Papers

Entanglement in multiphoton graph states is an important resource with various applications, such as measurement-based quantum computing and memory-less quantum repeaters. While some primitive instances have been successfully prepared, scalable generation of large-scale graph states with programmable connections remains an outstanding challenge. Fusion provides a promising "divide-and-conquer" approach by linking smaller resource states into larger, more complex graphs. However, its practical scalability has been limited by the probabilistic nature of conventional fusion protocols, which necessitates extensive hardware overhead and feed-forward resources to achieve deterministic outcomes. Here, we introduce and experimentally demonstrate a deterministic fusion operation with built-in error mitigation, capable of connecting small time-bin-encoded cluster states–originally generated on-demand from a quantum emitter–into larger, reconfigurable photonic graph states of increased sizes. The fusion operation is realized by nondestructively projecting pairs of flying microwave photonic qubits into Bell states using superconducting circuits with in-situ programmability. Crucially, the protocol features active reset and reuse of matter qubits during graph state generation, thereby circumventing the coherence constraints of the quantum emitter and enabling the generation of genuine multipartite entanglement across 13 photonic qubits. Our results establish a scalable framework for photonic graph-state synthesis, paving the way for fault-tolerant measurement-based quantum computation and distributed quantum networks.

Recent progress in programmable quantum simulators motivates exact benchmarks for nonequilibrium dynamics in topological quantum matter. We study the Kitaev honeycomb model driven through its critical regions by a linear ramp of the bond coupling $J_z$ over a ramp time $\tau$, comparing zigzag and armchair ribbons with fully periodic tubes. The production of excitations exhibits a geometry-dependent finite-size crossover controlled by $N_2/\sqrt{\tau}$, the ratio of the ribbon width to the Kibble–Zurek length. Periodic tubes obey the expected critical-line Kibble–Zurek scaling and serve as the boundary-free benchmark. Zigzag ribbons follow the same scaling until defect production is exponentially suppressed by a finite-width algebraic gap floor associated with the formation of Majorana edge modes, whose occupation is pinned by inversion parity. Armchair ribbons instead support transient Majorana edge modes with exponentially small gaps, producing width-parity-dependent defect plateaus: exactly one defect per unit length for odd widths and an approximate, transient plateau near one half for even widths. The quench-generated entanglement entropy and fermionic logarithmic negativity inherit the same geometry-dependent structure, and the negativity further distinguishes the coherence-borne entanglement of the Kibble–Zurek regime from the population-borne entanglement of the edge-mode plateaus. These results identify boundary Majorana modes as the mechanism controlling departures from ideal Kibble–Zurek dynamics and provide geometry-resolved benchmarks for programmable simulations of topological matter.

Quantum subspace diagonalization (QSD) with a Krylov space spanned by Chebyshev polynomials of the Hamiltonian is a natural ground-state method for fault-tolerant quantum computers, but every guarantee it offers—convergence rate, noise floor, and the cost of turning its classical output back into a physical state—is controlled by the overlap of the reference state with the true ground state, which decays exponentially with system size for any product state and non-trivial Hamiltonian. We propose quantum folding: for a system governed by a local Hamiltonian, seed the QSD with the product of the ground states of its subsystems, which differs from the target only through the interface terms. We prove a nonasymptotic error bound for the Chebyshev QSD that is linear in the measurement noise, by transplanting Kirby's effective-Hamiltonian analysis to the Chebyshev–Krylov basis, and identify the block-encoding rescaling of the Hamiltonian as a parameter of the guarantee. Exact simulations of antiferromagnetic Heisenberg chains show that the folded reference state reduces the Krylov dimension for a given accuracy severalfold and lowers the error under noise by two to five orders of magnitude relative to the Néel state. We show how the Ritz vector is prepared as a physical state and that the ground-state generation probability obeys a tight ceiling set by the overlap, so that recursive folding prepares ground states at polynomial cost. Taken together, these results allow for a scalable QSD framework that avoids the exponentially small ground-state overlaps associated with conventional product-state initialization. Finally we compute the fold fidelity itself: a slow power law for the gapless spin-1/2 chain, a size-independent constant for the gapped spin-$1$ chain, and an exact closed form converging to 1/4 for the AKLT chain.

