Papers

Quantum walks represent an excellent testbed for investigating the interplay between unitary coherent and incoherent dissipative processes. Thanks to photonic quantum interferometers of considerable size, experimental studies could be performed, devoted to investigating the consequences of different sorts of realistic noise in these systems. In this work we employ a 20x20 on-chip multimode interferometer to introduce another key aspect in the problem: the presence of edges in the walker lattice, enforcing a confined evolution. We show how noise can disrupt translational symmetry and reshape interference patterns. The non trivial probability distributions obtained along the temporal evolution of the system demonstrate how speed up effects, localization and coherent oscillations are pillar concepts to be fully characterized and understood when applied in realistic quantum dynamics.

This work advances the frontier of low-damping magnetic materials, directly addressing the demand for ultra-low-loss components in quantum computing and cryogenic electronics. Here we demonstrate a new approach to get single crystal micrometer-thick yttrium iron garnet (YIG) films with low damping through isolating and mitigating interfacial paramagnetic contributions of a paramagnetic substrate by a buffer-layer. The YIG films with the diamagnetic yttrium scandium gallium garnet buffer layer grown by liquid phase epitaxy on a gadolinium gallium substrate demonstrate homogeneity unprecedented for the thin planar YIG structures, yielding ferromagnetic resonance linewidths of 4.9 MHz at 4 K and 5.9 MHz at 16 mK, the lowest values reported to date. These results underscore the critical role of interfacial engineering in overcoming intrinsic material limitations, opening avenues for further optimization in spin-based technologies.

We extend non-invertible duality concepts from one-dimensional systems to two spatial dimensions by constructing a web of non-invertible dualities for lattice models with subsystem symmetries. For the $\mathbb{Z}_2 \times \mathbb{Z}_2$ subsystem symmetry on the square lattice, we build two complementary dualities: a map that sends spontaneous subsystem symmetry-broken (SSSB) phases to the trivial phase (the analogue of the Kramers-Wannier (KW) duality in 1+1D), and a generalized subsystem Kennedy-Tasaki (KT) transformation that maps SSSB phases to subsystem symmetry-protected topological (SSPT) phases while leaving the trivial phase invariant. These dualities are boundary-sensitive. On open lattices, both subsystem KW and KT transformations act as unitary, invertible operators. In particular, the KT map not only matches the bulk Hamiltonians of the dual phases but also carries the spontaneous ground-state degeneracy of the SSSB phase onto the protected boundary degeneracy of the SSPT phase. On closed manifolds, however, both maps become intrinsically non-unitary and non-invertible when restricted to the original Hilbert space. We demonstrate this non-invertibility via ground-state degeneracy matching (in two copies of the Xu-Moore/Ising-plaquette model), analysis of symmetry-twist sectors mapping, and the fusion algebra of the duality operator. Enlarging the Hilbert space to include twisted sectors allows the subsystem KW map to be formulated as a projective unitary preserving quantum transition probabilities, consistent with generalized Wigner-theorem-based constructions. We also show that the KT map faithfully transmits the algebraic content of bulk and edge invariants diagnosing strong SSPT order: although strictly local SSPT repair operators map to highly nonlocal objects in the dual SSSB phase, the essential commutation algebra and the bulk-edge correspondence remain intact.

The following paper presents a holistic approach to the processing of entangled links within entanglement based quantum key distribution protocols, whose security relies on the Bell inequality. We investigate the interactions, and the collective impact, of the whole processing chain on the final secure key rate. This includes the quantum mechanical preprocessing in the form of entanglement distillation, processing of the entangled states via measurements and the necessary classical postprocessing based on the measurement results. Our investigations are based on the principle idea of the Eckert 1991 protocol and utilize the secret key capacity introduced by Devetak and Winter in 2005. Our results include a proof on what measurement bases need to be chosen to achieve this capacity for the case of Werner states. It also presents a new processing strategy and compares it with the most common one that can be found within the literature. Furthermore, it answers the question on how much entanglement distillation is optimal. By doing so we propose a unified formalism, describing the whole processing chain, that can be used to make quantitative statements on the relation between the quality and quantity of entangled but noisy quantum states used for generating secure keys.

