Papers

We study the topological structure of the quantum phase diagram of gapped systems by identifying the noncontractibility of loops, so-called $S^1$-families, within the gapped phase diagram in which many-body Hamiltonians can have nontrivial ground-state degeneracy. We manifest the role of symmetries in such $S^1$-family classifications by the exotic symmetry interplay: (i) nontrivial mixed anomalies, (ii) semi-direct product relation between the spontaneously broken and the unbroken symmetries, and (iii) symmetry with noninvertible operators. We find that such structures lead to the novel $S^1$-family classifications inaccessible by earlier classifications based on “independent” symmetries. Furthermore, we construct lattice realizations of these $S^1$-families and explicitly demonstrate their novel algebraic structures.

Entanglement-based networks provide a scalable framework for multiuser quantum communication by passively routing spectrally correlated photon pairs across interconnected nodes. Several wavelength-allocation schemes have been demonstrated experimentally, but these designs do not yet give a general way to determine how spectral use, receiver load, repeated connections, and fan-out constrain one another. We address this problem through the network's connectivity graph, where the wavelength assignment becomes a resource-optimization problem. For one-sided fan-out, assigning each link to a center and grouping links with the same center gives an exact optimization for arbitrary networks and fan-out limits. We solve this for complete networks and for complete networks in which every user has one excluded partner. Allowing both conjugate wavelengths to fan out changes the resource landscape: a balanced binary hierarchy attains the minimum spectral-layer count for a complete network while reducing the maximum receiver load to logarithmic in the number of users. An eight-user complete network then makes explicit the competing roles of spectral efficiency, receiver load, redundancy, and fan-out. We include the passive-splitter loss and the dependence of the key rate on the delivered pair flux to determine the minimum total pair-generation rate required to meet the prescribed targets. Finally, we formulate the corresponding BBM92 quantum key distribution (QKD) secret-key-rate analysis for a continuous-wave-pumped broadband source, with true and accidental coincidences evaluated between detector channels at the two endpoint users and relative layer pair-generation rates fixed by the source spectrum. This framework, therefore, provides a direct route from exact network resource laws to the design and comparison of passive entanglement architectures under experimentally specified hardware constraints.

Numerical studies of noisy Rydberg-atom optimization almost universally compress decoherence into a single scalar, silently pricing spontaneous decay ($\Gamma$) and dephasing ($\gamma$) alike. We treat the two as independent axes, mapping a quantum-annealing heuristic for unit-disk maximum independent set on 20 random $N=10$ graphs across the $(\Gamma,\gamma)$ plane, with the annealing time re-optimized at every point. The mean approximation ratio does collapse onto one scalar, but onto $u=\kappa\Gamma+\gamma$ with $\kappa=8.05\pm0.5$ (stat) $\pm1.1$ (syst); the isotropic $\Gamma+\gamma$ fails by a factor of 30 in residual. First-order perturbation theory reproduces $\kappa$ from noiseless propagation alone and gives the mechanism: the objective is diagonal in the basis of the dephasing operator, so dephasing cannot change the answer once the drive is off, and a single driven atom already has $\kappa\simeq8.5$. The exchange rate is thus a property of the protocol as much as of the platform: the ramp-down fraction moves it between 2.3 and 16.3. At a fixed schedule it is stable across system sizes, interaction strengths, and estimators. Because the whole cost model is noiseless, a schedule can be tuned to a device's channel mixture without any noisy simulation: jointly tuning the drive ramp-down and the sweep's detuning ramp recovers about a third of the Markovian damage at no hardware cost, and the ramp the noise-aware objective selects is not the one noiseless optimization would choose. Per unit rate decay is eightfold the dearer channel, but the measured $T_1$ enters weighted by its branching ratio to the ground state ($b\approx0.4$ for the calibrated device), which leaves the two Lindblad channels comparably costly at a present-day operating point. One-parameter noise models remain serviceable, provided the parameter is $u$.

Grover's quantum search algorithm provides a fundamental quadratic speedup for unstructured datasets, reducing query complexity from $\mathcal{O}(N)$ to $\mathcal{O}(\sqrt{N})$. However, the algorithm's reliance on precise iteration counts leads to the “soufflé problem,” where over-rotation results in a sharp decline in success probability. This limitation is particularly restrictive when the number of solution states, $M$, is unknown. In this work, we present an ancilla-mediated fixed-point quantum search algorithm that achieves robust convergence by mapping the solution amplitude to a dedicated ancilla qubit. Unlike existing phase-matching fixed-point methods, our approach utilizes Grover's real-plane reflections, thereby maintaining the intuitive geometric architecture of the original algorithm. We demonstrate that this method achieves a success probability of at least $92.6\%$ with a query complexity of approximately $\mathcal{O}(\sqrt{N/M})$, effectively bridging the gap between standard amplitude amplification and robust fixed-point convergence.