Bound-entangled states with positive partial transpose (PPT) can exhibit quantum steering and Bell nonlocality, disproving the long-standing Peres conjecture and its stronger steering counterpart. These counterexamples, obtained through explicit constructions or numerical searches, raise the question of whether they share a common structural origin. We address this question in the low-rank regime by asking whether known counterexamples can be obtained, up to invertible local filtering, from the complement of an unextendible product basis (UPB). We find that the answer depends crucially on the local dimension. In $3\otimes3$, the rank-four structure of PPT entangled states implies that both the steerable PPT state of Moroder et al. and the Bell-nonlocal PPT state of Vértesi and Brunner can be obtained from UPB-complement states under invertible local filtering. For three qubits, in contrast, rank-four states that are PPT across every bipartition are separable across each cut. Moreover, comparison of the product-vector structure of the relevant kernels shows that the known three-qubit Bell-nonlocal PPT states cannot be obtained by invertible local filtering from the complement of any three-qubit UPB. Going beyond rank four, we further show that a known rank-eight three-qutrit state, supported on the complement of a UPB and PPT across every bipartition, is genuinely multipartite entangled. These results show that UPBs provide a unifying structural origin for important low-rank PPT entangled states in $3\otimes3$, but that nonlocal bound entanglement is not, in general, a UPB phenomenon.

We study quantum van der Pol oscillator in which single-photon pumping competes with a nonlinear two-photon dissipative channel to produce a quantum limit cycle, and the question of how two such oscillators with non-identical intrinsic frequencies synchronize in the sense of phase locking when coupled dissipatively to one another. For a single oscillator, starting from a Lindblad description of the dynamics, we derive the exact Wigner-function evolution equation, and show that its Fokker–Planck approximation admits in the appropriate regime an equivalent classical Itô stochastic description that reproduces remarkably well the full Lindblad dynamics. Notably, the stochastic approach provides an efficient means of capturing system dynamics in the semiclassical regime, where a large number of energy eigenstates contribute and direct numerical simulations become computationally demanding. Restricting to the three lowest Fock states and using a parity symmetry, we obtain in closed form the stationary-state density matrix and its Wigner-function representation that displays pronounced nonclassical features. For two non-identical oscillators, we study the full Lindblad dynamics numerically and characterize synchronization through the stationary-state order parameter as a function of frequency mismatch and dissipative coupling. We find that increasing the effective nonlinear dissipative strength suppresses the synchronized region. Restricting the two oscillators to the three-level qutrit subspace, a parity symmetry reduces the stationary-state problem to an exact $41$-dimensional linear system, allowing to compute the synchronization order parameter. In this reduced description, results in the limit of large dissipation agree closely with those from the full dynamics, while exhibiting in the limit of small dissipation a double-peak synchronization structure accompanied by a phase reversal.

Energy is arguably the main resource in classical physics; coherence is the prototypical quantum resource. In this paper, we study the interplay between these two resources in the task of optimal mode discrimination. This task, motivated by cryptography and metrology, consists of finding in which mode a signal has been encoded, for a given finite set of possible modes. After recalling that the task can be cast as a semi-definite program, we solve completely the case of two-mode discrimination under a hard energy constraint $n\leq N$. Specifically, we identify the region of modes overlap, for which the maximal energy state (the Fock state with N excitations) is the best choice for discrimination. For other overlaps, having access to coherence leads to better discrimination.

