performing best on chains and triangular lattices, and produce an ordering in one forward pass without candidate enumeration, simulated annealing, or fidelity evaluation.

Overcoming experimental errors is a central challenge in quantum science. This challenge is particularly acute in large and complex quantum circuits, where quantum information spreads into exponentially many paths, foiling any direct attempt to understand errors' impact. In this work, we present a novel approach to understanding and mitigating experimental errors, based on a surprisingly compact representation of a quantum circuit's information dynamics, the reactivity function. The shape of a circuit's reactivity function governs its noise response, and its amenability to different error mitigation methods. From this viewpoint, we introduce two complementary such methods. The first, Pauli-path zero-noise extrapolation, fits a parameterized model to a circuit's reactivity function and uses it to accurately extrapolate to zero noise. The second, tunable error cancellation, filters a circuit's reactivity function to cancel noise on all information up to a threshold locality. Crucially, both methods feature a tuning parameter that allows one to systematically improve their accuracy until convergence. Across three circuit families from published experiments, our methods overcome conventional zero-noise extrapolation biases as large as 30%; at $\sim$$10^{-2}$ root-mean-square error, they reduce sampling cost relative to probabilistic error cancellation by up to a factor of $10^3$.

Hybrid quantum methods have received limited study for resource-constrained facial biometrics. We present a hybrid quantum-classical facial recognition pipeline designed to run on standard computing hardware. Images undergo gamma correction, contrast enhancement, and principal component analysis before their features are encoded into an eight-qubit variational quantum classifier. Classical image matching then performs recognition. In experiments with 50,000 images, comprising 25,000 faces from CelebA and 25,000 non-face images from CIFAR-10, the method outperformed the reported CPU-trained FaceNet baseline in accuracy and training efficiency. The pipeline was also evaluated on GPU and quantum hardware. In an attendance monitoring deployment at Mahindra University in collaboration with Lloyds Technology Centre, CPU inference took 0.2 to 0.5 seconds per person, and the system remained robust to the use of spectacles. These findings support the feasibility of deploying hybrid quantum methods for facial recognition on existing CPU hardware.

Ensemble nitrogen-vacancy (NV) centers are widely used for quantum sensing and magnetometry, where performance depends on the accurate implementation of microwave pulse sequences. In these systems, inhomogeneous broadening and short coherence times limit reliable multi-pulse control, while hardware imperfections and off-resonant excitation distort implemented rotations, making direct calibration of arbitrary gates tedious. To address this, we implement a control framework with a ZXZXZ gate decomposition which uses fixed-angle, phase-parameterized pulses, enabling universal single-qubit control from a single calibrated $ \pi/2$ primitive ($X_{\pi/2}$) along with virtual Z operations. We compare a standard pulse with a composite pulse designed for high-power operation in a regime where the Rabi frequency is comparable to the hyperfine splitting, leading to non-uniform evolution across hyperfine levels. Using pre-determined combinations of $\pi/2$ pulse sequences, we observe that standard pulses rapidly deviate from ideal behavior under repeated application, while the composite pulse suppresses this error accumulation by more than 70$\%$ for longer sequences despite its longer duration. In contrast, randomized benchmarking yields similar decay factors for both implementations, highlighting its limited sensitivity to coherent control errors. These results establish a practical route to robust control in short-coherence ensemble systems and emphasize the importance of pulse-level characterization.

Selecting a data encoding is a central and poorly tooled decision in quantum machine learning. The feature map fixes the geometry of the Hilbert space, the expressibility of quantum kernels, and whether the circuit can run on near-term hardware. This paper presents Quantum Encoding Agents, an open-source system that turns encoding selection into a natural-language interaction. Given a dataset and an optional task description, it profiles the data, applies a hardware-aware policy using the gate-error threshold p* approximately 10^{-3}, returns a copyable Qiskit circuit with a justification in Portuguese or English, and scores the quantum kernel by Kernel-Target Alignment (KTA). When a numerical matrix is available, it estimates the correlation fractal dimension D_2 and selects original columns with FD-ASE, using q* = max(2, ceil(D_2)) as a qubit budget so that angle and IQP maps are not proposed at a width where the fidelity kernel has collapsed. The service implements seven encoding families: amplitude, angle, dense angle, IQP, basis, data re-uploading, and custom feature map. On benchmark datasets, KTA separates these encodings under realistic NISQ constraints.

