Papers

We develop a Schrödingerization algorithm for quantum linear systems problems in two higher dimensions. The earlier LC-Schrödingerization approach represents the solution as a time integral of a homogeneous convection response and implements this integral by a linear combination of unitaries (LCU) over evolution times. We instead use Duhamel's principle to incorporate the integral into an inhomogeneous convection equation with zero initial data. Fourier projection in the convection variable and Schrödingerization in a second auxiliary variable then realize the solution without the separate LCU step. A joint choice of the kernel and recovery procedure gives an evolution time independent of the target accuracy, a uniformly bounded $L^2$ kernel normalization, and accurate recovery on a fixed interval. We establish the periodization and discretization bounds and analyze the interval recovery probability. With block preconditioning, we retain a single logarithmic precision factor and obtain linear condition-number dependence without variable-time amplitude amplification. Under exact oracle access and given a valid constant-factor solution-norm estimate, the algorithm uses $\mathcal O(\kappa_A\log(1/\varepsilon))$ queries to each original input oracle, with constant success probability and $\ell^2$ state error at most $\varepsilon$. The matrix-query bound matches the standard worst-case scaling when the supplied norm bounds are tight. UnitaryLab simulations on positive-definite and indefinite systems demonstrate the solution accuracy and probability gain from interval recovery.

This thesis studies the intersection of quantum computing and artificial intelligence in two directions: quantum methods for machine learning and machine learning methods for quantum systems. For quantum machine learning, Neural Quantum Embedding learns data representations that increase the trace distance between embedded class ensembles, lowering an embedding-dependent bound on empirical risk and improving classification on noisy quantum hardware. A training objective based on the Hilbert-Schmidt inner product extends this approach to deterministic quantum computation with one qubit (DQC1) and is demonstrated on an NMR quantum processor. A margin-based generalization analysis then connects quantum neural network performance to quantum state discrimination. In the studied benchmarks, margin distributions predict generalization more reliably than parameter-count metrics. For quantum systems, a Mamba-based neural decoder for surface codes matches a reproduced Transformer baseline in memory experiments while reducing inference-cost scaling from quartic to quadratic in code distance. Under an explicit decoder-induced-noise model, it achieves lower logical error rates and a higher effective threshold. For neural quantum states, stochastic reconfiguration is interpreted as tangent-space ridge regression, with its diagonal shift controlling the bias-variance trade-off under finite Monte Carlo sampling. Multi-shift stochastic reconfiguration reduces checkpoint-local validation residuals and update variance relative to fixed-shift SR, at additional computational cost. Together, these contributions show how learned representations, statistical control, and hardware constraints shape the exchange between quantum computing and machine learning.

Trapped-ion quantum networks rely on efficient ion-photon interfaces, while objective-based free-space collection systems must balance high photon collection with sufficient working distance for practical integration with ion-trap hardware. Here, we design and characterize an ion-photon interface with a long working distance of 26.15 mm and a high numerical aperture of 0.5. The core of the interface is a photon-collection objective consisting of six commercial spherical lenses with optimized spacing. The interface achieved an overall fiber-coupled photon-detection efficiency of (1.29$\pm$0.09)% from the ion to the detector and maintains fiber coupling over several hours without active realignment, supporting stable operation of the ion-to-fiber interface. Photon-correlation measurements show clear antibunching in the fiber-coupled fluorescence, confirming the preservation of non-classical photon statistics. These results demonstrate a practical implementation of a long-working-distance photon collection interface for trapped-ion quantum network experiments.