Scattering of sound waves propagating in a compressible fluid is linked to the quantum dynamics generated by a class of non-Hermitian Hamiltonian operators. The scattering amplitude is expressed in terms of the corresponding evolution operator. This is used to provide a new proof of the reciprocity theorem in acoustic scattering, conduct analytic low-frequency acoustic scattering calculations, and study the scattering of sound waves by a finite planar array of delta-function point scatters embedded in an infinite acoustic slab. A detailed discussion of acoustic scattering properties of a homogeneous acoustic slab including a pair of delta-function point scatters on one of its faces is provided.

Coherent noise poses a fundamentally greater challenge to quantum error correction than independent s- tochastic Pauli errors, because unitary errors preserve interference between error paths, can accumulate over multiple quantum error correction rounds, and leave the encoded logical channel with a residual coherent com- ponent. If the parameters of such coherent noise can be accurately determined, this knowledge can be exploited to inject correlated priors into the decoding graph, and to perform maximum-likelihood decoding under poly- nomially tractable structures, significantly improving the accuracy of syndrome-based decoding. In this work, we introduce one protocol to determine the model and parameters of coherent noise, and reduce the complexity of the experiment from 16nto O(16), which is of great significance for correcting coherent noise in quantum error correction.

Fiber-optic sensors enable high-sensitivity measurements of various physical parameters. Here, we demonstrate a quantum-enhanced interrogation of an all-fiber-optic Fabry-Perot resonator, employing entangled two-photon interference to probe directly strain-induced optical phase shifts. The resonator is interrogated by a narrow-linewidth laser that is frequency-locked to its resonance mode, thereby exploiting the cavity's inherent sensitivity to variations in the fiber length. To access the phase fluctuations transferred to the interrogation field due to external perturbations on the sensor, we implement an in-fiber Mach-Zehnder interferometer readout. This configuration allows the sensor to operate both with classical coherent light and with entangled photon pairs generated via spontaneous parametric down-conversion. Harnessing two-photon entangled states corresponding to an N = 2 NOON state, we experimentally demonstrate a reduction of the measurement noise below the standard quantum limit. These results provide clear evidence of the quantum advantage in enhancing fiber-optic sensors under practical constraints on optical power.

We present a quantum-enhanced search for the Galactic dark-photon background (GDPB), a relativistic and anisotropic vector field that can be produced by dark-matter decay or annihilation in the Milky Way halo. We reinterpret an existing quantum-enhanced dark-photon dataset obtained with a superconducting circuit QED platform originally developed for wave-like dark-photon dark-matter searches, consisting of a high-$Q$ niobium cavity in the $\mathrm{TM}_{010}$ mode dispersively coupled to a transmon qubit. By preparing four-component cat states and performing repeated quantum non-demolition parity measurements, analyzed with a hidden Markov model, we extract photon-transition probabilities for multiple cat amplitudes and integration times. The coupling to the GDPB is governed by a polarization- and angle-dependent cavity overlap function, which predicts a distinctive diurnal modulation of the excitation rate for both longitudinal and transverse polarizations. From the absence of such modulation, we set 90% confidence-level bounds on the kinetic-mixing parameter $\epsilon$ for two benchmark production mechanisms (parametric and cascade decay) over the relativistic mass range $m_X \ll \omega_c$.

Through-substrate interconnects are a key technology for scaling surface-electrode ion traps (SEITs) toward large electrode counts and complex architectures. Dielectric substrates such as fused silica offer superior RF performance compared to silicon, but the reliable fabrication of void-free through-glass vias (TGVs) remains challenging. In this work, we demonstrate a SEIT fabricated on a fused silica substrate incorporating TGVs. The via-holes are formed using Selective Laser-Induced Etching and subsequently metallized with gold by electroplating. A patent-pending geometry-assisted bottom-up plating approach enables void-free filling using constant-current electroplating without electrolyte additives or pulsed deposition schemes. Electrical characterization across multiple wafers confirms a TGV-level yield above 98.8 %, demonstrating the robustness and reproducibility of the developed TGV technology. The TGVs are combined with multilayer SEIT fabrication, enabling vertical signal routing to all electrodes while maintaining an unaffected trapping surface without wire bonds. To interface the trap with external control electronics, a glass interposer providing signal fan-out to a larger pitch is designed and fabricated. The trap chip and the interposer are integrated using thermocompression bonding, forming a compact chip-to-chip assembly. The presented technology demonstrates the first fully integrated multilayer SEIT on fused silica incorporating void-free TGVs.