We investigate the dynamical behavior and spread complexity of quantum states within the mass-deformed BMN matrix model equipped with an emergent $U(1)$ global charge at finite temperature $\beta^{-1}$ and chemical potential $\nu$. Focusing on the strong-coupling regime ($\mu \gg 1$), we model the dynamics via a charged Thermofield Double (cTFD) state and trace the evolution of spread complexity across three distinct thermodynamic regimes. In the low-temperature gapped phase ($\beta \mu \gg 1$), discrete mass-gap bound states dominate, trapping wavepacket dispersion and producing non-chaotic, oscillatory early-time growth. Conversely, in the high-temperature continuum phase ($\beta \mu \ll 1$), thermal excitations overwhelm the mass gap, driving a transition to a continuous advection field that exhibits maximal chaotic scrambling with a Krylov Lyapunov exponent $\lambda_K = \pi / \beta$ that saturates the universal bound. In the intermediate temperature regime ($\beta \mu \sim 1, \beta \nu \sim 1$), the interplay between mass-gap bound states and the continuous thermal background induces a sub-leading correction to the Lanczos coefficients $b_n \sim \frac{\pi}{\beta} n + \gamma \sqrt{n}$, governing a continuous sub-exponential crossover before full chaotic thermalization. Technical derivations regarding KMS boundary conditions, grand canonical spectral moments, residue analysis, and time-reversal symmetry breaking in Krylov space are detailed in four dedicated appendices.

It is believed that the enhancement in qubit-resonator coupling allows a better dispersive readout but introduces greater Purcell loss. In this work, we propose that a dark mode in a coupled quantum system may violate this rule by introducing the ZZ interaction between the dark and a bright mode. The dark mode may exhibit an effective zero coupling strength, and zero Purcell loss with the resonator photons. Nevertheless, the dispersive shift is almost the same as the bright state, due to the higher order perturbation introduced by the higher excited states. Such a state demonstrates the measurability without a Purcell limit in circuit quantum electrodynamics.

Can finite-range correlations hide in the statistics of an extended quantum state? The Schrödinger-Nagasawa transform represents the wave function by positive forward and backward diffusion fields whose product is the Born density. We promote them to branching superprocesses, \(\Phi_F\) and \(\Phi_B\): diffusion samples stochastic paths, whereas Bohm/Fisher-controlled branching generates genealogies of alternative continuations. With rates evaluated on the prescribed Born density, their means reproduce Schrödinger dynamics exactly. The connected sector exhibits supercritical, critical, and subcritical clustering in confinement and has critical dimension \(d_c=2\) in free space. Stationary eigenmodes remain extended; subcritical clusters acquire the reduced de~Broglie scale. We then let the branching rate respond to the fluctuating product \(\Phi_F\Phi_B\). In the reciprocal basis, the fields equal a smooth reference \(R\) plus centered fluctuations \(\psi_F,\psi_B\), defining the signed kernel \(C_{\rm FB}(x,y)=\mathbb E_\omega[\psi_F(x)\psi_B(y)]\). On the anticorrelated branch, \(\rho_{\rm BSM}(x)=-C_{\rm FB}(x,x)\) is the positive organized connected weight. Stationary matching of this weight to the Born profile is imposed as a closure condition, while off-diagonal decay defines the correlation range. The pair equation splits into collective and relative sectors: spectral cancellation selects the Born collective mode, while suppression of the leading density fluctuation selects the anticorrelated source channel. With relative diffusivity \(D_{\rm eff}\) and positive relaxation rate \(\mu_{\rm FB}\), correlations have screening length \(\xi_{\rm FB}=\sqrt{D_{\rm eff}/\mu_{\rm FB}}\). Within this reciprocal closure, an extended Born-shaped connected weight and a finite correlation range can coexist in one stochastic kernel.