Scaling quantum control for atoms, ions, and solid-state emitters requires gigahertz-frequency spectral control of high-power visible light in a volume-manufacturable platform. Silicon nitride photonics provides high power handling and CMOS-foundry compatibility but has no intrinsic mechanism for high-speed modulation. Integration with piezoelectric materials enables acousto-optic phase modulation, and mechanical resonant enhancement has made it efficient at gigahertz frequencies. However, a single resonance restricts the modulation waveform to a single tone, imposing Bessel-function sideband amplitudes and limiting frequency-shifting efficiency to 33.9%. Here we engineer a silicon nitride acousto-optic microstructure to support harmonically spaced resonances at 1.14 GHz and 2.28 GHz, each strongly optomechanically coupled to a 730 nm guided optical mode, so that tailored non-sinusoidal modulation waveforms can be resonantly synthesized. By piezoelectrically controlling the two mechanical amplitudes and their relative phase, we demonstrate 50% conversion to one sideband (1.5x the single-tone theoretical maximum), a flat seven-line comb, and a frequency shift with 60 dB carrier and 53 dB image suppression - to our knowledge the highest reported for an integrated modulator. The devices are fabricated in a 200 mm CMOS foundry, and we measure 91.7% yield without post-fabrication tuning across 36 devices from three wafers. We also show how the technique can be straightforwardly scaled to three or more harmonics. This result overcomes the trade-off between resonant enhancement and spectral programmability, with important consequences including improved single-qubit gate efficiency for hyperfine qubits.

The realization of a scalable quantum network (QN) hinges on the efficient distribution of entanglement across heterogeneous hardware platforms. While traditional QN frameworks are often restricted to single-encoding schemes, relying exclusively on either discrete (DV) or continuous (CV) variables, such segregated architectures limit the capacity and interoperability of large-scale systems. Here, we propose a scalable hybrid entanglement distribution scheme that bridges these domains by mapping hybrid entanglement swapping and concentration at DV-CV interfaces onto a unified set of series and parallel graph rules. We demonstrate that our hybrid approach exhibits a potential performance advantage over traditional point-to-point generation of maximally entangled states, achieving enhanced end-to-end entanglement within series-parallel topologies. These results provide a robust theoretical foundation for designing resource-efficient, interpretable architectures for the future quantum internet.

Quantum state tomography provides a foundation for characterizing state preparation and predicting measurement outcomes. We characterize the minimax expected trace norm risk of quantum state tomography over classes with polynomial spectral decay under randomized nonadaptive single copy measurements. Under an explicit sufficient block size condition for the two layer periodic Clifford ensemble, we establish statewise expected trace norm oracle inequalities for operator norm minimum distance and measurement weighted projected least squares, with bounds that depend on each state's actual spectral tail, while the estimators require no prior knowledge of the state's structural characteristics, including its rank, eigenbasis, or spectral structure. Over these polynomial spectral decay classes, both estimators attain the minimax expected trace norm rates up to constants. As a direct consequence, the same estimators attain the minimax rate over every fixed rank constrained class, while remaining adaptive to the unknown structural characteristics of the state. For admissible logarithmic block sizes, the periodic Clifford measurements attain these guarantees with logarithmic elementary gate depth. The main technical ingredient is a uniform bound on the fourth moment of projectors for the periodic Clifford ensemble. The bound is sharp in dimension and holds for arbitrary test states, including those entangled across blocks. Covariance concentration and positivity yield adaptive oracle bounds, while a shared rotation information argument on spectral tail packings establishes matching lower bounds. We also provide polynomial time reconstruction algorithms, numerical comparisons, and Lean formalizations of all labeled theoretical results.

We introduce a bi-oriented interlaced matrix product on $2\times 2$ matrices over a unital, possibly non-associative algebra, extending a matrix mnemonic for Cayley–Dickson doubling. The opposite orientations $X_R$ and $X_L$ coincide precisely when the underlying algebra is commutative. For the canonical position and momentum operators $Q,P$ on $L^2(\mathbb{R})$, a matrix $D$ and its companion $\widetilde{D}$ satisfy, on the common Schwartz domain, $\widetilde{D} X_R D =\widetilde{D} X_L D =2H Id_2$, where $H=(P^2+Q^2)/2$. We study the associated interlaced eigenvalue equations for operator-valued columns. The combinations $\Phi=A+iB$ and $\Psi=A-iB$ decouple the equations into two-sided Sylvester equations. We construct explicit rank-one generalized eigenoperators from position and momentum eigenstates. Their distributional kernels belong to the doubled rigged Hilbert space $S(\mathbb{R}^2)\subset L^2(\mathbb{R}^2) \subset S'(\mathbb{R}^2)$; the corresponding position and momentum operators act on different tensor factors and therefore commute. The rank-one families do not exhaust the distributional solutions: higher-order generalized solutions are also exhibited. We distinguish the algebraic identities on the Schwartz core from questions concerning closed-operator realizations.

