Papers

Gravity from entropy (GfE) identifies its Lagrangian with the geometric quantum relative entropy (GQRE) between the spacetime metric and a metric induced by matter and curvature, treating the metric itself as a quantum operator. We extend this construction to the Tsallis, Rényi, and Sharma-Mittal families, which we call gravity from generalized entropy (GfGE), and determine their common Einstein limit, weak-field spectra, auxiliary-field formulation, and horizon entropy. The entropy choice controls the leading higher-curvature terms and additional modes. We confirm that the linearized GfE spectrum contains a healthy scalar and a Planck-scale tachyonic spin-2 ghost. We identify the conditions that remove this ghost: curvature must enter through its scalar trace, or the entropy generator must be flat to quadratic order at the identity. The latter gives exact general relativity for Tsallis at $q=0$ and ghost-free $f(R,L_m)$ theories for Rényi and Sharma-Mittal. On shell, the auxiliary G-field is proportional to the tensor in Wald's entropy formula. For analytic entropy functions, horizons with a single curvature scale have an area term followed by constant and inverse-area corrections. We also extend the volume-constraint cosmological constant to the full family; its leading entropy dependence is set by the scalar mass. A finite set of entropy-function derivatives controls the leading weak-curvature departures from general relativity.

Interactions turn a gas into a fluid. We show that two-body loss can take their place. Correlated loss induces elastic scattering, as required by the optical theorem, which dominates at strong loss via the quantum Zeno effect. A nondegenerate gas with only two-body loss thus flows hydrodynamically, with viscosity and thermal conductivity close to those of the unitary Fermi gas. As loss heats the gas, both grow in time with a universal exponent 3/8. Unlike single-particle loss, two-body loss can engineer collisions, and hence transport, in quantum matter.

Quantum federated learning trains a quantum neural network (QNN) across nodes that hold quantum data, such as the states of quantum sensors. To forget data, unlearning methods for quantum models replay them, and federated unlearning from stored updates removes whole nodes only. Quantum data cannot be replayed, since a state is consumed when measured and cannot be cloned. We propose Shadow-based Data Erasure (SHADE), in which each node records a classical shadow of every training state, a few randomized single-qubit measurements taken at training time. The gradient and curvature of a QNN on a state are expectations of observables, so SHADE estimates them for the forget data from the shadows at any later parameters and removes their effect by a federated Newton correction. Only classical estimates cross the network. We prove that the shadow size needed for a target unlearning error grows exponentially in the size of the backward light cone of the measured observable and not in the number of qubits. In simulation with 50 nodes and on edge boards, SHADE matches the forget accuracy of retraining within 0.5 points, without replay and in under 0.2 s.

Ultra-high-rate quantum error correction codes store many logical qubits in a single code block with few physical qubits. A fault-tolerant quantum computer, however, also requires a universal set of logical operations on individually addressable logical qubits, and the ancilla overhead of these operations may erode the advantage of the high encoding rate. Here, we propose the Cornucopia architecture, in which a universal set of logical operations is implemented at low overhead for the Cornucopia codes. In particular, we focus on the [[2844,1426,18]] Cornucopia code as an example and introduce a modular quantum computer built from such code blocks connected by bridges. Each block stores 1,426 logical qubits and serves as a universal logical processor. Exploiting the code's translation symmetry, we construct a family of reusable gadgets that individually address 1,422 logical qubits within each block. These gadgets support three universal logical instruction sets: basic, high-throughput and fixed-extractor. Excluding magic-state factories, a module with sufficient workspace to execute any instruction in the basic set requires an average of 4.1 physical qubits per logical qubit, compared with 3.0 for memory alone. The architecture thus preserves the resource advantage of ultra-high-rate quantum memory while enabling universal logical computation, providing a route towards low-overhead fault-tolerant quantum computers.