Contrary to the semiclassical expectation for fully chaotic systems, localization of resonances is found to be a common feature in open microcavities. In spiral-shaped dielectric microcavities, a substantial fraction of resonances localize on polygonal patterns in real space, are chiral, and their momentum distributions accumulate near the critical line for total internal reflection. Despite the extensive investigation, the physical mechanism responsible for their remarkable abundance has remained a long-standing question. Addressing this, we reveal a physical correspondence between an inhomogeneous-loss Hatano-Nelson model and the dielectric phase space of a spiral microcavity. We show that the combination of geometry-induced momentum drift and refractive escape yields a generalized non-Hermitian skin effect in the phase space momentum. We identify this mechanism as the origin of the critical-line localization of resonances in open chaotic spiral microcavities, extending the skin-effect concept beyond nonreciprocal lattices to phase space and to open chaotic wave systems.

Non-Hermitian control is difficult in solid-state systems due to fixed dissipation. Here, we show that in a spin-orbit-coupled planar Josephson junction, changing only the Josephson phase reverses the non-Bloch propagation of a low-energy Andreev band and switches its boundary accumulation between junction edges. The phase reshapes the band's spin and electron-hole composition, causing a fixed reservoir to unequally attenuate counterpropagating modes. Weak-loss theory links this phase-controlled loss imbalance to boundary-selected complex momenta, offering an in situ route to reconfigurable non-Hermitian transport in superconducting platforms.

We develop a symmetry-based theory of spin-orbit-valley coupling in silicon that reveals an intrinsic source of Dresselhaus spin-orbit coupling independent of interfaces or external electric fields. Treating the valley degree of freedom as a symmetry-carrying quantum degree of freedom, we show that the Dresselhaus interaction is necessarily valley off-diagonal and that a bulk contribution proportional to the valley Pauli matrix $\tau_1$ is symmetry allowed. Tight-binding calculations yield a bulk coupling more than an order of magnitude larger than typical interface-induced spin-orbit coupling; achieving the same energy scale through the interface-induced mechanism would require electric fields roughly 50 times larger than typical fields. We further derive the symmetry-allowed spin-valley couplings generated by magnetic-field gradients and show how they account for the valley-dependent Zeeman splitting observed in micromagnet experiments. A slight tilt of the background magnetic field out of the plane produces an additional isotropic contribution linear in $B_z$, providing an experimentally accessible signature of the corresponding coupling constant. Finally, we predict a spin-independent micromagnet-induced valley splitting in the $\tau_3$ channel, which is distinct from the $\tau_{1,2}$ channels generated by alloy disorder and therefore remains robust against disorder-induced cancellation. These results establish valley symmetry as a fundamental ingredient in the spin-orbit physics of silicon and provide new mechanisms for controlling and probing spin and valley degrees of freedom in silicon quantum devices.

Efficient simulation of dense gate-defined multi-quantum-dot arrays requires accurate and scalable modeling methods, compatible with asymmetries and imperfections of realistic voltage-controlled confinement potentials. We present a numerical localization procedure that rotates the eigenbasis of a general one-particle effective orbital Hamiltonian into $s$-, $p$-, $d$-, $\ldots$-shells of localized orbital wavefunctions associated with individual quantum dots. The pairwise tunnel couplings between such states are computed directly as matrix elements of the Hamiltonian. We demonstrate this procedure on a 2D triangular Si-MOS triple-quantum-dot array by obtaining the voltage dependencies of the tunnel couplings and their distributions in the presence of disorder. We discuss the implications of this evaluation method on the many-body calculations, and relate it to the experimental tunnel coupling measurements.

Randomized product formulas such as qDrift offer a resource-efficient alternative to deterministic Trotter–Suzuki decompositions for Hamiltonian simulation, removing their polynomial dependence on the number of Hamiltonian terms. qDrift, however, is intrinsically limited to first order in the evolution time, so its query complexity remains linear in the inverse of the target accuracy, $1/\epsilon$. We introduce Pathwise Random Hamiltonian Simulation (PRHS), which extends qDrift to arbitrary order by subdividing each time step into $M$ correlated slices, each evolving under a term sampled from a quasi-probability distribution that we construct in closed form and prove unique, with a bias decaying factorially in $M$. Optimizing jointly over the number of slices $M$ and the number of independent blocks $N$ interpolates between the standard qDrift protocol at long times and a high-precision regime where the query cost grows slower than any power of $1/\epsilon$, without requiring ancillary qubits. Numerical simulations of five molecular Hamiltonians confirm this advantage, with PRHS achieving accuracies two to four orders of magnitude beyond qDrift at equal query cost.

