Papers

The preparation of high-fidelity logical magic states is a crucial subroutine for universal fault-tolerant quantum computation (FTQC). Predicting the performance of FTQC and developing improved protocols rely on numerical methods to classically simulate logical magic state preparation in the presence of noise. Clifford logic on Pauli-stabilizer codes with circuit-level Pauli errors can be efficiently simulated using Pauli-stabilizer formalism, but the non-Clifford operations required to prepare logical magic states render generic simulation inefficient. We introduce Clifford-stabilizer simulation, an exact and efficient algorithm based on updating a Clifford-stabilizer group to simulate noisy preparation protocols for a broad class of logical magic states used to implement non-Clifford gates in the third level of the Clifford hierarchy under circuit-level Pauli errors. Clifford-stabilizer simulation applies to a range of operations that commonly appear in preparation protocols for such logical magic states, including Pauli-stabilizer measurements, logical Clifford measurements, and transversal non-Clifford gates. Our algorithm for Clifford-stabilizer simulation maps a non-Clifford circuit with sampled circuit-level Pauli errors to a Clifford circuit that exactly reproduces its measurement outcome distribution, achieving time and space complexities polynomial in relevant protocol parameters. We perform exact simulation of magic state cultivation up to fault distance 7 by Clifford-stabilizer simulation. Our method provides a route to perform exact benchmarking of large-scale logical magic state preparation protocols required for useful FTQC.

Ensemble nitrogen-vacancy (NV) diamond magnetometers combine high sensitivity with vector-field reconstruction, but practical deployment is limited by errors arising from high-frequency laser noise during short-duration operations and slow-varying gain fluctuations and offset drift during long-term operation. Here, we present an integrated digital architecture for achieving NV magnetometry stability across distinct timescales. A dynamic differential readout continuously balances fluorescence and reference channels to suppress correlated laser noise. Second-derivative Lorentzian lineshape tracking enables in-situ correction of slope variations arising from slow changes in gain and optical excitation. We further identify temperature-induced bias-magnet fluctuations as a dominant source of long-term drift and introduce a magnetic eigenvector transformation that uses the intrinsic response of NV resonances to eliminate these variations. We show, under unshielded ambient conditions, that this architecture achieves an off-resonance noise factor of 1.0 $\pm$ 0.1, matching the fundamental limit with ten-fold suppression of long-term drift, enabling stable, field-ready quantum magnetometry.

Optically readable molecular spins are attractive as quantum sensors due to their nanoscale modularity, synthetic tunability, and scope for sensitive readout. In particular, photoexcited spin-triplet states in organic molecules are appealing in supporting high optical-spin contrast at room temperature. Their utility is underpinned by their coherence, which warrants a detailed understanding of it. Here, from first principles, we systematically explore the Hahn-echo decoherence of the benchmark molecular system for room-temperature optically detected spin coherence—pentacene guest molecules coupled to a para-terphenyl host. Using generalized cluster-correlation expansion methods, we investigate the mechanisms of nuclear-spin-induced decoherence from zero to high magnetic field, exploring the role of guest vs host molecules, specific nuclei, zero-field splitting interactions, and hyperfine parameters. We describe how zero-field decoherence is driven by ~6 nuclei on the guest, while high-field decoherence is driven by ~600 nuclei in the host; how the longitudinal zero-field splitting parameter, $D$, can prolong $T_2$; and the magnetic-field-dependent processes which drive decoherence. These results advance our understanding of decoherence in optically readable molecular spins, providing insight for their synthetic enhancement and deployment as quantum probes.

Understanding how optical orbital angular momentum (OAM) is transferred to matter requires treating recoil and translational motion alongside the internal electronic dynamics. We develop a center-of-mass-resolved theory of one-photon ionization of hydrogen by a monochromatic Laguerre–Gaussian beam and show that the Bessel-vortex photoelectron predicted in fixed-target models is a preparation-dependent limit. For a sharply defined atomic center-of-mass momentum, the recoil records the photon-cone azimuth, and tracing over it generally destroys the coherence required for a pure electron vortex. In the small-transverse-retardation regime, the optical OAM is transferred predominantly to the center-of-mass motion and hence, in the laboratory frame, to the proton. Finite-retardation corrections redistribute angular momentum between center-of-mass and relative motion, while an additional correlation contribution to the electron and proton angular momenta can be tuned through the spatial uncertainty of the atomic center of mass. These results reveal atomic recoil as a key element of OAM transfer in photoionization.