A long-standing open question is to characterize the classical communication cost of simulating the correlations arising from measurements on finite-dimensional quantum systems. We consider this question in the prepare-and-measure scenario. First we construct a classical simulation model involving a finite average number of bits of one-way communication that simulates exactly the correlations arising from arbitrary $d$-dimensional quantum states and arbitrary measurements. Second, we show that no classical simulation protocol involving a finite average message dimension can exist for $d\geq 4$, hence strengthening a recent result of de Gois, Santos and Vieira. Our first result relies on a more general simulation theorem which can be applied to certain continuous variable (i.e. infinite-dimensional) quantum systems, and even beyond quantum theory, e.g. to generalized probabilistic theories. In particular, we show that multimode Gaussian states of bounded average energy and general Gaussian measurements admit an exact classical simulation with a finite expected number of bits. Overall, our results show that the classical simulation cost of quantum communication is essentially as high as it could be.

A deep understanding of quantum information theory is essential for quantum science and technology. However, quantum mechanics and particularly quantum information theory suffer from a lack of intuitive images. Visualization tools offer novel perspectives on many problems in quantum physics by revealing important properties of quantum states and processes that are otherwise obscured by abstract mathematical formalisms. Here, we extend the previously established BEADS representation of pure states to the so-called generalized BEADS representation of mixed quantum states. We introduce spherical functions, so-called beads to visualize correlation structures of mixed quantum states. A recursive optimization scheme is used to obtain minimum-entanglement pure state decompositions of all subsystems of a given N-qubit state. We show how correlation function components can be decomposed into individual contributions that directly correspond to different types of correlations of mixed states. This allows us to visually characterize the total correlation, genuine n-partite entanglement, nonclassical quantum-discord-type correlations as well as classical correlations. After outlining the mathematical details relevant for constructing the representation, we examine the generalized BEADS representations for various classes of mixed states including product, classically correlated, separable but nonclassically correlated, as well as entangled states. As exemplary applications of the generalized BEADS representation, we showcase entanglement distillation and the effects of noise channels.

Quantum error correction (QEC) can strongly suppress noise, but predicting whether a computation succeeds requires understanding not only how much effective noise persists after QEC, but what form that noise takes. To thoroughly characterize this noise, we introduce logical gate set tomography (“logical GST”). Logical GST produces detailed representations of noisy logical operations that can be used to derive higher-level metrics, such as gate fidelity and diamond distance, and to test for non-Markovian and coherent logical errors. We use logical GST to obtain the first full, self-consistent characterization of a universal single-qubit logical gate set, implemented in the seven-qubit Steane code using Quantinuum System Model H1, a 20-qubit trapped-ion quantum processor. In the experimental data from H1, logical GST identified predominantly logical Pauli-stochastic errors, found no evidence of logical non-Markovianity, and detected weak potential signatures of coherent logical error. By contrast, higher-shot datasets generated with Quantinuum's detailed system emulator, identify mechanisms for weak but statistically significant logical non-Markovianity and strong evidence of coherent logical error. Finally, we use logical GST to perform error attribution with the system emulator, revealing how specific physical error sources shape logical error mechanisms.

Under local Lindbladian evolution, the growth of conditional mutual information and its associated Markov length scale is not limited by Lieb-Robinson bounds, yet it has been unclear how quickly the Markov length can increase. We show that an arbitrarily short, strictly local Lindbladian can generate infinite Markov length from a product state. We also construct strictly local Lindbladians that converge rapidly to steady states with algebraically decaying conditional mutual information. Despite their long-range conditional correlations, the states we construct are local reversibly connected to a product state by sublinear depth circuits. Thus infinite Markov length does not imply slow relaxation nor obstruct phase stability when suitably defined.