Inserting a resolution of the identity between two operators turns a matrix element of their product into a phase-space integral. For unbounded operators the product need not exist on the vector at hand, while the integral may still converge. We follow this gap through the chain $e^{\mu a^2}e^{\lambda a^{\dagger2}}$ of two-photon exponentials, where it can be traced completely. Five regions of parameter space appear: where the Bochner conditions of the strong formulation hold, where the product exists as a vector, where it exists as a sesquilinear form, where the coherent-state integral converges, and where the Fock-space series converges. The first three are strictly nested inside the intersection of the last two, and these two overlap without either containing the other. A single Hermite-type function agrees with the matrix element where it exists and with the integral and the series wherever they converge, so the integral carries the analytic continuation of the matrix element beyond the domain of the product and beyond the convergence of its Fock series. On the real slice of parameter space, an iterated form of the integral also reaches every point where the series converges. The analysis rests on a weak composition lemma whose hypotheses concern only the bra, the ket and the resolving family. For bounded chains the same identity is unconditional, and worked examples of that kind are given in a companion paper.

Encoding quantum information in $d$-dimensional systems (qudits) with $d>2$ offers appealing new directions for resource-efficient quantum computing. However, protecting the coherence of nonclassical qudit resource states remains an open challenge. Dynamical decoupling (DD) is a well-established technique for extending coherence, but its application to qudits is hindered by the quadratic scaling of the decoupling sequence overhead with the dimension $d$. As a result, demonstrations of qudit DD have so far been limited to low-dimensional qudits. Here, we show that noise-biased qudits enable a nontrivial reduction of this overhead, for example, from quadratic to linear. We perform qudit DD on a model $d=8$ qudit, the nuclear spin of an antimony donor in silicon. We benchmark DD performance on highly nonclassical states such as uniform superpositions, cat states, and Haar random states and measure coherence improvements up to a factor $5$ to $10$. For a spin-cat error correction code, continuous DD extends the coherence time of the logical superposition $|+\rangle_L$ to $225$~ms, compared to $19$~ms under free evolution and $85$~ms with a Hahn echo. This improvement shows that DD sequences tailored to a system's noise bias can significantly enhance the lifetime of encoded logical qubits.

Strong eigenstate thermalization (ETH) in operationally mean-ergodic, non-chaotic systems provides an opportunity to investigate whether Floquet eigenstates retain information about classical transport beyond their leading thermodynamic behavior. We address this question using the double kicked top (DKT), which exhibits nonmixing transport and dynamics consistent with weak mixing transport under variation of its control parameters. We show that the coefficient $m$ of the leading finite-size correction to the normalized eigenstate entanglement entropy (EE) $s$ tracks the restructuring between these transport regimes even when the thermodynamic-limit entropy $c$ becomes nearly insensitive to them. This coefficient $m$ is positive for nonmixing transport and negative when dynamics consistent with weak mixing transport dominate. The coefficient's sign reversal in the coexistence regime remains stable as the semiclassical resolution increases. Our results demonstrate that finite-size eigenstate structure can encode signatures of classical transport that are invisible in the thermodynamic-limit entropy, providing an eigenstate-based diagnostic of dynamical organization beyond the leading thermodynamic behavior associated with strong ETH.