Here we concerned with quantum key distribution - a way to establish common cryptographic key between several parties. The work proposes a combination between quantum key distribution and systematic polar coding (an error correction algorithm) frameworks - quantum key distribution based on systematic polar coding. This results in obtaining key rates greater than standard quantum key distribution (BB84) and its efficient version (eBB84) when finite-size regime and lower-error-rate quantum channel are considered.

We propose an end-to-end quantum algorithm to simulate rapidly distorted turbulence via linear combination of Hamiltonian (LCHS). The algorithm comprises three primary stages: the efficient preparation of an initial turbulent state with a prescribed energy spectrum, its subsequent time evolution via LCHS, and the direct measurement of key turbulence statistics. Our analysis indicates that the algorithm can offer a practical quantum speedup over the classical simulation methods for a sufficiently large computational grid. We evaluate the quantum resource requirements for simulating a minimal instance of non-trivial turbulence with classical validation. The numerical results show excellent agreement with ground-truth solutions, capturing both the qualitative evolution of turbulent fields and the quantitative behavior of statistics, including the Reynolds stresses and the fluctuating velocity spectrum. Despite its linearity, rapidly distorted turbulence captures essential turbulence mechanisms and may inform the development of quantum algorithms for the Navier-Stokes equations. Our work establishes a foundation for addressing more complex turbulent phenomena on future fault-tolerant quantum computers.

Blocks composed of {CNOT, Rz} are ubiquitous in modern quantum applications, notably in circuits such as QAOA ansatzes and quantum adders. After compilation, many of them exhibit large CNOT counts or depths, which lowers fidelity. Therefore, we introduce HOPPS: a SAT-based hardware-aware optimal phase polynomial synthesis algorithm that could generate {CNOT, Rz} blocks with CNOT count or depth optimality. Sometime {CNOT, Rz} blocks are large, such as in QAOA ansatzes, HOPPS's pursuit of optimality limits its scalability. To address this issue, we introduce an iterative blockwise optimization strategy: large circuits are partitioned into smaller blocks, each block is optimally refined, and the process is repeated for several iterations. Empirical results show that HOPPS is more efficient comparing with existing near optimal synthesis tools. Used as a peephole optimizer, HOPPS reduces the CNOT count by up to 50.0% and the CNOT depth by up to 57.1% under OLSQ. For large QAOA circuit, after mapping by Qiskit, circuit can be reduced CNOT count and depth by up to 44.4% and 42.4% by our iterative blockwise optimization. Index Terms-Phase Polynomial, Quantum Circuit Synthesis, Quantum Circuit Optimization.

We investigate the ground-state Hanle effect in alkali-metal vapor irradiating by a resonant elliptically polarized light wave. The magneto-optical resonances are observed as a change in the ellipticity parameter of the light wave polarization when scanning the transverse magnetic field near zero. We use a miniature ($\approx\,$$0.125$ cm$^3$) glass cesium vapor cell heated to a relatively low temperature of $\approx\,$$85^\circ$C. Under the current experimental conditions, the sensitivity of magnetic field measurements is limited by a technical noise, reaching $180$ fT/$\surd$Hz in a $200$ Hz bandwidth. The ultimate photon-shot-noise-limited sensitivity of the method is estimated to be $\approx\,$$5$ fT/$\surd$Hz. The proposed scheme is promising for the development of a zero-field atomic magnetometer with reduced heat dissipation of the sensor head and relaxed requirements for magnetic shielding compared to counterparts operating in the spin-exchange relaxation-free regime. These features are of particular value for biomedical applications.