Strong coupling between mobile charge carriers or excitons and lattice vibrations gives rise to polarons: quasiparticles formed by charge carriers dressed by a cloud of phonon excitations. Polaron formation determines transport properties of systems ranging from transition-metal oxides and organic semiconductors to light-harvesting complexes. In excitonic systems that admit a hard-core boson description, mapping the excitations to pseudospins provides a natural framework for studying polaron physics, including the nonperturbative regime in which hopping amplitudes, phonon energies, and coupling strengths are comparable. Here, we propose a trapped-ion blueprint for realizing spin-phonon Hamiltonians with programmable spatial coupling between excitation density and phonon displacements, encompassing local Holstein and long-range Fröhlich-type interactions. To access strongly dressed quasiparticles whose bare spectral weight is suppressed, we introduce displaced Green's functions implemented through spin-dependent phonon displacements. Their spectral response reveals the polaron band spectrum, including binding energies and phonon-excitation sidebands, while spatially resolved measurements probe the structure of the phonon dressing cloud, providing a route to polaron tomography. We further complement this spectroscopy with direct and ancilla-assisted measurements of spin-phonon correlations that track the coupled dynamics of the excitation and its environment. These approaches connect the emergent quasiparticle spectrum to the microscopic buildup of its dressing cloud, enabling controlled studies of how the spatial range of coupling shapes polaron formation and mobility.

Non-Abelian anyon chains whose interactions favor a single fusion channel host quantum critical ground states described by minimal-model conformal field theories (CFTs) protected by a topological symmetry. We show that their measurement-only counterpart, where non-commuting fusion charge measurements act locally on the anyons of a chain of $L$ sites, provides a fundamental example of a non-unitary CFT controlling a non-Abelian learning problem. Mapping the monitored dynamics to a random tensor network, we numerically find $1/L$ scaling Lyapunov gaps, logarithmic entanglement scaling with the chord length, and an effective central charge in the Shannon entropy of the measurement record. The conserved topological charge sharpens with dynamical exponent $z= 1$ and is learnable by a decoder on an $O(L)$ time scale. As the topological symmetry is a non-invertible symmetry of the $SU(2)_k$ anyon theories, we establish the monitored golden chain $(k=3)$ as a non-Abelian generalization of the weakly (Kramers-Wannier) self-dual quantum critical point of the toric code $(k=2)$, and the first of a family for $k\geq 3$.

Stabilizer Rényi entropy quantifies magic relative to a complete Pauli frame. In settings such as helicity states of massless particles, unsynchronized qubit registers, energy eigenbases, and systems under superselection rules, the computational basis may be fixed while the transverse Pauli axes remain unspecified. The stabilizer Rényi entropy then depends on the choice of those axes. We define a phase-averaged stabilizer Rényi entropy by averaging the Pauli moments before taking the logarithm. It is exactly invariant under independent local rephasings. For pure states, it vanishes precisely when the state is a stabilizer state in every phase convention. For a broad class of sparse supports, it reduces to a closed-form function of the basis-state probabilities alone. Within this class, the ceiling for $n$ channels is $\ln[n^{3}/(6n-5)]$ for $n\geq3$ and $\ln\frac{7}{5}$ for two channels. We apply the invariant to tree-level gluon scattering at four and five points, where the helicity-basis phases are unspecified. It saturates the two- and three-channel ceilings: $\ln\frac{7}{5}$ at four points and $\ln\frac{27}{13}$ in $3\to2$ scattering. In same-helicity $2\to3$ scattering, it lies between a floor of $\ln\frac{8}{7}$ and a ceiling of $\ln\frac{184}{125}$, reached in the resolved soft limit and particular collinear limits, respectively. In every configuration studied, the invariant is independent of the fixed external colors.

Quantum simulators with disordered spin Hamiltonians offer a natural route to Haar-like unitary ensembles, but face a competition. Disorder enhances randomness, yet strong disorder suppresses dynamics and localizes the system in the computational basis. This suggests an optimal intermediate disorder strength for approximating a unitary $k$-design, which has so far been identified mainly empirically. Here, we develop a perturbative theory for the moment gap $\Delta^{(k)}$, the deviation of the $k$-th moment operator from its Haar value, for the full spectrum of the interacting XXZ chain in a fixed-magnetization sector. We find the non-monotonic asymptotic scalings $\ln \Delta^{(k)}\sim -\sigma^2$ at weak disorder and $\ln \Delta^{(k)}\sim -1/\sigma$ at strong disorder, whose crossover sets an optimal disorder strength $\sigma_c\sim J_{xy}$, where $J_{xy}$ is the energy scale of the non-random interaction. We further show that a multi-quench protocol further suppresses the gap exponentially in the number of quenches. Numerical simulations confirm both scalings and this exponential suppression, and we demonstrate the usefulness of the protocol for classical shadow tomography. This work suggests that strong disorder may block both thermalization and the formation of unitary designs through a common localization mechanism.