In this study, quantum spin pumping in an antiferromagnetic chain driven by time-dependent potential is investigated. The aim is to explore the possibility of generating and controlling spin currents in the absence of external bias and to examine the role of exchange field and periodic driving in the separation of spin-up and spin-down currents. The system is described using a tight-binding model, and spin-resolved currents are calculated employing the Keldysh non-equilibrium Green's function formalism. Two time-dependent potentials with a specific phase difference are applied to the two ends of the chain, while the chemical potentials of both electrodes are set equal. The results demonstrate that in the adiabatic regime (low frequencies), the response of the two spin channels is nearly identical. However, as the driving frequency increases and the system enters the nonadiabatic regime, absorption and emission processes of energy quanta become activated, leading to significant differences between spin-up and spin-down currents. The pumped current exhibits strong dependence on the chemical potential, allowing for the control of both magnitude and direction of the spin current through its adjustment. With increasing frequency, the spin current enhances, and parameters can be tuned such that the charge current nearly vanishes while a considerable spin current persists. This finding indicates the feasibility of achieving nearly pure spin pumping without net charge transfer in the antiferromagnetic chain. The results provide a promising perspective for designing spin-pumping devices based on antiferromagnetic systems.

We have observed that Hadamard matrices whether real or complex lead to a dense output of identical probabilities for any given single input state. Complex Hadamard matrices have unusual orders and introduce phase which prove useful when controlled phase transformation gates are used. By taking a superposed combinations of input states, we discovered that the Hadamards generate non-uniform probabilities which is practically significant towards amplitude amplification without the need for manual parameterization like Grover's operator~\cite{grover1996}. A variety of graph theoretic properties are applied to TSS graphs and their trends were explored. Additionally, graphs turn out to be nearly isomorphic for the same set of input states which has potential applications for developing Quantum Algorithms. Keywords: Quantum Algorithms, Hadamard Matrices, Unitary Matrix Approach, Topological Structure of Superpositions (TSS), Graph Theory

We investigate the quantum Mpemba effect, whereby a system initially farther from equilibrium relaxes faster than one initially closer to equilibrium, emerging in a quantum harmonic oscillator linearly coupled to a bosonic environment. Starting from factorized thermal states at different temperatures, we derive exact analytical criteria for the occurrence of the quantum Mpemba effect valid also beyond the typically considered weak-coupling and Markovian approximations. Most importantly, we show that the effect is enabled by the initial-slip dynamics generated by the sudden switch-on of the system-bath interaction. Neglecting this contribution completely suppresses the anomalous relaxation, identifying transient system-bath correlations as the key ingredient underlying the quantum Mpemba effect.

Entangling distant quantum sensors is a key application of future quantum networks, allowing for the estimation of global functions of local parameters, with precision that is not possible with stand-alone, individual, quantum sensors. However, with this advantage comes the risk of information leakage over the network via possible malicious parties. It is often particularly important that local parameters remain unknown and that only the global function is shared across the network. Recently, the notion of privacy has been introduced in this context, which ensures that only the agreed function of parameters is shared over the network, even when malicious parties control the network itself, whilst maintaining the estimation advantage. In this work, we introduce a noise-robust protocol for private quantum networked sensing, which we realise using a high-fidelity Greenberger-Horne-Zeilinger (GHZ) state source. We further run a comparative analysis and simulate attacks using three different quantum states, a four-qubit GHZ state, two Bell pairs, and a fully separable state. Our results highlight the clear advantage of GHZ states in maintaining high precision, accuracy, and privacy for the distributed estimation task.

We refine Gavinsky's framework (arXiv:2608.18784) for exponential separations between quantum and randomized communication complexity of total functions and obtain larger separations: polylogarithmic quantum communication versus $\tilde\Omega(\sqrt n)$ randomized communication with two quantum messages, and versus $\Omega(n^{1-\varepsilon})$ for every fixed $0<\varepsilon<1$ with more quantum messages.