In 2010, Pál and Vértesi found a family of finite-dimensional strategies for the $I_{3322}$ Bell inequality whose optimized values appeared to converge as the local Hilbert-space dimension grew. They conjectured that this limit is the supremum over all finite-dimensional quantum strategies, but that no finite-dimensional strategy attains it. We prove both claims. The proof uses the symmetry of the Bell functional to associate every strategy with a finite matrix of probabilities, one for each pair of spectral subspaces of Alice and Bob. This matrix gives an upper bound on the Bell value, and finite-dimensional strategies built from the repeating structure found by Pál and Vértesi approach it as the dimension grows. If the bound were attained exactly in finite dimension, the optimality conditions would then require a state that cannot be normalized. Consequently, the set of finite-dimensional quantum correlations is not closed in the $(3,3,2,2)$ scenario, the smallest Bell scenario where this can happen. Moreover, approaching the supremum requires unbounded local dimension. The core of the proof was formalized in Lean~4.

Pure three-qubit states with the same pairwise concurrences and three-tangle can still have different Kempe invariants. We show that the Kempe invariant orders the entanglement dynamics of all three pairs under identical, independent local depolarizing channels, with smaller values giving greater robustness. The same ordering also holds for the sum of squared pairwise entanglements of formation and the sudden-death thresholds of pairwise entanglement.

Imaging astrophysical sources with a multi-station interferometer is intrinsically a multiparameter quantum-estimation problem. {Using tools from multiparameter quantum metrology,} we show that time-resolved repetitive or adaptive measurements in an \(N\)-station array suffer a fundamental array-level incompatibility among visibility estimators. Collective measurements, {which coherently process the received starlight across multiple time bins in a single joint readout}, remove the array-size penalty up to an order-unity factor, yielding an asymptotic \(O(\sqrt{N})\) enhancement for the {directional-averaged} SNR of visibility measurement. We then propose a memory-assisted interferometric architecture designed to implement collective readout through coherent storage and joint quantum processing. Imaging simulations and Fisher-information analyses demonstrate that collective measurements improve image reconstruction in near-term arrays and enhance the resolving power of future long-baseline architectures, with pronounced benefits for representative AGN targets such as NGC~4151 and 3C~273. These results highlight collective measurement as a promising building block for future quantum-assisted interferometric arrays for stellar imaging.

The bosonic Kitaev chain under open boundary conditions has attracted recent attention due to its realization in driven-dissipative systems and its intriguing non-Hermitian boundary physics. The model is known to be solvable via local squeezing transformations in the position-momentum representation. In this paper, we present an alternative, purely algebraic solution that relies entirely on the standard bosonic Bogoliubov transformation. For an $N$-site chain, we propose an asymmetric plane-wave ansatz with unequal left- and right-moving momenta to analytically solve the associated $2N\times 2N$ non-Hermitian “associated matrix". The left eigenvalue problem yields $N$ distinct eigenvalues, each of which is twofold degenerate. By carefully resolving these degeneracies using the bosonic commutation relations, we construct the $N$ physical Bogoliubov quasiparticle operators. The construction reveals non-uniquenesses that in special cases exactly mirror the freedom in the local squeezing transformations of the original approach. The diagonal form of the Hamiltonian is obtained explicitly and is shown to be equivalent to the original Hamiltonian. The proposed asymmetric plane-wave ansatz and degeneracy-resolution technique are not limited to the present model and can be generalized to other bosonic pairing systems, including those with inhomogeneous pairing or hopping terms.

Dynamical instability in parametrically driven bosonic systems is generally associated with diverging occupations and the absence of a stationary state, but its implications for long-time entanglement remain unclear. We investigate this question in a dissipative bosonic dimer with beam-splitter and two-mode-squeezing interactions, local loss, and a tunable common bath. The non-Hermitian dynamical spectrum governing the Gaussian moments partitions the parameter space into distinct regimes and provides a unified description of population and entanglement dynamics across both stable and unstable regions. We find that dynamical instability does not imply unbounded entanglement growth: although the bosonic population diverges, the logarithmic negativity remains bounded and approaches a finite asymptotic value. We further characterize the finite asymptotic entanglement and show that asymmetric local dissipation shifts both the stability boundary and the threshold for nonzero asymptotic entanglement. For identical local dissipation, the presence of a common bath leaves the dynamical-region boundaries unchanged while qualitatively reshaping the long-time entanglement landscape, producing broad enhancement regions within the stable regimes and a narrow enhancement region within the unstable regime. In the common-bath-only limit, this enhancement is attributed to an exact dark-mode (bound-state-in-the-continuum, BIC) protection mechanism, which reduces to a quasi-BIC remnant under independent dissipation. Our results establish the non-Hermitian dynamical spectrum as a framework for connecting stability, nonequilibrium dynamics, and asymptotic entanglement in open quadratic bosonic systems.