We show that $1.4<K_G^{\mathbb{C}}<1.404898554746$, where $K_G^{\mathbb{C}}$ is the complex Grothendieck constant. The upper bound improves on Haagerup's bound of $1.40490913\ldots$ from 1987, and the lower bound improves on Davie's bound of $1.33807$ from 1984. The upper bound combines ideas from the real and noncommutative complex cases of Grothendieck's inequality.

Strong entanglement limits the reach of tensor-network descriptions of quantum many-body systems. We study Gaussian-augmented matrix product states (GAMPS), formed by applying a free-fermionic (Gaussian) unitary to a matrix product state. To explore the capabilities of this family, we consider random GAMPS}, a minimally structured ensemble obtained by independently sampling random matrix product states and Gaussian unitaries. Exploiting the algebraic structure of Gaussian unitaries, we develop a replica tensor-network method that computes averages over the random GAMPS ensemble for hundreds of qubits. Random GAMPS exhibit nearly maximal volume-law entanglement already at modest bond dimension, while other quantum resource quantifiers rapidly approach Haar-random state values as the bond dimension increases. The entanglement scaling suggests an exponential reduction in the bond dimension needed to approach the volume-law entropy compared with unaugmented matrix product states. We find a state two-design behavior of random GAMPS at fixed accuracy with a bond dimension independent of system size. Our results reveal how Gaussian augmentation expands the expressive power of tensor networks.

In prior complementarity tests, path markers were measured and remained causally accessible, leaving the collapse-locality loophole open. We address this loophole using a quantum eraser that isolates the encoding of path information in the joint quantum state from its later measurement and causal accessibility. We launch idler photons – the sole path markers for entangled signal photons in an interferometer – on outgoing null trajectories while the joint state remains in a coherent superposition of both interferometer path alternatives. Our flat $\Lambda$CDM transmission model predicts that 73-82% of launched idlers will propagate forever without absorption, scattering, or environmental path-record formation. For these modeled survivors, each path marker remains perpetually unmeasured, and propagation along its outgoing trajectory precludes later causal contact with its interferometric record. Unconditioned signal detections show no statistically significant launch-induced change in interference, as standard quantum theory predicts. Normalized to the modeled survivors, the 95% confidence upper bound on any launch-induced fringe is 0.16 of full restoration.

The quadratic growth of the density matrix with Hilbert-space dimension D is the central obstacle to simulating large open quantum systems. We introduce a deterministic algorithm that eliminates it for Lindblad dynamics whose Hamiltonian consists of a time-dependent diagonal part plus terms that are tridiagonal after reordering the basis. The state is a low-rank ensemble of vectors, propagated by tridiagonal split-operator steps and ensemble rank truncation of short-time Kraus branches, so that memory and cost per step are linear in D at fixed rank. For a driven nitrogen-vacancy-cavity model, rank 16 reproduces full density-matrix observables to relative error below $10^{-5}$, the method is up to two orders of magnitude faster than QuTiP already at $D \approx 500$, and its runtime scales nearly linearly.