In the existing quantum algorithms for the lattice Boltzmann method, resolving the unitarity problem of the BGK collision operator from first principles remains a fundamental challenge, and a systematically constructed unitary alternative that reproduces the BGK relaxation structure to leading order has not yet been established in the literature. In this work, we propose a novel quantum lattice Boltzmann method (QLBM) based on the rotation collision operator, in which the non-unitary BGK relaxation is replaced by a unitary rotation in the amplitude space of the distribution function, and the corresponding gate-level quantum circuits are also constructed. Specifically, the rotation collision operator is developed for both the D2Q5 model of the convection-diffusion equation and the D2Q9 model of the incompressible Navier–Stokes equations. It is worth noting that, for the D2Q5 model, the equilibrium-state preparation circuit can be precompiled and reused, and the resulting unitary blocks can be sequentially composed once the state-dependent collision parameters are specified. Finally, some numerical experiments are performed to validate the developed QLBM, demonstrating its accuracy and effectiveness.

Regularization choice changes the recovery phase diagrams of annealing-based binary compressed sensing. We develop a regularization-selection method that combines systematic parameter search with random forest regression. Under noiseless Gaussian measurements with known sparsity, reference parameters are selected from a candidate grid by minimizing mean squared reconstruction error over repeated simulated annealing (SA) trials. The fitted model predicts these reference values from signal dimension, sampling ratio, and sparsity. With predicted regularization, the SA recovery transition broadly follows the asymptotic reference boundary for box-constrained $\ell_1$ recovery at the larger signal dimensions examined. Without retraining, the same predictor supplies identical regularization values to SA and a quantum–classical hybrid solver. On matched problem instances, the hybrid solver yields smaller mean squared reconstruction errors than SA in parts of the evaluated parameter space. The resulting rule reuses the searched information for subsequent reconstruction without repeating candidate searches at each setting. The results quantify empirical performance under the stated finite candidate grid and solver settings; they do not constitute a solver-independent recovery guarantee or a time-to-solution comparison.

While optical manipulation of atomic arrays has reached a high degree of precision and scalability, the stable optical confinement of solution-based artificial atoms like colloidal quantum dots (CQDs) remains hindered by weak trapping forces and thermal fluctuations. High-intensity trapping often compromises the quantum properties of these emitters, creating a significant trade-off between mechanical stability and optical integrity. To overcome this, we propose encapsulating CQDs within a transparent polymer matrix, thereby increasing the effective interaction volume and optical restoring force without altering the emitters themselves. This strategy allows for stable spatial confinement under standard experimental conditions, as evidenced by the direct resolution of positional fluctuations through photoluminescence imaging and trajectory tracking. With averaged position fluctuations below 20 nm, the intrinsic emission spectra and photoluminescence decay dynamics remain largely unaffected, and photon-correlation measurements confirm the full preservation of single-photon emission. These findings establish a robust method for the controlled confinement of colloidal quantum emitters and in-situ quantum-optical measurements for future advancements in quantum-optical manipulation of artificial atoms.

Mechanical frequency-shift sensors have never reached their fundamental thermomechanical or quantum limits. Every material, size, and transduction scheme yet examined yields a $1/f$ floor 1-3 orders higher, with a flicker-noise coefficient $h_{-1} \propto 1/V_{\varepsilon}$. Surveying the published record, I find the invariant $h_{-1}\,V_{\varepsilon} \equiv \sigma_A ^2\, V_{\varepsilon}/(2\ln 2)$ independent of device size across 13 decades; volume-independent noise is excluded by 9$\sigma$, site-averaging by 3.8$\sigma$. No $Q$ dependence appears: reported $Q^{-n}$ laws scale equivalently when $Q$ and volume co-vary; only volume scaling survives when they do not. Mass resolution follows as $|\delta m| \propto \sqrt{h_{-1}\,V_{\varepsilon} \cdot V}$.

For the standard Clifford+$T$ gate set, deterministic, ancilla-free synthesis now attains the minimal $T$-count for general single-qubit unitaries (Morisaki et al., arXiv:2510.05816). The $\sqrt{T}$ gate rotates by half the angle of $T$, generating a finer lattice of implementable operations. It was assumed that access to this magic state lowers the cost of deterministic and ancilla-free synthesis of general single-qubit unitaries, but no direct Clifford+$\sqrt{T}$ algorithm existed for this case. We provide one by extending the integer lattice-point enumeration method of Morisaki et al. We adopt a resource state cost model based on the magic-state catalysis approach of Gidney and Fowler (arXiv:1812.01238). On Haar-random targets synthesized to precisions ranging from $\varepsilon=10^{-3}$ to $10^{-8}$, the cost of Clifford+$\sqrt{T}$ circuits scales as $2.4\log_2(1/\varepsilon)$ compared to $3.0\log_2(1/\varepsilon)$ for the provably $T$-count-optimal Clifford+$T$ circuits. Once a one-time catalyst state is amortized, the Clifford+$\sqrt{T}$ circuits are never costlier than their Clifford+$T$ counterparts.