Theoretical studies on how quantum systems are affected by external factors are often formulated through parameter changes in the system's Hamiltonian. Beyond Berry connections and phases, which focus on specific Hamiltonian eigenstates, recent studies inspired by non-Hermitian quantum formalisms provide a framework for obtaining general state evolution generators for real-valued parameters. This study extends the applicability of the evolution generator formalism to complex-valued parameters via Wirtinger derivatives. By treating a complex parameter and its conjugate as independent variables, the evolution equations are derived for both quantum states and the metric of the Hilbert space bundle. The analysis demonstrates that while state evolution with respect to a complex parameter is naturally governed by its corresponding evolution generator, metric evolution requires a coupled contribution from both the generator and its conjugate counterpart to preserve state normalization. Explicit examples are worked out to illustrate the implementation and physical consistency of the formalism.

The stationary scattering properties of transverse parity-time ($\mathcal{PT}$) symmetric systems have been extensively studied, yet their dynamical stability, a prerequisite for any stationary description, remains largely unexplored. Here we uncover a thresholdless dynamical instability in such systems, driven by symmetry-protected bound states in the continuum (BICs). Without gain and loss, the up-down mirror symmetry of the transverse geometry generically protects a BIC, which manifests as the coalescence of an $S$-matrix pole and zero on the real axis of the complex wave-number plane. A Hermitian symmetry-breaking perturbation shifts the poles into the lower half-plane, converting the BIC into a resonance with a Fermi-golden-rule decay width. An anti-Hermitian $\mathcal{PT}$-symmetric perturbation instead reverses the sign of the second-order energy shift, driving the poles into the upper half-plane and producing a time-growing bound state with $\operatorname{Im}E=\gamma^{2}\Gamma_{V}/2+O(\gamma^{3})$, where $\gamma$ is the gain-loss strength and $\Gamma_{V}$ is the golden-rule coupling of the BIC to the continuum. The instability therefore sets in at arbitrarily small $\gamma$ whenever $\Gamma_{V}>0$. We confirm this mechanism in a three-site side-coupled model that is unstable despite possessing a unitary scattering matrix, and in a four-site rhombic model where transverse and longitudinal gain-loss placements yield vanishing and finite thresholds, respectively. These results establish a microscopic stability criterion and a design principle for stable $\mathcal{PT}$-symmetric scattering devices.

The enhancement of atom-photon interactions with F-P cavities provides a suitable platform for studying quantum optics and atomic physics. However, the emission fields in linear F-P cavities are in the standing-wave mode, which leads to non-uniform atom-photon coupling and a short storage lifetime of cavity-enhanced spin-wave quantum storages. This study experimentally demonstrates traveling-wave atom-light interactions in an F-P cavity that can preserve light helicity. First, a bias magnetic field is applied along the z-axis to define the quantization axis, which lifts the Zeeman degeneracy and breaks the time reversal symmetry. Next, non-classically correlated pairs of Stokes photons and spin waves are produced based on the Duan-Lukin-Cirac-Zoller scheme. The Stokes photons initially emitted from a single circularly polarized atomic transition have left-and right-hand circular polarizations when propagating along the +z (forward) and -z (backward) directions, which are preserved in the chiral cavity within the atom-photon interaction region. Thus, when the forward and backward Stokes fields resonate with the cavity, they may interact with the atoms in a traveling-wave manner. This is confirmed by measuring the time-dependent retrieval efficiencies of spin waves correlated with the forward and backward Stokes fields. This work paves the way for demonstrating traveling-wave atom-photon interactions in F-P cavities.