This paper proposes a scheme and design of cryogenic multiplexing control chip (MCC) which enables one microwave cable to control many superconducting qubits. Designed based on adjustable inductor, MCC is a non-reciprocal device which generates microwave signals between 4 and 8 GHz and constructs XY control circuit to operate qubits. The effects of filters, isolators, power splitters, qubits and load impedance on MCC are analyzed in the frequency-domain simulation. And in time-domain simulation, the response time, Gaussian pulses, single-sideband, amplitude and frequency compensation of MCC are examined. The MCC can be integrated with the superconducting qubits on the same package at 20 mK temperature stage, and output specific microwave pulses used to drive the superconducting qubits without crosstalks. The MCC can greatly reduce the number of microwave control lines and is beneficial to the development of large-scale superconducting quantum processor.

This paper reconstructs the Michelson interference phenomenon based solely on the binary (on-off) statistics of a single-photon counter and macroscopic path-difference data, without the a priori assumptions of complex wave superposition or prior spectral information. In contrast to the conventional approach that assumes light as a continuous complex wave function and considers interference between them, this study focuses on the algebraic properties inherent in discrete detection statistics. We verify that the discrete response data collected across various path differences form a positive semi-definite matrix, and apply Herglotz's theorem to this result. Consequently, we show that the harmonic form of the interference fringe is not a consequence of adopting a wave model as an axiom, but rather it is uniquely decomposed into a cosine average of wavenumbers dictated by testable algebraic constraints satisfied by the statistical data. Through this approach, the logical basis of the interference phenomenon can be described by the characteristics of the binary data itself, perfectly aligning with the modern optical experimental environment that relies entirely on discrete event statistics.

Pauli correlation encoding (PCE) encodes $m$ binary variables in the signs of $k$-body Pauli correlators of $n=O(m^{1/k})$ qubits, and trains a parameterized circuit on a relaxed loss of sharpness $\alpha$. The strongest published schedules sharpen this loss aggressively and are benchmarked with exact expectation values, whereas a quantum computer estimates correlators from a finite number of shots. We show that the sharpness is a hidden shot budget. Since the expected sign of a correlator estimated from $S$ shots, $\mathrm{erf}(c\sqrt{S/2})$, agrees with $\tanh(0.851\sqrt{S}\,c)$ to within $0.019$, the edge term of the relaxed loss at $\alpha=0.851\sqrt{S}$ approximately equals, up to a constant, minus twice the cut expected from decoding $S$ shots. This explains why schedules tuned with exact expectation values lose their advantage at realistic budgets, and yields a shot-aware schedule whose final sharpness is set by the shot budget. On five G-set graphs with $800$ variables on $13$ qubits, this schedule outperforms every published schedule at its target budget in all $150$ paired comparisons of the decoded circuit output, owing to the sharpness at $1.6\times10^4$ shots and mostly to switching off the regularization at $10^3$; after a classical bit-swap search, it remains the best on average at $1.6\times10^4$ shots. Device noise damps the correlators by a factor $s$, which amounts to a smaller shot budget $s^2S$. On the IBM Heron processor ibm_fez, an all-to-all ansatz of the type used for the best published G-set results compiles to $835$ CZ gates and decodes to a random cut, while our $96$-CZ hardware-native circuit, trained in simulation and sharpened to $\alpha\simeq0.65\,s\sqrt{S}$, retains up to $0.919$ of the best-known cut. For new circuits, a damping and an offset calibrated on other circuits of the same graph predicted the decoded cuts at $10^3$ shots to within $0.002$.

Magneto-optical traps (MOTs), indispensable to cold-atom-based quantum computing and quantum precision measurement, are increasingly desired in compact and stable form. Particularly, the six-beam 3D-MOT, distinguished by symmetric geometry and superior trapping performance, finds particularly broad applications. Conventional implementations, however, rely on complex and bulky free-space optics, hindering miniaturization, practical assembly, and long-term stability. Here, we demonstrate a compact six-beam 3D-MOT system that employs two multifunctional optical metasurface chips to implement the optical-field functionalities required for cooling and trapping atoms. By combining two metasurface chips and a vacuum cell, a photonic-integrated cell module (PICM) is implemented as the core assembly and the volume is only" 73*73*107 mm^3" . In success, 1.3 * 10^3 Rb atoms are trapped and cooled to the temperature of ~183 {\mu}K. It should be noticed that the laser beam is guided to the metasurface through optical fiber, thus such fully fiber-coupled architecture enables straightforward and stable operations. We believe that this work would pave a practical route toward compact and portable 3D-MOT.