Noise spectroscopy with quantum sensors is a powerful tool for characterising the properties of the sensor environment and detecting critical magnetic phenomena. While replacing single sensors with large ensembles promises substantial gains in measurement sensitivity and field of view, the output becomes difficult to interpret when there is a variable coupling to targets across the sensing ensemble. In this work we present an analysis procedure for accessing the true source noise spectrum using ensemble coherence from dynamical decoupling measurements. We show that sequence timing plays a dual role in ensemble noise spectroscopy, setting both the frequency selectivity and the weighted collection of signal across the ensemble, and demonstrate how incorporation of the coupling distribution allows accurate parameter extraction of the noise. We apply this procedure to a model system, shallow nitrogen-vacancy centres in diamond, and show that consistent information about the spectral character of MHz-range surface noise can be obtained from two sensing ensembles featuring distinct depth distributions. Our results pave the way for using large quantum sensor ensembles for quantitative, broadband noise spectroscopy, with straightforward extension to other solid-state and molecular sensing platforms.

Molecular sequence data are used to reconstruct evolutionary relationships among taxa, but reconstruction accuracy depends not only on the tree-building method but also on how pairwise sequence relationships are represented. We evaluated sequence-to-affinity representations in a recursive normalized-cut (Ncut) framework whose graph-partitioning subproblems were formulated as quadratic unconstrained binary optimization (QUBO) models and solved using Simulated Bifurcation. Using simulated amino-acid and nucleotide datasets spanning multiple tree-generation settings and evolutionary divergence, we compared normalized bit-score affinities with representations derived from transformed sequence similarities and evolutionary distances, examined post-swap refinement, and used neighbor joining (NJ) as a distance-based comparator. Affinity representation substantially affected internal split recovery, particularly for nucleotide data. JC69-based local affinities maintained comparatively high accuracy as divergence increased, whereas normalized bit-score and BLAST-derived kernel representations declined more markedly. Post-swap refinement generally improved recovery, but not consistently across individual reconstructions. NJ achieved higher mean split recovery than corresponding recursive Ncut reconstructions for WAG and JC69 distances across all evaluated conditions, whereas recursive Ncut outperformed NJ for BLAST-derived logarithmic distances under some conditions. These results show that graph construction is an important determinant of recursive Ncut-based phylogenetic reconstruction. A representation that performs well within Ncut does not necessarily provide the most accurate use of the underlying pairwise distances. Pairwise representation, affinity transformation, optimization, and recursive tree construction should therefore be evaluated jointly.

The 0-{\pi} qubit promises longer lifetimes than the transmon, making it a strong candidate for a next-generation, lower-error qubit. Gyenis et al. experimentally demonstrated an unprotected single-qubit gate in the soft 0-{\pi} regime [1], but no corresponding two-qubit gate has yet been proposed. We propose an unprotected CZ gate for capacitively coupled soft 0-{\pi} qubits. The gate uses a direct transition between a computational state and a higher non-computational state. Assuming negligible device disorder and a phenomenological noise model, the simulated CZ gate achieves a fidelity of approximately 99.9% at a gate time of approximately 160 ns.

Two-dimensional massive Dirac systems feature a gapped Dirac-cone dispersion central to a broad range of phenomena in condensed-matter and topological physics. While quantum simulations have demonstrated one-dimensional Dirac dynamics and two-dimensional massless Weyl dynamics, programmable simulation of massive two-dimensional Dirac dynamics remains experimentally unexplored. Here, we realize a programmable two-dimensional free Dirac Hamiltonian in circuit QED, with independently tunable spin-momentum couplings and mass, using a single Rabi-driven qubit coupled to two modes of a multimode cavity. Using this Hamiltonian, we observe rotational Zitterbewegung of a two-dimensional massive Dirac particle and its dependence on the effective mass. Time-dependent master-equation simulations incorporating measured decoherence, corrections beyond the rotating-wave approximation (RWA), and anharmonicity of the transmon reproduce the observed dynamics. Our results establish multimode circuit QED as a compact, programmable platform for higher-dimensional relativistic quantum dynamics and provide a foundation for exploring dynamical and topological phenomena in gapped Dirac systems.