Pessiland is a world where NP is hard on average but one-way functions (OWFs) do not exist [Impagliazzo 1995]. Because almost all classical cryptographic primitives imply OWFs [Impagliazzo and Luby 1989], there is almost no classical cryptography in Pessiland. On the other hand, quantum cryptography can exist even when OWFs do not [Kretschmer 2021; Morimae and Yamakawa 2022; Ananth, Qian and Yuen 2022]. Is there a quantum analogue of Pessiland where NP is hard on average but even quantum cryptography does not exist? In this paper, we show that such a miserable world, Quantum Pessiland, exists: there is a quantum oracle relative to which $UP\cap coUP$ is hard on average against quantum polynomial-time algorithms with quantum advice, yet auxiliary-input EFI pairs do not exist. We also show that there is a classical oracle relative to which $UP\cap coUP$ is hard on average against quantum polynomial-time algorithms with quantum advice, yet classically-secure auxiliary-input one-way puzzles (OWPuzzs) do not exist. Almost all quantum cryptographic primitives imply EFI pairs or OWPuzzs, and therefore these results mean that there is almost no quantum cryptography relative to these oracles. We further show that relative to the classical oracle, SampBQP = SampBPP, and therefore there is no sampling-based quantum advantage in Quantum Pessiland. Finally, because our average-case hardness of $UP\cap coUP$ implies $P^{\#P}\not\subseteq i.o.BQP/qpoly$, our result also implies that a non-relativizing proof technique is necessary to construct OWPuzzs solely from $P^{\#P}\not\subseteq i.o.BQP/qpoly$, which gives a partial negative answer to the open problem of [Khurana and Tomer 2025].

Quantum encrypted cloning encodes an unknown state into several encrypted components, each offering an alternative way to recover it later. We show that this redundancy can also serve for one-shot fault diagnosis: instead of inspecting the encrypted state, we measure relational Pauli observables testing consistency conditions imposed by the encoding. The canonical Yamaguchi–Kempf scheme encodes the input into \(n\) signal–key pairs, all carrying the same coherent Bell label, plus a transformed copy of the input qubit. Comparing the labels of two pairs yields a deterministic check that localizes an anomalous pair and identifies its Pauli-error class without revealing the label. Such checks cannot tell whether the signal or the key of that pair is faulty, and no measurement on the pairs can (we prove that they already generate the whole group of deterministic state-blind observables supported there, of rank \(2(n-1)\)). This ambiguity matters: a faulty signal costs one redemption path, a faulty key threatens them all. However, retaining also the transformed input qubit contributes exactly two further independent checks, at any multiplicity, and these suffice to identify any single fault drawn from the single-qubit Pauli set. For three clones this gives six checks in all, and we prove that no smaller set of state-blind observables achieves the same resolution. Across clone multiplicities, parity governs how many components must be measured jointly to reach this resolution, not the resolution itself. These findings are then abstracted into a general framework — state-blind observables, deterministic healthy references, syndrome-induced fault partitions, redemption-oriented sufficiency — yielding relational diagnosability: a syndrome need not identify every fault, only enough of it to select a safe redemption path.

The exponential decay of an unstable quantum state, as described by standard Markovian theories such as Fermi's Golden Rule, assumes a simple, structureless environment. However, in complex environments characterized by disorder, long-range interactions, or strong fluctuations, local decay rates fluctuate, leading to non-Markovian dynamics and power-law “long-time tails.” In this paper, we apply the recently proposed hyperstatistics framework to the problem of quantum decay in such complex environments. By considering a $\gamma$-distribution of local decay rates across mesoscopic domains, we derive a macroscopic survival probability governed by a $q$-exponential function. We then use the $q$-generalized Gamma function, defined via the Mellin transform of the $q$-exponential, to calculate the moments of the decay-time distribution. We show that the mean quantum lifetime is $\langle t\rangle = \int_0^\infty P(t)\,dt= [\langle\Gamma\rangle(2-q)]^{-1},$ and is therefore finite for $q<2$. The convergence of the second moment, and hence of the lifetime variance, instead requires the stricter condition $q<3/2$. These results provide a refined physical interpretation: for $1<q<3/2$ both the mean lifetime and its variance are finite; for $3/2\le q<2$ the mean lifetime remains finite but lifetime fluctuations become infinitely broad; and for $q\ge2$ the mean lifetime itself diverges, corresponding to a truly trapped, localized, or Griffiths-like regime.