We propose a complete quantum-classical hybrid branch-and-bound algorithm (QCBB) to solve binary linear programs with equality constraints. That includes bound calculation, convergence metrics and optimality guarantee to the quantum optimization based algorithm, which makes our method directly comparable to classical methods. Key aspects of the proposed algorithm are (i) encapsulation of the quantum optimization method, (ii) utilization of noisy samples for problem reduction, (iii) classical approximation based bound calculation, (iv) branch and bound traits like gap-based stopping criterion and monotonic increase in solution quality, (v) integrated composition of many different solutions that can be improved individually. We show numerical results on set partitioning problem instances and provide many details about the characteristics of the different steps of the algorithm.

This work establishes a new probabilistic bound on the number of elements to generate finite nilpotent groups. Let $\varphi_k(G)$ denote the probability that $k$ random elements generate a finite nilpotent group $G$. For any $0 < \epsilon < 1$, we prove that $\varphi_k(G) \ge 1 - \epsilon$ if $k \ge \operatorname{rank}(G) + \lceil \log_2(2/\epsilon) \rceil$ (a bound based on the group rank) or if $k \ge \operatorname{len}(G) + \lceil \log_2(1/\epsilon) \rceil$ (a bound based on the group chain length). Moreover, these bounds are shown to be nearly tight. Both bounds sharpen the previously known requirement of $k \ge \lceil \log_2 |G| + \log_2(1/\epsilon) \rceil + 2$. Our results provide a foundational tool for analyzing probabilistic algorithms, enabling a better estimation of the iteration count for the finite Abelian hidden subgroup problem (AHSP) standard quantum algorithm and a reduction in the circuit repetitions required by Regev's factoring algorithm.

We explicitly show that the quantum teleportation protocol can be employed to completely reconstruct arbitrary two- and three-qubit density matrices. We also extend the present analysis to n-qubit density matrices. The only quantum resources needed to implement the teleportation-based quantum state tomography protocol are the ability to make Bell measurements and the ability to prepare a few different single qubit states to be teleported from Alice to Bob.

Fractional calculus has become an essential framework in geophysics, optics, and biological systems to capture long-range correlations and anomalous transport. In this article, we extend this framework to explore a particle in a periodic potential, where the Schrodinger equation is extended to its fractional form. This allows us to study how the Levy index $q$ governs the formation and inversion of energy bands, offering a pathway to engineer new physical behaviors by tuning $q$ in periodic quantum systems. We solve the fractional Schrodinger equation (FSE) for periodic rectangular potentials of varying height $V_0$, barrier thickness $L$, and well width $W$ using an imaginary-time evolution algorithm, supplemented by Gaussian process regression. This analysis reveals a qualitative shift in the system's band structure at $q = 2$, separating into distinct regimes of dispersion for $q > 2$ and $q < 2$. For $q > 2$, the energy bands invert as symmetric minima emerge within the first Brillouin zone and shift from $k = 0$ toward $k=\pm \pi/a$ with increasing $q$. These degenerate minima define a Bloch-momentum qubit, suggesting an analog to valley degrees of freedom in valleytronics. The $q$ at which inversion completes scales as $q \propto V_0^{-0.28\pm0.05}$, $q \propto L^{-0.35\pm0.08}$, and $q \propto W^{-0.49\pm0.06}$ when varying parameters individually, indicating a tunable sensitivity to potential geometry. In contrast, for $q < 2$, the ground band hardens around $k = 0$, with a dispersion following $C|k|^q+E_0$ near $k = 0$. This suggests an effective mass of 0 for $1<q<2$ at the band's lowest energy state. These results demonstrate that the Levy index serves as a tunable degree of freedom in quantum periodic systems, capable of driving band inversion, modulating the band gap, and reshaping carrier dynamics through effective-mass control.