Chiral topological order is incompatible with strictly two-dimensional local commuting-projector Hamiltonians on finite-dimensional tensor-product Hilbert spaces. Invertible subalgebras (ISAs) provide an alternative framework. We construct an ISA supporting chiral semions, together with its anti-semion commutant, on a square lattice with one qubit per edge. We give explicit non-Pauli generators for both algebras and prove that together they generate all local operators on the Hilbert space. Starting from the $\mathbb{Z}_4$ toric code, we condense the boson $e^2m^2$ and identify the semion and anti-semion algebras. We then decompose each $\mathbb{Z}_4$ qudit into two qubits and use a finite-depth circuit to disentangle one qubit per edge fixed by the condensation constraints. Pumping the semion ISA along the $z$ direction defines an explicit three-dimensional non-Clifford quantum cellular automaton (QCA). We show that pumping eight times is equivalent to a translation followed by a finite-depth quantum circuit with ancillary qubits. We also give an explicit finite-depth circuit relating this construction to the semion QCA previously obtained from topological quantum field theory. A similar condensation construction yields a $U(1)_4$ ISA on a square lattice. Together with the semion and earlier odd-prime ISAs, finite stacking realizes every pointed Witt class of bosonic Abelian anyon theories. Finally, we extend both constructions to all spatial dimensions $d=4k{-}2$, with one qubit or $\mathbb{Z}_4$ qudit on each $(2k{-}1)$-cell for the semion or $U(1)_4$ ISA, respectively.

Loss and noise limit the use of light to distribute entanglement, transmit quantum information, and establish secret keys. Gaussian states have a compact description in terms of means and covariance matrices, but their entanglement still requires global optimization. We develop a framework for computing Gaussian-restricted versions of the relative entropy of entanglement and Rains entanglement. An integral representation reveals a convex geometry under matrix geometric means and reduces Gaussian Rains entanglement to relative entropy minimized over Gaussian states with positive partial transpose. We obtain unique optimal reference states and additivity for independent Gaussian input states. Our convex-majorization algorithm has an explicit geometric convergence rate, uniform in the faithful regularization parameter and valid for pure input states. Controlled numerical integration and approximate convex subproblem solutions give a bit-complexity bound that is polynomial in accuracy bits for each fixed rational input covariance matrix, with explicit dependence on covariance size. These calculations bound extractable entanglement and, through the relative entropy of entanglement, extractable secret key. Teleportation simulation, energy allocation, and a convex optimization of passive-basis loss cores give bounds on quantum and private communication under an input-energy constraint, allowing arbitrary two-way classically assisted protocols. Two- and three-mode examples compare the bounds with achievable rates, including matching pure-loss benchmarks. Finally, we separate the Gaussian-restricted quantities from their unrestricted counterparts and give a photon-number truncation method with controlled error for computing the latter.

It is proved that every Borel ensemble of pure states on a separable bipartite Hilbert space with finite average entanglement admits a countable ensemble with the same barycenter and arbitrarily small additional average entanglement. Consequently, the discrete and continuous versions of the Entanglement of Formation coincide on the whole space of states of infinite-dimensional bipartite quantum system (with infinite values allowed). The main idea of the proof (realized with the AI-assistance) is the lifting a Borel ensemble of pure bipartite states to a Borel probability measure on the unit sphere in the space of Hilbert–Schmidt operators followed by dividing the support of this measure into appropriate cells and replacing each cell by its conditional barycenter. The resulting countable ensemble is obtained by a recursive construction.