The geometric phase (GP) of a periodically driven symmetricspin-boson model (SBM) is investigated using the process-tensor time-evolving matrix product operator (PT-TEMPO) method. A longitudinal monochromatic field drives the qubit along the same coordinate that couples to an Ohmic bosonic environment. The gauge-invariant kinematic GP is evaluated from the reduced-statetrajectory, and a circular non-additivity measure quantifies the combined effects of driving and dissipation relative to driven-unitary and undriven-dissipative references. Amplitude, frequency, coupling-strength, and bath-cutoff sweeps reveal regimes in which periodic driving reduces or enhances environmental phase deformation relative to the unitary counterpart. The one-cycle GP exhibits pronounced nonmonotonic drive frequency dependence, while its bath-induced shift depends sensitively on both coupling strength and cutoff. These trends are interpreted qualitatively in terms of Floquet dressing and bath spectral structure. A two-cycle echo provides a complementary reversibility diagnostic, whose persistence signal does not generally measure the Tong GP. The results characterize the non-additive influence of driving and dissipation on geometric-phase dynamics and identify parameter regimes of reduced bath-induced deformation.

This paper reports the proof of a strong converse for the unconstrained quantum capacity of the pure-loss bosonic channel. At every fixed rate above capacity, the entanglement-generation fidelity of every code is bounded by a constant times the reciprocal of the number of channel uses. The bound holds without an energy constraint and for arbitrary encoded states, including states correlated across all input modes, and arbitrary joint decoders. The proof combines quantum Chebyshev and hockey-stick testing inequalities with a uniform relative-entropy-variance bound for the balanced pure-loss channel, corresponding to transmissivity $\eta=1/2$. The variance bound follows by expressing the balanced beam splitter in bright and dark modes: the dark modes are exactly in vacuum, and any state orthogonal to that vacuum contains at least one dark photon. For general transmissivity, dilating the degrading attenuator reduces the problem to this balanced-channel setting and bounds the decoder test by precisely the factor that produces the known quantum-capacity threshold. The resulting argument establishes the strong converse at the unconstrained quantum capacity for every pure-loss bosonic channel.

The computation of transport coefficients in interacting quantum many-body systems is rarely analytically accessible. Here, we develop a new Krylov-space mechanism that makes the leading density dependent correction to Green-Kubo diffusivity exactly calculable in the strong-dissipation regime of a one-dimensional noisy spin-$\frac{1}{2}$ XXZ chain. This is done by showing that the density-polarization-dressed bond coherence generates a Krylov subspace where repeated action of the dissipator closes exactly on an explicitly identifiable operator family. Within this subspace, the dissipative dynamics is then mapped onto a self-similar semi-infinite chain with a boundary defect. Surprisingly, all Lanczos coefficients of the Krylov chain and its boundary Green's function can be determined exactly. The latter then determines the exact leading density-dependent correction to the diffusivity. Finally, we calculate analytically the full boundary-to-bulk Green's function and find that it decays exponentially along the emergent Krylov chain.

Sample-based quantum diagonalization (SQD) is a hybrid quantum-classical method for electronic-structure calculations. We applied SQD to a titanium-based metallocene catalyst system for 1-hexene production, where free-energy differences must be predicted within 1 kcal/mol to accurately determine product selectivity. However, currently accessible active spaces on quantum computers are limited in size, leaving significant dynamical correlation effects outside the active space. To address this challenge, we combined SQD with Tailored Coupled Cluster (TCC) theory. In this SQD-TCC framework, static correlation is treated by SQD, while dynamical correlation is incorporated through CCSD and its perturbative triples extension, TCC(T). We calculated the relative energies of two transition states governing 1-hexene selectivity. While SQD alone did not yield converged relative energies within practically accessible active spaces, SQD-TCC and SQD-TCC(T) provided reasonably converged results. Importantly, the relative energy obtained from SQD-TCC(T) differed by more than 1 kcal/mol from the corresponding CCSD(T) result, demonstrating the significance of static correlation in this system and its impact on predicted selectivity. Although TCC(T) calculations based on CASCI are feasible for small active spaces, the present system requires substantially larger active spaces that are beyond the reach of CASCI. By using SQD, we were able to access active spaces impractical for classical CASCI calculations. These results demonstrate that both static and dynamical electron correlation are essential for a reliable description of this chemistry and highlight the importance of incorporating dynamical correlation into quantum-computing approaches targeting chemically accurate simulations.