We bound the magic of a post-selected logical measurement by the resource that produced it. The setting is one code block with one logical qubit and an adaptive protocol that measures, feeds forward and accepts. The witness reads the accepted effect against the free set of the resource theory of magic, outcome by outcome and not on the averaged channel, since a channel can be free while one of its outcomes measures the magic axis. Our first bound is unconditional. The accepted magic is at most a constant times the summed distance of the cells from the free set. The second is the main result. When the resource cells sit inside a bounded-spread exact-recovery skeleton, the recovery puts every insertion history below a threshold onto a single free branch, transcript by transcript, so only connected clusters reaching the threshold contribute and an exact-component expansion controls their weight. With a threshold linear in the code distance, polynomially many cells of bounded insertion degree and per-cell dilation amplitude $O(1/d)$, the accepted magic times the acceptance probability is at most $\exp[-\Omega(d\log d)]$. Post-selection is disposed of before accepted transcripts are summed, so a branch of vanishing probability cannot be amplified into a magic effect. The threshold is certified from a circuit, and we run it on one exact round of stabilizer measurement followed by a split readout, which measures logical $X$ on the accepted fibre and logical $Z$ on the rejected ones. That certifies a threshold equal to the code distance for every single-layer pattern of weak $Z$-rotations, one per data qubit, so the hypotheses are met by a family and not one design. A member carries magic only if its support contains a logical $Z$ string. One member attains the exponent, again at the level of the accepted effect. Suppression is set by the threshold and not by the topology of the block.

Superconducting circuits play a crucial role in the advancement of quantum computing and quantum sensing. Typically such circuits require the presence of a non-linear element, where the engineered anharmonicity (Kerr factor) and resonant linewidth determine the potential applications of the circuit. In this work we have fabricated Nb-based CPW resonators embedded with a DC SQUID incorporating Nb nanobridges as the weak links. We use two-tone spectroscopy to study the non-linear behaviour of the device at 15 mK up to a field of 2.48 mT. Under the application of a blue-detuned pump, the device shows a decrease in the resonant frequency which is used to estimate the Kerr factor. We further apply a red-detuned pump to go beyond the bifurcation threshold and observe the appearance of an additional idler mode with net gain. The gain of the device was maximized by further decreasing the pump frequency, showing a maximum amplification of 15 dB. Finally, we show agreement between the Kerr non-linear oscillator model and the measured transmission spectrum, and highlight further design modifications to improve the gain and bandwidth of such devices.

Quantum optomechanics (QOM) explores the interaction between a quantum field, often confined in a cavity, and the quantum motion of mirrors, membranes or material media, usually assumed slow enough with negligible particle production, which is the central concern of dynamical Casimir effects, and a drive laser field for effective control. This rapidly developing field has a wide range of applications, from quantum sensing to the detection of gravitational waves. Because the opto-mechanical coupling is nonlinear, most theoretical investigations assume that the amplitude of mirror motion $x$ remains small. Recent years saw several papers treating $x^2, x^3$ orders in the mirror displacement. In our work we take a different route, deploying the functional perturbative method presented in [1] and enriched in [2], applicable for sufficiently weak opto-mechanical couplings. With this we can treat arbitrary displacement of the mirror, not just at a higher order in a power series expansion in $x$. We first derive the influence action of the quantum field and its non-Markovian noises back-reacting on the moving mirror with self-consistency. From it we derive a nonlinear Langevin equation driven by these back-action noises from the quantum field. We then show how results from our general modeling and treatment can be linked with the models and the Langevin equations presented in the literature, starting with the popular radiation pressure $Nx$ coupling, with $N$ the photon number, up to the recent $x^3$ order results. We hope this new approach and the results presented here can provide useful theoretical support for high precision QOM experimentation in the future.

Bandwidth-tuned quantum kernels have been shown to lose their advantage over classical kernels and to resemble radial basis function kernels, but the analytical support for that observation rests on separable encoding circuits and captures entangling circuits only qualitatively. We close this gap for the ZZ feature map. We prove that in the small-bandwidth regime the induced kernel has, to leading order, the anisotropic Mahalanobis geometry defined by M = I + pi^2 Q, where Q is the signless Laplacian of the entanglement graph, and that it admits a parameter-free Gaussian surrogate matching it through second order. The quadratic structure persists at any fixed depth as a pullback of the Fubini-Study metric. The anisotropy depends entirely on a phase convention: under the unshifted convention the metric is the identity irrespective of entanglement, which accounts analytically for the isotropic resemblance previously reported. The derivation is verified against direct simulation for path, cycle and complete graphs, with relative error below 10^-3. The corresponding classical kernel requires no fitted parameters and no quantum simulation. Compared with the quantum kernel on two near-infrared spectroscopic benchmarks, across four targets, five preprocessing pipelines and 100 resampled splits per cell, the paired 95% bootstrap interval contains zero in 18 of 20 cells, the typical relative difference in test error is 2.7%, and the two families select the same preprocessing pipeline in 96% of splits. The regime in which the reduction fails adds no robust predictive value: restricting the grid to the classical regime improves mean test error by 3.8%, a gain that an equally large random restriction does not reproduce.