A series of recent works has established EFI pairs as the "minimal" assumption for quantum cryptography. Recently, Cavalar et al. [CCC+26] showed that EFI pairs are equivalent to non-uniform expanding single-copy pseudorandom state generators (1PRS), and obtained a non-uniform meta-complexity characterization of EFI pairs. We remove the non-uniformity in their construction and prove that EFI pairs are equivalent to expanding 1PRS. As a corollary, we obtain the first uniform meta-complexity characterization of EFI pairs. Together with the equivalence of statistically verifiable one-way state generators and commitments proved by Batra and Jain [BJ24], this gives a quantum analogue of the classical equivalence between one-way functions, commitments, and pseudorandom generators.

We develop and analyze an entropic descent method for a nonconvex optimization problem on probability simplices arising in classical and quantum secure communication. The optimization variables describe a randomized encoder, allowing its input distribution and stochastic preprocessing to be optimized jointly. An exact relative-entropy identity yields a channel-independent majorization bound and an explicit mirror-descent iteration with a fixed unit step size. We establish quantitative descent, convergence of objective values, and stationarity of accumulation points on their support faces for arbitrary finite classical channels, without assuming degradedness or less noisiness. For strictly positive transition matrices, a square-root parametrization and a Kurdyka–Łojasiewicz argument establish finite length of the transformed trajectory and convergence of the entire sequence, including limits on the simplex boundary. For less-noisy channels, a restricted convex formulation admits global convergence with an explicit \(O(1/t)\) objective-error bound. We extend the relative-entropy construction to noncommuting quantum outputs and derive monotone alternating updates for covariant encoders, including correlated preprocessing over a fixed block. Numerical experiments compare the method with analytic benchmarks and constrained optimization, reveal multiple attracting values, and demonstrate strict improvements from stochastic preprocessing.

Multimode mechanical resonators offer a large set of densely packed, long-lived bosonic modes within a single compact device, making them attractive for quantum simulation, quantum information processing, and quantum-enhanced sensing. Many such applications rely on multipartite entanglement, yet deterministic mechanical entanglement has so far been largely limited to pairs of modes. Here we demonstrate the deterministic and programmable preparation of multipartite entangled states among the phonon modes of a high-overtone bulk acoustic wave resonator coupled to a superconducting transmon qubit. By sequentially applying optimal-control-engineered isometries between the qubit and successive modes, we generate matrix product states of bond dimension two, including $W$, Greenberger-Horne-Zeilinger (GHZ), and cluster states. We fully characterize these states via quantum state tomography and certify genuine multipartite entanglement among up to four modes. We further demonstrate correlated-noise sensing by exploiting the complementary decoherence responses of the stored $W$ and GHZ states, isolating inter-mode phase correlations from local decoherence and placing quantitative bounds on collective dephasing. Our results establish a scalable approach to preparing multipartite entangled states in mechanical systems, with promising applications in multiparameter sensing and tests of quantum mechanics with massive objects.

Massive mechanical oscillators couple directly to forces, accelerations and gravity, making them attractive probes of new physics and of quantum mechanics at macroscopic scales. Pushing sensitivities beyond the standard quantum limit for signals of unknown phase requires non-Gaussian quantum states, whose metrological advantage has so far been confined to lighter systems such as trapped ions. Here we operate a microgram-scale acoustic mode of a high-overtone bulk acoustic wave resonator as a phase-insensitive quantum-enhanced sensor. A transmon qubit prepares the mode in Fock states of up to seven phonons by optimal control, and resolves its phonon-number distribution after interaction with a weak resonant signal. Bayesian analysis yields a Fisher information five times the vacuum value, a 7.0 dB gain in signal-amplitude sensitivity over any classical probe state, irrespective of its energy, currently limited by state preparation infidelities. We then train a neural network on the measured sensor response to perform Bayesian estimation without any analytical model of the system, showing the same sensitivity gain with half the systematic bias. Our results establish acoustic resonators prepared in non-Gaussian states as quantum-enhanced probes for high-frequency gravitational waves, dark matter and wave-function collapse.