In a recent work \cite{Shaikh:2026nsi}, it was shown that for a non-relativistic particle, the operator equations of motion can be cast in the same differential form as Newton's equation of motion. This establishes a correspondence between quantum operator dynamics and classical mechanics at the level of the equations of motion. In this work, we investigate whether this correspondence extends to quantum field theory and linearized gravity. We explicitly show that the Heisenberg equations of motion for quantum field operators reproduce the corresponding classical equations of motion for a broad class of field theories. The Klein-Gordon equation, Maxwell's equations, Yang-Mills equations, and linearized Einstein equations are shown to arise at the operator level without taking the limit $\hbar\rightarrow0$. We then extend the analysis to curved spacetime and show that the quantum field operators satisfy the corresponding covariant field equations at the operator level. In the weak-field approximation, we show that the Heisenberg evolution of the metric-perturbations reproduces the linearized Einstein equations at the operator level. For a quantum particle in curved spacetime, the Heisenberg equations for position and momentum reproduce classical geodesic motion in the semiclassical limit, thereby extending the operator-level quantum-classical correspondence from fields to particle dynamics.

The Mpemba effect occurs when a state initially farther from stationarity overtakes a closer one during relaxation. We show that this anomalous ordering can coexist with superradiant emission in a collectively damped ensemble of two-level systems. In the symmetric Dicke manifold, zero-temperature decay is a population cascade with rates $\Gamma n(N-n+1)$. We construct the sparse family $\rho_A=|\lceil2N/3\rceil\rangle\langle\lceil2N/3\rceil|$ and $\rho_B=(|0\rangle\langle0|+|N\rangle\langle N|)/2$. Although $A$ is initially more energetic and more distant from the stationary ground state, it crosses $B$ in both energy and trace distance because it starts in a more radiative region of the Dicke ladder. Both states develop emission peaks larger than their independent-emitter references. The crossing persists for all examined sizes from $N=6$ to $60$, while the peak intensities show an effective scaling close to $N^2$. The same pair has no crossing under independent decay, identifying collective radiative kinetics as the origin of the effect.

A system evolving unitarily does not dephase or thermalize by definition. Yet, if one considers a part of a unitary system, situation is different. Here we analyze an isolated set of coupled qubits taking one qubit at a time as a subsystem, and writing self-consistently a weak-coupling master equation for it. Weakly anharmonic oscillators and ideal qubits (two-level systems) demonstrate dephasing, i.e. the diagonal elements of the density matrix reach a steady-state in the long-time limit, and the off-diagonal elements of ideal qubits decay exponentially. For the linear coupling between the qubits, only the degenerate ones interact, and the system does not reach thermal distribution. However, non-linearity, in our analysis in form of three-wave mixing, ensures a thermal distribution in the long time limit, where the temperature is determined uniquely by the energy in the initial non-thermal state. Finally, we present a potential experimental scheme based on a superconducting quantum circuit.

We apply the momentous quantum mechanics formalism to the non-perturbative study of superconducting circuits in the transmon regime, deriving effective equations of motion for the bare Josephson junction (JJ), the cavity–JJ system, and a dissipative resonator. A Gaussian closure on the hierarchy of quantum moments resums the full cosine nonlinearity into the closed-form effective Hamiltonian $\tfrac{1}{2}[V(\phi+\phi_s)+V(\phi-\phi_s)]$, which is non-perturbative and preserves the periodicity and boundedness of the Josephson potential at all phase amplitudes; the standard Kerr (Duffing) approximation is recovered as a special case. We derive the quantum-dressed frequency $\omega_{\rm eff}=\Omega_p\sqrt{\cos(\phi_{\rm zpf}/\phi_0)}$, and benchmark the effective dynamics against exact Mathieu-function diagonalization, with the quantum width $G^{2,0}(t)$ providing the most sensitive diagnostic of the closure's validity and marks the boundary of the Gaussian approximation more sharply than $\langle\hat\phi\rangle(t)$ does. We compare the Caldirola–Kanai, Bateman, and Lindblad descriptions: the Bateman dynamics, quantized with a switched symplectic structure, preserves the Heisenberg bound, admits exact closed-form moment solutions, and reproduces the Lindblad benchmark for weak damping, i.e., within the analytic error bound $(\lambda/\omega_1)^2\,\phi_{\rm zpf}^2$.