We report the first quantum-hardware implementation of Real-time Estimators for Scattering Observables (RESOs). The physical model is a one-dimensional lattice theory of non-relativistic spin-1/2 fermions with a single contact interaction. The lattice sizes studied are up to $N_x=54$ lattice sites and up to $20$ time steps. Spacetime correlation functions were computed on IBM's quantum computers, using $109$ qubits with $10,806$ CZ gates applied, reaching a two-qubit gate depth of $246$. We demonstrate how to study bound states and extract scattering amplitudes from these correlation functions.

We investigate the relation between two complementary descriptions of the Anderson transition on small-world random graphs: finite-size scaling of eigenfunction moments and renormalization-group (RG) flows of multifractal dimensions $D_q$. The RG flows recover the qualitative structure previously reported for the information dimension $D_1$, while their extension to other $D_q$ with smaller moment orders $q<1/2$ confirms the strongly multifractal nature of the localized phase characterized by a clear separation between multifractal and localized behaviors at strong disorder. On the other hand, we show that we can construct another beta function characterizing the flow of eigenfunction moments, whose collapse onto a single function across different disorder strengths provides a clear confirmation of single-parameter scaling property. These results indicate that the family of RG trajectories observed for the information dimension $D_1$ need not imply two-parameter scaling and Kosterlitz-Thouless like critical behavior. To characterize these properties, one should consider different observables, such as large $q>1/2$ and small $q<1/2$ eigenfunction moments, which are associated with distinct critical behaviors, in particular different critical exponents.

We study a family of locally excited states in two-dimensional conformal field theories in different setups, defined on the plane, on the cylinder, or at finite temperature. These states are constructed by assigning independent chiral and anti-chiral regulators to a local primary operator, leading to excitations carrying net momentum. We analytically calculate the first few Lanczos coefficients and the early time behaviour of the spread complexity associated with these states. Then, using numerical methods, we obtain the coefficients reaching larger Krylov indices and find the associated spread complexity for a longer range of time evolution. We also compare the rate of change of the resulting spread complexity with the proposed holographic dual quantity, related to the proper momentum of an infalling particle in the dual bulk, but we observe a mismatch.

Reduced Bloch models of spin-exchange-relaxation-free (SERF) magnetometers commonly describe the coupled electron–nuclear spin dynamics using a single nuclear slowing-down factor. We show that this scalar description becomes inaccurate when the polarization magnitude changes appreciably. We derive an effective Bloch equation with separate longitudinal and transverse slowing-down factors, $q_\parallel(P)$ and $q_\perp(P)$, governing changes in polarization magnitude and direction. For $^{87}\mathrm{Rb}$ under representative SERF conditions and undergoing free-induction decay (FID), comparison with master-equation simulations shows that the dynamic scalar model produces a magnetic-field estimation bias of up to $4.2\%$ at high initial polarization, while fixing the slowing-down factor at a reference value increases the error to $10.1\%$. Lowering the polarization suppresses this bias but also reduces the magnetic-field information contained in the FID signal. We further show that the anisotropic response modifies noncollinear optical pumping and introduces an additional nonlinear contribution to the harmonic response under periodic driving. The resulting model retains the simplicity of a three-component Bloch description while improving the quantitative accuracy of transient and driven SERF magnetometry.

Quantum processes can exhibit indefinite causal order, allowing coherent superpositions of distinct orderings of events. Whether such processes generate genuinely noncausal statistics, however, depends not only on their global causal structure but also on the local operations available to the parties. Here, we restrict communication to the classical outcomes of local operations, yielding a causal polytope with new causal inequalities that can be violated using measure-and-reprepare, entanglement-breaking instruments requiring no coherent transmission through the laboratories. Using a semidefinite-programming framework, we bound the achievable violations and reveal noncausal correlations that satisfy all conventional input-signalling inequalities, demonstrating that restricting the information available for communication can uncover forms of indefinite causal order inaccessible under less restrictive operational assumptions.