We study quantum communication, entanglement distribution, and secret-key generation through multimode bosonic loss and fading channels, assisted by local quantum operations and two-way classical communication. Using sector teleportation, we determine the exact two-way quantum and secret-key capacities of multimode pure-loss channels under a mean photon-number constraint, allowing arbitrary adaptive quantum protocols. We extend these results to continuous frequency-dependent loss under a power constraint and identify the optimal allocation of photons among optical modes. For constant loss over an unlimited bandwidth, we obtain a closed-form capacity proportional to the square root of power. For randomly varying loss, we determine exact finite-energy capacities when the channel realization is publicly revealed, distinguishing knowledge before and after transmission. When fading remains unobserved, we derive capacity bounds and explicit formulas for an on/off channel. We also establish strong-converse bounds, with exact thresholds for the deterministic loss models considered here, observed fading, and unobserved fading with finitely many possible transmissivities. Under mean energy constraints, these thresholds generally exceed the corresponding finite-energy capacities. These results guide energy allocation and provide benchmarks for energy-constrained optical quantum communication with multimode signals and variable loss.

We introduce PULSUS, a direct frequency-domain framework for multidimensional spectroscopy of open quantum systems beyond the impulsive rotating-wave approximation. Coherence-frequency intervals are represented through Liouvillian resolvents, while finite Gaussian pulses are incorporated through operator-valued functions of the field-free Liouvillian. This enables direct evaluation on Cartesian grids or arbitrary spectral coordinates while retaining molecular evolution during the pulse envelopes and, when required, the complete light–matter interaction. The implementation is validated against analytical and independent time-domain benchmarks and supports targeted spectral sampling that reduces the number of evaluated coordinates when the response is spectrally localized. A controlled hierarchy of finite-pulse, rotating-wave, short-pulse, and impulsive models separates the errors introduced by each approximation. For a coupled electronic dimer, the total impulsive-RWA error is nonmonotonic in pulse duration: an intermediate regime provides the highest accuracy, whereas ultrashort pulses expose coupling-enabled beyond-RWA pathways and longer pulses develop substantial finite-pulse corrections. These results show that the impulsive and rotating-wave approximations cannot be assumed to improve simultaneously and should be tested when quantitatively interpreting multidimensional spectra. PULSUS provides a direct frequency-domain framework for carrying out that comparison.

Explicitly correlated methods, which represent dominant short-range correlations by a diagonal Jastrow-type correlator, are designed to accurately describe systems of strongly correlated electrons, such as the fully periodic 2D Fermi–Hubbard model. However, as the reference state is compact in momentum space whereas the correlator acts naturally in real space, there is a fundamental mismatch of bases that classical algorithms resolve only by restricting the reference or the correlator. Here we propose a hybrid algorithm in which a quantum processor prepares a low-entanglement momentum-space matrix product state (MPS), precomputed classically by the transcorrelated method at the cost of a nonvariational energy, rotates it to real space, and measures in bases fixed by the Hamiltonian. Because the measurement bases are independent of the correlator, the correlator can be variationally optimized entirely in classical post-processing with no quantum-classical feedback loop. We demonstrate our algorithm on 32 qubits of Quantinuum's H2-2 with a bond-dimension-4 MPS for the half-filled $4 \times 4$ lattice and achieve a relative ground-state energy error of $16 \pm 4\%$ after postselection, reduced to $3.5 \pm 0.5\%$ by calibration using low-order moments from the MPS. Compared with other feedback-free hybrid algorithms, even under generous assumptions, our method requires fewer samples than quantum-selected configuration interaction and fewer two-qubit gates than quantum Krylov methods.

We propose a protocol to prepare and probe dark states in a single-molecule electron spin resonance based on atomic force microscopy (ESR-AFM), thus extending existing techniques developed to address Rabi oscillations. To this end, we simulate in analogy to atomic physics the coherent manipulation of a three-level system in the V-configuration using a multifrequency magnetic field. More specifically, we consider a neutral molecule with a zero-field-split (ZFS) first excited triplet and analyze within a pump-probe scheme the dynamics of the total triplet population. In the triplet subspace, the dark state is a coherent superposition formed by two ZFS states which does not evolve in time despite a continuous resonant driving towards the third one. We characterize the properties of this state comparing it to its fully incoherent counterpart. Within a density-matrix formalism for open systems, we then compute the expected dark state signatures both for ideal scenarios and for the realistic parameterization of ESR-AFM on pentacene.