We apply a finite-state geometric formulation based on Bargmann invariants to a two-band Weyl Hamiltonian and the one-dimensional Kitaev model of a p-wave superconductor. For the Weyl system, a symmetry-antisymmetrized third-order Bargmann combination selects the chirality-sensitive component of the local pseudospin geometry and extends to a two-band lattice Weyl model. For the Kitaev chain, a normalized ratio involving a third-order Bargmann invariant and a second-order overlap factor removes the dependence on an intermediate state and reproduces the $Z_2$ distinction between its two gapped phases. We further construct a fourth-order loop connecting localized Majorana edge-mode profiles with finite-energy BdG states and an alternating fourth-order loop involving opposite Weyl pseudospin sectors. These constructions illustrate how suitable Bargmann combinations can probe chirality-sensitive, topological, and higher-order geometric information directly through quantum-state overlaps, providing an alternative state-based route without requiring a continuous description of the underlying state-space geometry.

Quantum comparators decide the order of two operands. They rely on reversible logic acting on basis-encoded integers, so their width grows with the precision. We introduce the Quantum Phase-based Comparator (QPC), which compares two values carried in relative phases instead. The circuit places the two phases, entered with opposite signs, between a pair of Hadamard gates, and a fixed offset centers the interference, so that the probability of measuring zero falls below one half exactly when the first phase is the smaller. We give two implementations. With hard-coded values, the two values are written into the parameters of two phase gates, and the comparison costs one qubit and five gates. With the register-driven cascade, the values are drawn from two $t$-qubit registers through binary-weighted controlled-phase gates, at a cost of one qubit beyond the registers and depth linear in $t$; since the cascade induces each phase linearly from the register content, one circuit handles a superposition of operand pairs. The readout yields a biased coin rather than a definite bit, and we quantify the shots that a decision takes at a given phase separation. Scaling both phases by an integer widens the decision margin at no cost in width or depth, and an adaptive doubling schedule turns this amplification into a shot count logarithmic in the inverse separation.

Concatenated quantum error-correcting codes have recently gained popularity because they improve the effective distance of a joint code without requiring the discovery of new codes with desirable parameters. A common building block for such studies is the $[[4,1,2]]$ Iceberg code, the smallest error-detecting code and therefore the one with the lowest resource overhead. However, it has an asymmetric number of $X$ and $Z$ checks, and concatenating it produces skewed logical error rates (LERs) between the $X$ and $Z$ observables. This asymmetry can be mitigated by Clifford-deforming the individual blocks of the concatenation, but the space of possible Hadamard deformations grows doubly exponentially with the number of concatenation levels. We formalize this deformation space and investigate it by proposing six concrete deformation strategies, which we compare under a code capacity (with and without bias) noise model using a concatenated maximum-likelihood soft-information decoder. Among the strategies we study, one one of them achieves near-identical $X$ and $Z$ LERs in a logical-memory experiment while simultaneously reducing the total LER (the sum of the $X$ and $Z$ error rates).

Quantum technologies promise computational capabilities beyond the reach of classical systems. A forward-looking application lies in satellite missions, which increasingly depend on onboard computing under stringent constraints on size, weight and power. Quantum photonics is particularly attractive here: photon interference can enhance the machine-learning models needed to process large onboard data volumes, at fixed hardware resources. However, harnessing this interference requires more than generating single photons, as they must remain mutually indistinguishable: a fragile condition that is hard to maintain within the technically demanding framework of a space mission, which includes a rocket launch, strong thermal drifts, and radiation. This is why quantum states of light, though already generated and transmitted in orbit for secure communication and fundamental tests, have never been used as a computational resource. Here, we report a programmable quantum photonic platform operating on a nanosatellite, processing two photons in a six-mode universal integrated circuit. By programming distinct unitaries and tuning the photons into indistinguishability, we observe two-photon interference, establishing the on-board generation, manipulation and detection of non-classical light. This extends space-based technologies towards in-orbit quantum-assisted computing, for instance local encoding of Earth-observation data, or nodes in a distributed quantum network.