We prove that if we take a rooted product of a circulant graph with universal perfect state transfer with a path of fixed length whose end edge is weighted with a transcendental number, then there is pretty good state transfer between any pair of endpoints of these paths. As a consequence, in a path with an even number of vertices with transcendental weights on the two edges incident to the endpoints, there is pretty good state transfer.

Projected ensembles reveal information about quantum many-body dynamics beyond the reduced density matrix. Here we investigate how spatial constraints affect the emergence of this information in a kicked Ising chain with a spatially varying longitudinal field. We consider partial projected ensembles, obtained by measuring a remote region while leaving an intervening buffer unobserved. Our numerical results reveal a pronounced contrast between nearly ballistic correlation onset in the ergodic regime and strongly delayed onset in the tilt-constrained regime, corroborated by quantum mutual information. Despite these different onset scales, the conditional-state fluctuations decrease approximately exponentially with buffer length in both regimes. Full projected ensembles additionally exhibit slow relaxation and persistent measurement-basis dependence in their higher moments. We establish an information-theoretic characterization of the connected second moment and use a solvable dephasing model with effective-basis measurements to illustrate the separation of phase accumulation and coherence loss. Within this model, a factorially suppressed coupling envelope yields sublogarithmic spreading consistent with the finite-distance onset trends. Our results identify partial projected ensembles as probes of the distinction between the time required for correlations to develop and the information that remains accessible under partial observation.

An $[[n,k,d]]$ stabilizer code is phantom if every in-block logical CNOT gate can be realized by a permutation of its physical qubits. This eliminates the large and complicated physical overhead normally required for logical entangling gates. Yet this symmetry is highly restrictive: phantom codes are rare, the number of logical qubits is limited to $k=O(\log n)$, and no phantom qLDPC family with growing logical dimension was previously known. We make three contributions. 1. We prove that recognizing phantomness of a given stabilizer code is at least as hard as Graph Isomorphism, even for CSS codes encoding only $k=2$ logical qubits. 2. We propose the first rate optimal phantom qLDPC families: for every fixed $D$, our CSS families achieve the maximal logical scaling $k=\Theta(\log n)$ and distance $d\geq D$. 3. We prove a distance no-go theorem: every phantom code family with $k=\omega(\sqrt{\log n})$ and check weight $w=O(1)$ satisfies $d\leq w$ for sufficiently large $n$. Thus our fixed-distance qLDPC families are distance-scaling optimal at the maximal logical scaling $k=\Theta(\log n)$.

Simulation of quantum many-body systems is a principal application of quantum computing, but available devices remain limited by the number of qubits and cannot accommodate systems of the desired size. One approach is to host a large evolution across several modest distributed systems that exchange classical information alone. Current protocols such as circuit knitting incur a quasi-probability sampling cost that grows exponentially with the number of remote gates across the cut, even when physical correlations across the cut are actually bounded. In this work, we present a truncated hybrid tensor network (THTN) framework in which a remote two-body gate is applied as a sum of local unitaries on the subsystems, linked by a classical connecting tensor, and an interface truncation retains Schmidt modes across the cut. Remote gates between the same subsystems can be merged on one connector, so non-one-dimensional models, such as layered partitions with strong intra-layer and weaker interlayer couplings, may be cast onto a one-dimensional cut. The retained non-negative Schmidt coefficients also define a sampling rule for local observables. We validate this distributed protocol by classical simulation against time-evolving block decimation (TEBD) at the same bond dimension. The truncated dynamics track the TEBD references on chains and ladders, with the clearest gain on a layered model.

We investigate finite-time field-induced ionization from a one-dimensional attractive delta-function well in a uniform dc electric field of arbitrary strength. Our aim is to determine the physical bound-state survival amplitude \(a_b(t)\) at any observation time without constructing the complete time-dependent propagator or wavefunction. In the gauge-equivalent Kramers–Henneberger representation, the field appears as motion of the contact point, and the resulting dynamics reduces to a closed Volterra equation. Exact endpoint-phase factorization organizes the full chronological rescattering history into a relative-time convolution hierarchy and an exact resolvent. By introducing the accumulated bound-state amplitude and reorganizing its two-time domain in relative and complementary center times, the final contact contribution becomes an explicit boundary integral. All spatial integrations are carried out analytically. The field-driven contact-free term is obtained in closed form using the Faddeeva function, while the direct and repeated-rescattering terms are expressed as explicitly evaluable time integrals. The result applies at arbitrary dc-field strength and finite time, with no weak-field expansion, rescattering truncation, or asymptotic-time approximation. It is verified through the exact field-free limit and an independent numerical solution of the original physical Volterra equation. The formulation gives an exact nonperturbative solution of a fundamental ionization model and reveals otherwise hidden analytical structure in driven quantum dynamics.