We construct Clifford+$T$ circuits implementing arbitrary $n$-qubit unitaries with worst-case $T$-count $\widetilde{O}(N^{8/7})$ at constant operator-norm error, where $N=2^n$, improving the previous exponent $5/4$. The construction uses $\widetilde{O}(N^{6/7})$ clean ancillas. The main idea is to reduce the data addressed by each query to the block-encoding circuit for a sparse piece while controlling the additional simulation work needed to combine the pieces. We simulate a Hermitian logarithm of the target by flattening its traceless part with a two-layer random similarity transformation, randomly partitioning the transformed generator into block-sparse Hermitian pieces, and combining their evolutions using qDRIFT. For a target operator-norm error $\epsilon\in(0,1/2)$, let $L=\log_2(N/\epsilon)$, the qubit count plus the requested bits of accuracy. By successively correcting the approximation error, we obtain a circuit using $\widetilde{O}(N^{8/7}L^{3/7}+NL)$ $T$ gates and $\widetilde{O}(N)$ clean ancillas whenever $L\le N$. We also prove that, at constant precision, the exponent $8/7$ is optimal within a sequential block-SELECT model.

We investigate how unresolved quasistatic disorder in system bath coupling affects non-Markovian dynamics in spin environments. The coupling is fixed within each experimental shot but varies between shots, so repeated shot tomography reconstructs a disorder averaged dynamical map. For a single spin bath with pure dephasing Ising interaction, disorder can drive a transition to CP-divisible dynamics for fixed bath preparations, with a critical strength set by bath polarization along the interaction axis. However, when the bath state fluctuates physically between shots, the averaged dynamics remain CP indivisible at any finite disorder strength. We extend these results analytically to inhomogeneously coupled pure dephasing baths of any number \(N\) of non-interacting spins. At any finite disorder strength, one unpolarized bath spin suffices to retain CP-indivisible dynamics, whereas a fully polarized bath yields Markovian (CP-divisible) dynamics. Dynamics with physically fluctuating bath states likewise remain non-Markovian (CP indivisible) at finite disorder for arbitrary \(N\) in the pure dephasing case. For anisotropic Heisenberg interactions, any nonzero transverse exchange eliminates the disorder driven transition to CP divisibility in a single spin bath. Exact diagonalization of anisotropic models with inhomogeneous couplings up to \(N=12\) reveals persistent trace distance revivals for fixed bath preparations, sampled Haar random preparations, and physically fluctuating bath states, showing that this effect of transverse exchange extends beyond a single bath spin. Increasing disorder still suppresses experimentally accessible revivals and can make memory effects unresolvable at finite measurement resolution even as the dynamics remain CP indivisible. Thus, transverse exchange and physical bath state fluctuations preserve dynamical indivisibility against unresolved coupling disorder.

We consider a closed macroscopic quantum system in a pure state $\psi$ evolving unitarily with Hamiltonian $H$ in a finite-dimensional Hilbert space $\mathscr{H}$. Following von Neumann, we assume a decomposition of $\mathscr{H}$ into mutually orthogonal subspaces $\mathscr{H}_{\nu}$, where each $\nu$ represents a macro state, and $\mathscr{H}_\nu$ contains the pure states compatible with $\nu$. We define the quantum Boltzmann entropy for a macro state $\nu$ as $S_\mathrm{qB}(\nu) = k_{\mathrm{B}} \log \dim \mathscr{H}_{\nu}$, where $k_\mathrm{B}$ is the Boltzmann constant. Goldstein et al. [http://arxiv.org/abs/1903.11870] have suggested, as a version of the second law of thermodynamics, that $S_\mathrm{qB}$ predominantly increases with time for realistic macroscopic systems. Here, we discuss precise versions of this statement and confirm them for several simple models of $H$ and $\mathscr{H}_\nu$.