Learning quantum Hamiltonians from low-temperature thermal state measurements is a fundamental problem in quantum physics. Scalability of existing methods is limited by the complexity of semidefinite optimization problems or partition function computation. Here, we develop a quantum analog of classical score matching method that exploits generalized notions of derivatives and integration by parts in operator algebras. We introduce a new Operator Score Matching loss function that recovers Hamiltonian parameters by a simple gradient descent without the need to compute intractable normalization constants. Numerical experiments on the Gibbs states of the transverse-field Ising model, XXZ spin chain, Fermi-Hubbard model, and lattice $\phi^4$ theory demonstrate efficient parameter recovery using finite-depth truncations of nested commutator expansions. Our results establish Operator Score Matching as a practical, partition-function-free framework for quantum Hamiltonian learning.

We present a dual-region experimental apparatus for trapping single atoms of the fermionic isotope ytterbium-171 (${}^{171}\mathrm{Yb}$) with optical tweezers in a science chamber containing an in-vacuum nanofiber cavity. A source region is located approximately $240\,\mathrm{mm}$ from the science chamber, preserving optical access around the chamber for high-numerical-aperture tweezer optics. A pulsed transport sequence based on longitudinal moving molasses launches atomic pulses toward the science chamber, where they are decelerated and recaptured in a magneto-optical trap. We subsequently load single atoms into a $2\times2$ tweezer array located approximately $50\,\mathrm{\mu m}$ from the nanofiber and measure a $1/e$ lifetime of $9.5(7)\,\mathrm{s}$. These results demonstrate that the dual-region architecture provides sufficient ${}^{171}\mathrm{Yb}$ atoms for single-atom tweezer operation near an in-vacuum nanofiber cavity.

Motivated by two-dimensional bilayer systems we numerically study an anti-ferromagnetic spin-$1/2$ Heisenberg model on the honeycomb lattice with a nearest-neighbour exchange coupling $J_1$, and a next-nearest-neighbour exchange coupling $J_2'$ for the B sublattice sites only. Using infinite Projected Entangled-Pair States (iPEPS), variational uniform matrix-product states on cylinders, and exact diagonalization, we find an extended symmetric regime $0.4\lesssim J'_2/J_1\lesssim0.6$, in which local observables show no magnetic, valence-bond, or chiral spin order. At $J'_2/J_1=0.5$, the PEPS correlation length grows systematically with bond dimension, and an inverse-correlation-length extrapolation favors a vanishing limit. We also find that various observables scale algebraically with the finite bond-dimension-induced correlation length, which points to a gapless spin liquid ground state. We propose a $\mathbb{Z}_2$ Dirac spin liquid parton state, with Dirac points that are protected by translation, time-reversal and three-fold rotation symmetry, as a promising candidate state to explain the numerical results. We also discuss the possibility that the symmetric ground state is a featureless, short-range entangled state with a small gap.

Whether a nonequilibrium quantum-critical steady state can be described by an effective temperature remains an open question. We address it in a voltage-biased electronic Lipkin–Meshkov–Glick model, a minimal driven-dissipative model of a collective spin coupled to metallic leads. A controlled large-$N$ treatment reveals an overdamped open quantum-critical regime distinct from the closed model. The surrounding quantum critical fan, organized by temperature and voltage, is explored and fluctuations are found to be governed by an effective temperature $T_{\rm eff}$. At strong bias, the transition becomes first-order through a tricritical point. Remarkably, the same $T_{\rm eff}$ governs the strongly driven regime, but now varies across the entire order-parameter landscape. The steady state is therefore selected by a non-Boltzmann rule, shifting the first-order transition away from the equal-depth point of a deterministic potential. Driven criticality thus remains organized by an effective temperature while revealing non-thermal state selection.