Frequency inhomogeneity can obscure the metrological advantage of squeezed spin states, making the choice of readout crucial. We study interacting spin-1/2 ensembles with static local frequency disorder and optimize a common collective readout over independent disorder realizations. Using Bayesian optimization of the full measurement-outcome distribution, we identify observables combining dipole and quadrupole operators that yield greater classical Fisher information than the optimized dipole readout considered here. For ensembles of up to 17 spins, their disorder-averaged CFI surpasses the standard quantum limit at both disorder strengths studied, including a regime where the dipole readout remains below it. For the larger ensembles studied, fixing the encoding axis to the direction that maximizes the disorder-averaged quantum Fisher information retains nearly the same performance. These results identify a route to extracting metrological information from frequency-disordered spin ensembles through the choice of collective observable.

We construct quantum codes from codewords of a cyclic code and the minors of a polynomial matrix. The construction uses a two-row, three-column matrix whose minors yield a second matrix satisfying the CSS orthogonality condition. We derive the code dimension from the greatest common divisors of the entries and minors, with a simplified formula for odd lifting factors. A residue characterization identifies additional common factors of the minors and leads to a method for controlling the dimension through polynomial selection. We also give a condition for changing the minor generator without changing the code. Explicit polynomial constructions yield 13 quantum codes with verified minimum distances, including a $[[255,80,12]]$ code of rate $80/255$.

We show that limit-periodic Jacobi matrices in the weak exponential class $EC(\eta)$ have purely absolutely continuous spectral type when $\eta$ is sufficiently large, depending only on the $R$-boundedness constant. The proof first establishes homogeneity of the spectrum from the weak exponential approximation rate. A closure theorem for reflectionless Jacobi matrices then transfers reflectionlessness from the periodic approximants to the limit, and a theorem of Poltoratski and Remling rules out singular spectrum on a homogeneous set.

A common problem with physical qubits is that the state can leak outside the computational subspace. To characterize the problem, it is desirable to measure both the leakage probability and the fidelity of gates inside the computational subspace. Randomized benchmarking is a readily accessible method for estimating average gate fidelities and can be modified to account for leakage. However, in the presence of state preparation and measurement errors (SPAM) there are parameter degeneracies, and fidelities and leakage become underdetermined. We study the example of qudits with any number of leakage levels under the assumption of gate-independent noise. We show that randomized benchmarking sequences with leakage level decoherence can be analyzed as a Markov process with noisy classical preparations and measurements. This result generalizes to randomized benchmarking with random gates from an arbitrary group that contains a phase-decohering subgroup. We characterize the parameter degeneracy in inferring the Markov process, preparations and measurements. Based on this characterization we develop a measurement and inference method taking advantage of known conservative bounds on SPAM to constrain fidelity, leakage and other parameters of the Markov process, state preparations and measurements. As part of our study, we experimentally implemented the measurement method for a qubit defined on the one-excitation subspace of two transmons, for which there are two leakage levels. We determined confidence intervals accounting for parameter degeneracy for a number of performance parameters of the system. For leakage and fidelity, we compare these intervals to those obtained for several conventional methods for leakage benchmarking.