We investigate the rotational properties of a zero-temperature Bose-Einstein condensed gas, which is confined in a hard-wall potential. For weak interactions the gas carries its angular momentum via vortices of multiple quantization. As the coupling increases and for sufficiently slow rotational frequencies of the trap, the multiply-quantized vortex states become unstable against a mixed state. For stronger couplings, as the angular frequency of the trap increases, there is a transition from a vortex lattice, to a vortex lattice with a hole at the trap center, and finally to a giant vortex. For weak effective attractive interactions we still have vortices of multiple quantization. These states become unstable towards states which break the axial symmetry of the problem and resemble center-of-mass excitation, as the coupling becomes more negative. Finally, for even more attractive forces, the system becomes unstable against collapse.

In order to execute quantum algorithms on bosonic quantum computers, it is necessary to encode their inputs into a desired target quantum state, with a process called state preparation. In real settings, state preparation methods operate in stochastic scenarios, where the prepared state is represented as a mixed state, that is a probabilistic ensemble of pure states. Therefore, existing state preparation methods optimize a variational ansatz by averaging over all possible sequences of photon loss events contained in the prepared ensemble, yielding an output state which approximates the desired target with a certain average fidelity. Such an approach, however, does not take into account directly the distribution of fidelities across states in the ensemble. In this work, we aim to maximize the fidelity of only a subset of pure states sampled from the prepared ensemble, at the cost of reducing the average fidelity overall. This trade-off is relevant when the goal is to obtain high-fidelity states with a certain probability, rather than maximizing the average fidelity of the prepared ensemble. We borrow and adapt objective functions from risk-sensitive optimization, a framework that optimizes specific characteristics of a distribution rather than only its expectation, and that has been successfully applied in Reinforcement Learning. In the considered experimental settings, our results show that the infidelities of some pure states in the prepared ensemble can be reduced by up to four orders of magnitude when using risk-seeking objectives, compared to those achieved using the standard optimization of the average fidelity. Furthermore, we show that it is possible to control the trade-off between the probability of obtaining high-fidelity states and the lowest infidelity threshold reached, providing the flexibility to select the operating point that best suits a certain application.

Quantum computing promises new capabilities beyond classical computation. Mid-circuit measurements (MCMs) enable error correction and outcome-dependent control, but their reliability is limited by noise on superconducting hardware. These operations depend on accurate quantum state discrimination (QSD), which assigns measured signals to state labels. Neural network-based (NN-based) QSD improves this assignment, yet its error remains bounded below by the Bayes risk of the available readout distributions. A complementary challenge is state deterioration as successive measurements accumulate and circuit execution advances, making static calibration less representative of the workload. We present Lifting, a QSD framework that addresses both challenges through repetition encoding, neural decoding, and in situ calibration. Encoding supplies joint in-phase and quadrature (I-Q) readout signals from the target and auxiliary qubits, while contextual calibration trains the decoder for the conditions encountered during execution. Our theoretical analysis shows that retaining additional channels from a fixed joint distribution cannot increase Bayes risk and establishes sufficient conditions for contraction of an overlap-based upper bound. Experiments across three IBM processors evaluate the framework on repeated stabilizer measurement, parity-check, and teleportation workloads.

Fast entangling gates and low-interaction idling require distinct operating conditions in superconducting quantum processors. We experimentally realize a transmon-C-shunt-transmon (TCT) device in which a flux-tunable, three-junction capacitively shunted flux-qubit coupler connects two transmon data qubits. The C-shunt coupler provides a flux-tunable, positively anharmonic spectrum for tailoring the interactions between the data qubits. Conditional Ramsey and swap measurements identify an idle region with near-zero residual ZZ interaction strength and suppressed transverse exchange. At this bias, simultaneous single-qubit interleaved randomized benchmarking yields X-gate fldelities above 99.7%, consistent with individual operation. A 45 ns nonadiabatic controlled-Z (CZ) gate achieves an interleaved randomized benchmarking fldelity estimate of 99.23(15)%. Numerical simulations identify coupler energy relaxation as an important limitation on CZ-gate fldelity and indicate that extending the coupler lifetime can improve gate performance. These results demonstrate the experimental feasibility of C-shunt flux-qubit couplers for combining low-interaction idling with fast entangling operations between transmon qubits.