We present FIREQ (FPGA Instrumentation for Readout and Qubit control), an open-source RFSoC-based framework for the control and readout of superconducting qubits. FIREQ combines a modular AXI-compliant firmware architecture with a PYNQ-based software stack designed to support extensible hardware integration, deterministic experiment timing, and low-overhead execution of repeated calibration and characterization workflows. The firmware implements direct RF synthesis and acquisition, trigger-based sequencing, programmable pulse generation, frequency-multiplexed readout, and memory-efficient acquisition and waveform buffering. The software adopts a client-server architecture with streamed data transfer and dependency-aware configuration updates to reduce host-device and reconfiguration overhead during parameter sweeps. On an AMD Zynq UltraScale+ RFSoC ZCU216, FIREQ generates RF pulses up to 9.3 GHz with a pulse-duration resolution of 107 ps and an event-timing resolution of 1.7 ns. FPGA resource utilization is compared with representative open-source RFSoC control frameworks, showing a low BRAM footprint while retaining full-rate I/Q generation and acquisition. The RF output is characterized in terms of phase noise, noise spectral density, and inter-channel timing skew. End-to-end operation is validated on a superconducting qubit through resonator spectroscopy, Rabi, Ramsey, and relaxation measurements, yielding T1 = 6.94 us and T2* = 13.50 us. FIREQ can therefore be used both as a qubit-control platform and as an experimental environment for evaluating alternative control and readout IP architectures.

Information can be converted into work, but in quantum mechanics information about a state is not freely available: it must be inferred statistically from measurements on a finite number of copies. We study work extraction in this finite-resource setting by introducing a partial-information and finite-resources (PIFR) quantum Maxwell's demon. Given $N$ identical copies of a state with known Hamiltonian, the demon measures $M$ copies to estimate the state and the corresponding ergotropic unitary, which is then applied to the remaining $N-M$ copies. This protocol induces a trade-off between information acquisition, reconstruction accuracy, and thermodynamic yield, making the total extracted work normalized to the ideal ergotropic benchmark the relevant figure of merit. As our central result, we derive a universal closed-form trade-off bound that places this ergotropic efficiency between a Carnot-type ceiling $1-M/N$ and a floor controlled by a reconstruction precision rooted in finite-sample quantum estimation theory; optimizing the copy allocation yields $M^*\propto N^{2/3}$ and an $N^{-1/3}$ approach to the ideal limit, set by a conservative, worst-case reconstruction precision. By considering standard quantum state tomography, we numerically verify the presence of an optimal resource distribution, which also depends on the purity of the state under consideration. Our results identify finite-copy work extraction as a genuinely task-dependent inference problem, in which estimation strategies should be judged by thermodynamic performance rather than reconstruction fidelity alone.

Since the seminal work of Selinger and Valiron, the standard design for quantum lambda calculi has kept the quantum state outside the program: terms manipulate pointers to an external register. This is largely due to the difficulty of eliminating tensor products. For example, the calculus $\lambda_\rho^\circ$ embeds density matrices directly within terms, where terms carry the entire computation state, a feature particularly appealing for program verification. However, lacking a tensor elimination construct, it can neither access the individual qubits of a compound state nor discard them. Borgna showed that this inability to discard qubits makes the calculus strictly less expressive than the quantum lambda calculus of Selinger and Valiron. In this paper we show that tensor elimination is possible in this setting. The key observation is that the Pauli decomposition, combined with the spectral decomposition of the Pauli matrices, allows any $n$-qubit density matrix to be expressed as a real linear combination of tensor products of single-qubit density matrices. Exploiting this fact, we extend $\lambda_\rho^\circ$ with a construct $\mathrm{let}\ x^{\otimes n} = \rho\ \mathrm{in}\ t$, which binds each $x_i$ to a single-qubit density matrix arising from the decomposition of $\rho$. We equip the extended calculus with a rewrite system, a type system, and a denotational semantics, and prove Subject Reduction, Progress, Strong Normalisation, Soundness, and Adequacy. The new construct also recovers the missing ability to discard qubits, thereby restoring expressiveness. Moreover, we show that this is achieved in a physically principled way: a variable unused in $t$ is interpreted exactly as being partial-traced out, as dictated by the no-deleting theorem. We illustrate the resulting compositionality through quantum teleportation and the three-qubit bit-flip code.