Accurately predicting turbulent flows remains a central challenge in fluid dynamics due to their high dimensionality and intrinsic nonlinearity. Recent developments in quantum algorithms and machine learning offer new opportunities for overcoming the computational barriers inherent in turbulence modeling. Here we present a new hybrid quantum-classical framework that enables faster-than-real-time turbulence prediction by integrating machine learning, quantum computation, and fluid dynamics modeling, in particular, the reduced-order modeling. The novel framework combines quantum proper orthogonal decomposition (QPOD) with a quantum-enhanced deep kernel learning (QDKL) approach. QPOD employs quantum circuits to perform efficient eigenvalue decomposition for low-rank flow reconstruction, while QDKL exploits quantum entanglement and nonlinear mappings to enhance kernel expressivity and dynamic prediction accuracy. The new method is demonstrated on three benchmark turbulent flows, our architecture achieves significantly improved predictive accuracy at reduced model ranks, with training speeds up to 10 times faster and parameter counts reduced by a factor of 1/N compared to classical counterparts, where N is the input dimensionality. Although constrained by current noisy intermediate-scale quantum (NISQ) hardware, our results demonstrate the potential of quantum machine learning to transform turbulence simulation and lay a solid foundation for scalable, real-time quantum fluid modeling in future quantum computers.

We study neural-network approximation of density functionals in a Banach-space setting. Since the exact continuum functionals are discontinuous in the natural density topology, we apply $p$-Moreau-Yosida regularization. We construct finite-rank ReLU networks that preserve convexity and nonnegativity, lie below the regularized functional, and approximate it uniformly on compact sets. For energies obtained by minimization over compact density sets, we account exactly for the energy shift caused by regularization and bound the remaining error by the localization on these compact sets and network approximation errors. We apply this framework to canonical and grand-canonical density-functional theory at fixed particle number and fixed mean particle number, respectively. We obtain uniform energy convergence on norm-compact classes of external potentials, including molecular Coulomb potentials. We illustrate our results through numerical experiments on a simple model system.

A computational model of adiabatic evolutionary quantum system (or AEQS, pronounced "eeh-ks") was introduced in [Yamakami,2022] as a sort of quantum annealing and its underlying input-driven Hamiltonians are generated quantum-algorithmically by various forms of quantum automata families (including 1qqaf's). We study an efficient way to accomplish certain machine learning tasks by training these AEQSs quantumly. When AEQSs are controlled by 1qqaf's, it suffices in essence to find an optimal 1qqaf that approximately solves a target relational problem. For this purpose, we develop a basic idea of approximately utilizing well-known quantum algorithms for quantum counting, quantum amplitude estimation, and quantum approximation. We then provide a rough estimation of the efficiency of our quantum learning algorithms for AEQSs.

The intriguing physical phenomena associated with exceptional points have established non-Hermitian physics as a frontier of modern research. Recent investigations have extended non-Hermitian physics into the fully quantum domain. However, existing studies predominantly concentrate on discrete-variable quantum systems, while non-Hermitian quantum effects in continuous-variable encoded systems remain largely unexplored. In this work, we investigate the exceptional structure for a driven-dissipative Kerr-cat qubit, realized with a Kerr nonlinear resonator. We find that the dissipation leads to a bidirectional jump between the two basis states of the cat qubit, which is in distinct contrast with the unidirectional jump associated with normal two-level systems. The competition between this jump and a single-photon drive gives arise to the emergence of third-order Liouvillian exceptional points (LEP3s), each corresponds to a crossing point of two lines of LEP2s. We further show that the LEP3 can exhibit the topological character of the Hamiltonian EP3s, which cannot be realized with a single qubit. Our work opens the possibility of realizing non-Hermitian phenomena with continuous-variable quantum systems.

We theoretically investigate a quantum battery architecture where two identical two-level atoms are charged by a cavity-magnomechanical system, which includes a microwave cavity, a magnon mode hosted in a YIG sphere, and phonon mode due to the deformation of the YIG sphere. The charging process relies on coherent energy exchange, where the atoms couple to the cavity, which in turn, it interacts with the magnon mode via a beam-splitter mechanism. By deriving the system Hamiltonian under the rotating-wave approximation and employing a Lindblad master equation to rigorously model dissipation, we analyze the complete dynamical evolution of the battery. Our study demonstrates that strong, resonant light-matter interactions are crucial for enhancing the key performance metrics: charging efficiency, stored energy, and ergotropy (extractable work). We systematically investigate the deleterious effects of detuning and decoherence, and critically, we uncover a non-trivial interplay between the system's coupling strengths. This reveals optimal operating regimes where constructive interference maximizes performance, while excessive coupling in specific channels can degrade it. Ultimately, our findings provide a quantitative framework for engineering high-efficiency quantum batteries in hybrid magnonic platforms, offering a design roadmap for future experimental realizations.