Nanophotonic cavities provide strong atom-photon coupling in a compact, directly fiber-coupled geometry, while a reconfigurable array of $^{171}$Yb atoms combines high-fidelity gates with a metastable qubit state coupled directly to a telecom-band transition, making the two a natural interface between neutral-atom quantum processors and telecom quantum networks. Here, we realize strong atom-cavity coupling on the ${}^{3}\mathrm{P}_0 \leftrightarrow {}^{3}\mathrm{D}_1$ transition of ${}^{171}\mathrm{Yb}$, establishing, to our knowledge, the first neutral-atom cavity-QED system to reach the single-atom strong-coupling regime on a telecom-band atomic transition. Reflection spectroscopy of a single-sided cavity yields a single-atom internal cooperativity of $C_{\mathrm{in}}=5.6(1.0)$ and collective coupling following $\sqrt{N}$ scaling up to $N=5$ atoms, with homogeneous coupling at antinodes over $\sim$200 $\mathrm{\mu}$m along the nanofiber. Thermal tuning of a fiber Bragg grating provides in situ control of the cavity outcoupling rate over two orders of magnitude from the undercoupled to the overcoupled regime, relevant for various atom-cavity protocols. We confirm compatibility with reconfigurable atom arrays by demonstrating 99.95(6)% imaging fidelity and trap lifetimes comparable to free-space array, at 1 $\mathrm{\mu}$m from the nanofiber axis. Moreover, the diameter-engineered antireflection design of the nanofiber enables tweezer-based atom transport across the nanofiber with no measurable loss or heating at 4.5 $\mathrm{\mu}$m above the nanofiber, supporting a two-layer architecture for the nanofiber-integrated atom array. From the demonstrated atom-cavity coupling, atom capacity, and cavity mode profile, we project time-multiplexed remote atom-atom entanglement generation at 40 kHz, with prospects for further scaling through technical enhancements and channel multiplexing.

Decoherence is conventionally regarded as a detrimental process that suppresses quantum coherence and limits the performance of quantum technologies. Contrary to this view, we show that spatially localized decoherence can instead be exploited as an interferometric tool. Beyond its conceptual implications, localized decoherence provides a novel approach to prepare arbitrary macroscopic spatial superpositions for testing quantum physics with massive particles. We demonstrate the proof of principle by making use of the correspondence between optics and matter-waves through the equivalence of the respective propagation functions. By employing stochastic phase fields to the optical counterpart to model the decoherence, our experiments confirm the expected interference. The results establish localized decoherence as a resource for quantum state engineering.

Quantum correlations have recently attracted significant attention in collider physics, with Nonlocal Advantage of Quantum Coherence (NAQC) representing the strongest form of quantum correlation studied so far. Owing to its strength, NAQC is considerably more challenging to observe than Bell nonlocality since it is only present in narrower regions of phase space. Unlike other systems, tau-lepton pair ($\tau^+\tau^-$) production in electron–positron ($e^+e^-$) collisions provides an ideal testing ground, as it exhibits strong quantum correlations and, in particular, NAQC over a large region of phase space. In this paper, we investigate NAQC in $e^+e^- \to \tau^+\tau^-$ production at center-of-mass energies of 10.58 and 91.19~GeV, corresponding to the ongoing Belle~II and future FCC-$ee$ experiments, respectively. Remarkably, for our experimental proposal, we develop a dedicated NAQC witness, which allows to certify NAQC presence by measuring one single magnitude. We estimate the experimental sensitivities needed to establish the presence of NAQC, finding that a large fraction of the number of events (specifically, 0.18 for Belle~II and 0.31 for FCC-$ee$) contribute to the NAQC signal. A 5$\sigma$ observation of NAQC requires a precision of approximately 1% at Belle~II, while a precision of a few percent is sufficient at FCC-$ee$. The resulting observation would constitute the strongest form of quantum correlation measured in a collider to date. In addition, we design an experimental scheme to implement the steering game leading to the NAQC definition, representing the first implementation of a steering game in a high-energy collider. Our results are easily extendable to other electron–positron colliders with different center-of-mass energies.