Magic $|T\rangle$-state preparation dominates the cost of fault-tolerant quantum computation on surface codes, yet cultivation and distillation are typically provisioned statically, leaving much of the program's error budget unused. We present Gap-Priced $|T\rangle$ States (GP$|T\rangle$-S), a lattice surgery scheduler and factory allocator that co-optimizes both methods under a total $T$-error budget. GP$|T\rangle$-S uses the complementary gap of each cultivated state as a fidelity estimate and dynamically adjusts the cultivation gap cutoff, converting budget slack into speed by giving the scheduler control over the cultivation post-selection. GP$|T\rangle$-S also characterizes distillation factories by size, $|T\rangle$-state production rate, and budget slack, and introduces cultivating factories that embed cultivation within routing channels, achieving fidelities otherwise requiring two-level distillation at a single-level footprint. GP$|T\rangle$-S organizes these characterizations into a factory catalog, and performs distillation factory allocation over this catalog in tandem with the gap cutoff using dynamic-programming to achieve one of i) minimum spacetime volume, ii) minimum execution time, or iii) minimum space overhead, all within a user-provided $T$-error budget. Across sixteen benchmarks under high and low $T$-error budgets of $10^{-3}$ and $10^{-5}$ respectively, GP$|T\rangle$-S consistently outperforms cultivation-only and single-factory baselines without exceeding the budget, achieving a 5.5$\times$ geometric mean speedup in logical cycle count and a 3.4$\times$ geometric mean reduction in space-time volume.

The mutual information of measurement of a local operator between two spatial regions characterizes the reduction in the uncertainty of measurement outcomes in one region given the outcome in the other. We study the Rényi-Shannon mutual information of measurement in conformal field theories (CFTs). Explicit calculations for scalar primaries and descendants in large $N$ CFTs are performed in the two extreme limits of the intervals being adjacent or largely separated. The results depend on only the cross ratio and the scaling dimension $\Delta$ of the operator being measured, with striking similarities to the mutual information of entanglement. We find a surprising quadratic dependence as $(\Delta-1/2)^2$ for adjacent intervals. This dependence superficially seems to violate the information processing inequality, which we discuss and resolve. We also offer a holographic interpretation of the mutual information of measurement.

Choosing which information to use as the context changes is a basic cognitive operation. We introduce a new task of this kind for quantum reservoir computing (QRC): a binary cue indicates which of two simultaneous input streams the reservoir must reproduce. In simulated spin reservoirs with a trained linear readout, infinitely many measurements (exact expectation values) let the reservoir reproduce the cued stream accurately. At a finite number of measurements \(N_M\), the score exceeds that of a linear readout of the raw inputs only at large \(N_M\) because of sampling noise. Performance increases with both entanglement and coherence in the computational basis, and then saturates. These results show that QRC can select and reproduce a cued stream, and they are a starting point for harder cognitive tasks.

Generators of continuous-time quantum Markovian evolution, known as Lindblad operators, play a key role in the theory of open quantum systems. The question of how to define and characterize random Lindblad operators has attracted considerable attention in recent years. Purely dissipative random Lindbladians have been extensively studied using toolboxes of free probability and non-Hermitian random matrix theories, which helped, among other results, to uncover a characteristic lemon-like spectral support. In this work, we focus on random Lindbladians with a Hamiltonian component. We analyze three ensembles of increasing complexity, designed to illustrate the joint effects of dissipative and Hamiltonian dynamics. While the first two ensembles allow for an exact analytic treatment with standard probabilistic and free-probability methods, the generic case of independently random Hamiltonian and dissipative components requires a novel framework that combines operator-valued free probability with sequential noise averaging. For this ensemble, our approach preserves the underlying tensor-product structure of the Lindblad operator and derives a general equation for the spectral boundary. We characterize the effect of Hamiltonian-induced spectral squeezing and explain how the spectral support changes with the relative Hamiltonian strength and the rank of the dissipative component.