Linear constraint systems (LCS) provide a compact algebraic language for nonlocal games and state-independent contextuality. In the binary case the Mermin–Peres square shows that inconsistent LCS can be solved by promoting variables to local Pauli operators, whereas a series of no-go results excludes analogous Pauli-, Clifford- and monomial unitary-based constructions at odd prime modulus. We first isolate the reason for this difference: for tensor-product quantum solutions, the obstruction to a classical solution of a LCS over $\mathbb{Z}_n$ decomposes into obstruction classes carried by the individual factors. As a consequence, a genuinely global obstruction cannot arise solely by tensoring locally unobstructed systems. The argument is specific to odd modulus; at even modulus the reordering phase need not vanish, as in Pauli-based examples. Given this distinction, we instead associate LCS to finite arrangements of rank-one projectors and resolutions of the identity in finite-dimensional vector spaces. Quantum solvability for such LCS is automatic and the search for a quantum-classical gap rests entirely on proving classical unsatisfiability of the underlying modular incidence problem of the arrangement. By relating such LCS with group-valued frame functions, we identify a family of examples in the work of [Harding, Jager, and Smith, Int. J. Theor. Phys. 44, 539 (2005)]. To establish the (non)existence of classically unsatisfiable LCS over $\mathbb{Z}_n$ with quantum solutions in all dimensions $d$ and for all $n\in\mathbb{N}$, we further construct explicit examples for the cases $d=n$ prime. Our main result thus positively resolves the existence problem of such LCS beyond the binary case: such systems exist if and only if $d\geq 3$ and $\gcd(n,d)>1$. Moreover, we establish the existence of LCS with a quantum-classical gap over finite fields if and only if $d\geq 3$ and $p\mid d$.

Flux-activated two-qubit gates in superconducting processors require correction of line distortion, which otherwise produces residual detuning, conditional-phase error, and leakage. Prior demonstrations of cryoscope-based distortion calibration have generally used commercial solutions that specify the filter models but not their FPGA implementation. These details matter for custom and open-source systems, where the fixed-point coefficient and datapath formats set how accurately the correction is realized, and the IIR feedback loop in its standard form does not meet timing at the required clock rate. We derive the coefficient formats of the correction filters from a step response error tolerance, using bounds on the quantization-induced displacement of the poles and zeros over the physical parameter range of each distortion, and the accumulator format from the smallest input change that must remain resolvable at the output. The same analysis gives the conditions under which quantization preserves filter stability. We implement the resulting FIR/IIR cascade on the QubiC platform at a fabric clock rate of \SI{500}{MHz}, using a super-sample-rate structure with scattered look-ahead pipelining, which removes the feedback recursion from the critical path without changing the target transfer function. A representative cascade for our \SI{1}{GS/s} flux lines, comprising an integrator, a second-order section, and a 20-tap FIR, consumes 88 DSP slices and adds \SI{162}{ns} of latency. We confirm the hardware implementation by correcting characteristic bias-tee distortion, an intermediate step toward full cryoscope-based calibration.

At a fixed thermal exposure, the same stabilizer processor can be classically simulable or quantum universal, depending on which environmental records its controller retains. We give an exact computational classification of energy-counting thermal-idle instruments in a quantum processor with ideal stabilizer control and independent local Markov baths. The relaxation time $T_1$, homogeneous coherence time $T_2$, and equilibrium excited-state population $p_e$ determine an exact computational boundary at $(1-p_e)T_2/T_1=1$. If every location lies at or below it, branchwise nonnegative stabilizer decompositions give an explicit efficient classical sampler for the adaptive circuit and its full time-resolved exchange record. Above it at a single repeatedly accessible location, a suitable idle duration and no-exchange conditioning supply distillable ancillas and enable universal quantum computation with polynomial overhead. At finite temperature on the resource side, erasing the record at a sufficiently long, unsplit exposure makes the averaged channel stabilizer measure-and-prepare, and even a terminal parity check then yields only simulable branches. Yet at that same exposure, retaining only the bit recording whether any exchange occurred still heralds distillable ancillas, because a thermal round trip restores the parity after its first exchange has already removed the coherence.