Demonstrating that a machine performs genuinely quantum operations is a central challenge in quantum information processing. Existing proofs of quantumness typically rely on computational tasks that are infeasible for classical machines under assumptions such as computational hardness, or explicit bounds on classical runtime, memory, or oracle queries. Here we introduce an alternative paradigm: a thermodynamic proof of quantumness based on energy consumption. Using the search problem of Yamakawa and Zhandry with a structureless uniformly random oracle, we show that any classical machine solving the task with constant success probability must generate entropy that grows exponentially with the security parameter. By Landauer's principle, this implies an exponential lower bound on heat dissipation and hence on the energy consumption of any cyclic classical implementation. In contrast, the corresponding quantum prover solves the task with polynomial query and gate complexity, giving polynomial energy consumption under standard assumptions for quantum implementations. Thus, in the random-oracle setting, sufficiently low energy consumption in a successful implementation certifies quantumness through a macroscopic thermodynamic observation of energy consumption.

Fast, high-fidelity qubit initialization is a key primitive for scalable quantum information processing, but conventional reset protocols either require long relaxation times or discard information contained in continuous measurement records. We demonstrate an adaptive measurement-based reset protocol for superconducting qubits that uses Bayesian inference to update the qubit-state estimate after each readout and dynamically adjust the feedback threshold. Unlike fixed-threshold or repeat-until-success (RUS) protocols, the method utilizes the full analog measurement history, enabling the reset decision to become progressively more conservative as confidence in ground-state preparation increases. Implemented with real-time FPGA-based feedback on a dispersively readout transmon qubit, the protocol achieves a ground-state initialization fidelity of $99.44\pm0.04\%$ after a small number of reset rounds. We further compare adaptive reset with RUS strategies in multi-qubit experiments and show that adaptive thresholding provides deterministic reset duration while maintaining a five-qubit simultaneous-reset fidelity of $98.78 \pm 0.19\%$. These results establish Bayesian adaptive thresholding as a practical and scalable route to fast qubit reset in superconducting quantum processors.

An entanglement transition can occur without a corresponding transition in purification. We demonstrate this separation in spatially local monitored Clifford circuits with a fixed number of layers per Floquet period, where a spatially random pattern of Clifford gates and Pauli measurements is repeated exactly in time. Rare spatial structures persist under this repetition and break the correspondence between entanglement and purification found in conventional spacetime-random circuits. In one spatial dimension, the late-time entanglement produced with an initial product state remains area-law, while the system remains extensively mixed in the thermodynamic and long-time limits if the initial state is maximally mixed. In two or more dimensions, we find a transition between volume-law and area-law entanglement while the system remains mixed on both sides of this transition. An extensive amount of quantum information survives indefinitely in both phases and evolves unitarily despite the repeated measurements. We introduce the logical-support radius to characterize its spatial spreading and identify the volume-law and area-law phases with delocalized and localized logical dynamics, respectively. We further introduce the logical Krylov dimension, which counts the independent logical operators dynamically generated from an initially local operator. Its scaling resolves the transition and provides evidence for a new universality class of measurement-induced phase transitions.

Quantum simulators are beginning to prepare long-sought phases of matter that remain difficult to realize cleanly in materials. Yet identifying such phases remains a major challenge when their defining properties are inherently non-local and cannot be captured by conventional local measurements. Here we establish multiple-quantum coherences (MQCs) as phase-sensitive diagnostics for gapped $\mathbb{Z}_2$ quantum spin liquids. Focusing on the extended toric code and using large-scale quantum Monte Carlo simulations, we build a direct correspondence between the elementary anyonic excitations and the weights of different MQC sectors. MQCs thereby reveal anyon condensation across the phase transitions through characteristic signatures that remain robust against fluctuations that obscure conventional diagnostics. Subsystem-resolved MQCs further provide a bipartite entanglement witness that distinguishes a classical loop gas from a quantum-coherent closed-loops gas. We develop and benchmark a practical protocol to extract MQCs based on the return fidelity of adiabatic round trips, and show that local coherence measurements retain experimentally accessible signatures of the phase transitions. Our results establish MQCs as a practical diagnostic for the excitations, phase structure and global constraints of quantum spin liquids.