Quantum-walk algorithms can quadratically reduce the dependence of spatial search on the classical hitting time $\mathrm{HT}$. Realising this speedup using standard quantum-walk algorithms, however, requires deep coherent circuits, limiting their applicability on near-term and early fault-tolerant quantum devices. We derive a parameterised family of hybrid quantum-classical spatial search algorithms that continuously interpolates between the classical and fully coherent quantum regimes, trading off circuit depth for total query complexity. For any $\gamma\in[0,1]$, our algorithms use circuits of depth $\widetilde{O}(\mathrm{HT}^{\gamma/2})$ and find a marked vertex with constant success probability at total cost $\widetilde{O}(\mathrm{HT}^{1-\gamma}\mathsf{S} + \mathrm{HT}^{1-\gamma/2}(\mathsf{U} + \mathsf{C}))$, where $\mathsf{S}$, $\mathsf{U}$, and $\mathsf{C}$ denote the setup, update, and checking costs, respectively. We also derive an optimal continuous depth-query trade-off for fixed-point amplitude amplification, providing a potential building block for other hybrid designs.

We realize the mesoscopic Bose-Hubbard model at unit-filling on a two-dimensional array of transmon qubits and selectively excite collective modes associated with amplitude or phase fluctuations of the superfluid order parameter. We identify these modes respectively as the Higgs and Goldstone modes using complementary local observables, extracted from measuring the number of particles on each site. Modulation of the coupling between sites excites the Higgs mode, which we detect via the density of doubly occupied sites. In contrast, modulation of the local chemical potential with an appropriately chosen spatial profile excites the lowest-frequency Goldstone mode, which we detect via changes in the local density. The two modes have different symmetries and do not couple to one another. By varying the system geometry, we characterize the impact of finite system size on the evolution of both modes. In the thermodynamic limit, decay into a continuum of lower-energy excitations can obscure the Higgs response. In our mesoscopic system, however, the finite system size leads to spectral gaps and allows us to detect the Higgs mode as a coherent, long-lived excitation. Our work demonstrates how finite quantum simulators can isolate and probe physical phenomena that become difficult to resolve in the thermodynamic, large-scale limit.

Dynamic nuclear polarisation transfers polarisation from electron to nuclear spins by relying on a dissipative channel. Here we introduce a cavity-based DNP mechanism which uses the radiative relaxation of the electronic spin through the Purcell effect to bring about the nuclear spin polarisation. We implement this protocol on an ensemble of bismuth donor spins (I=9/2, S=1/2) in isotopically purified silicon coupled to a superconducting resonator. A single cycle, combining adiabatic microwave and radio-frequency pulses with Purcell relaxation, increases a target ground state's population by a factor of $1.79\pm0.04$; a cumulative enhancement of $4.6\pm0.2$ is reached with additional cycles, to be compared with the theoretical limit of ninefold set by the degeneracy of the ground manifold. We explain this difference by the competition between Purcell and intrinsic relaxation on the one hand and a collective effect that slows down the electronic spin radiative decay as the nuclear spin population grows on the other hand. Our results place radiative DNP as an available mechanism at millikelvin temperatures where phonon-mediated relaxation is frozen.

Circuit depth and measurement count are the main limitations for chemical applications of the leading variational quantum algorithms on quantum computers. We show that both resource requirements can be reduced by augmenting adaptive variational quantum algorithms with post-optimization corrective techniques. We focus on two such techniques—Hamiltonian-moment Krylov subspace diagonalization and the identity-augmented quantum self-consistent equation of motion (q-sc-EOM)—applied to optimized ADAPT-VQE states without further ansatz growth or nonlinear optimization. Across molecular systems studied with up to 20 qubits, first-order Krylov correction reduces the optimized iterations (and the corresponding number of adaptive layers) needed to reach the $1.6~\mathrm{m}E_h$ threshold by up to approximately sixfold, with a general trend toward larger reductions at higher determinant Rényi entropy. We also find measurement-cost reductions of up to approximately fortyfold using a suitable resource-cost model. Identity-augmented q-sc-EOM improves molecular potential-energy curves obtained from truncated ADAPT-VQE ansätze with limited expressivity and recovers accuracy from states produced by sampled operator ranking without additional gradient-based operator selection, providing an advantage when small pool gradients make selection measurement intensive. Together, these post-optimization corrections offer routes to improve energy accuracy and reduce adaptive circuit growth in quantum algorithms as quantum hardware advances.