The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational quantum algorithm introduced to tackle classically intractable combinatorial optimization problems. This tutorial offers a comprehensive, first-principles introduction to QAOA and its properties, focusing on its application to Quadratic and Polynomial Unconstrained Binary Optimization (QUBO and PUBO) problems. The tutorial begins by outlining variational quantum circuits and QUBO problems, focusing on their key properties and the encoding of problem constraints through quadratic penalty terms. Next, it explores the QAOA in detail, covering its Hamiltonian formulation, gate decomposition, and example applications, along with their implementation and performance results. This is followed by an analysis of the algorithm's energy landscape, where proofs are provided for its symmetry and periodicity, and where a resulting parameter space reduction is proposed. Finally, the tutorial extends these concepts to PUBO problems by generalizing the results to higher-order Hamiltonians and discussing the associated symmetries and circuit construction.

Until recently, attosecond optical spectroscopy and quantum optics evolved along non-overlapping directions. In attosecond science, attosecond pulses have been regarded as classical waves, applied to probe electron dynamics on their natural time scale. Here, we transfer fundamental concepts of quantum optics into attosecond physics, enabling control of both the properties of the XUV attosecond pulses and the quantum fluctuations of matter on attosecond time scales. By combining bright squeezed vacuum (BSV) with a strong laser field to drive high-harmonic generation, we transfer the quantum properties of the BSV onto the resulting XUV attosecond pulses. Applying advanced attosecond interferometry, we reconstruct the quantum state of the XUV high harmonics and their associated attosecond pulses with attosecond precision. Finally, we resolve the squeezing of the electron's wavepacket during one of the most fundamental strong-field phenomena - field induced tunneling. The ability to measure and control quantum correlations in both electrons and XUV attosecond pulses establishes a foundation for attosecond quantum electrodynamics, manipulating the quantum state of electrons and photons with sub-cycle precision.

Controllable nonlinear quantum interactions are a much sought after target for modern quantum technologies. They are typically difficult and costly to engineer for bespoke purposes. However controllable nonlinearities may have always been in reach via the natural and fundamental forces between quantum particles. The Coulomb interaction between charged particles is the simplest example. We show that after eliminating the harmonic part of the Coulomb force by an auxiliary linear force, the remaining reciprocal nonlinear part results in a directly observable non-reciprocal nonlinear effect: increase of the signal-to-noise ratio (SNR) of the coherent displacement of one particle, driven by the position noise, or uncertainty in quantum regime, in another particle. This essential evidence of nonlinear forces is present across large ranges of trap frequency and mass scales, as well as visible in both stochastic and quantum regimes.

Characterizing the nonlocal nature of quantum states is a central challenge in the practical application of large-scale quantum computation and simulation. Quantum mutual information (QMI), a fundamental nonlocal measure, plays a key role in quantifying entanglement and has become increasingly important in studying nonequilibrium quantum many-body phenomena, such as many-body localization and thermalization. However, experimental measurement of QMI remains extremely difficult, particularly for nonequilibrium states, which are more complex than ground states. In this Letter, we employ a multilayer perceptron (MLP) to establish a universal mapping between the QMI and local correlations only up to second order for nonequilibrium states generated by quenches in a one-dimensional disordered XXZ model. Our approach provides a practical method for experimentally extracting QMI, readily applicable in platforms such as superconducting qubits. Moreover, this work will establishes a general framework for reconstructing other nonlocal observables, including Fisher information and out-of-time-ordered correlators.

We present a general algorithm, based on machine learning, which can create optimal unitary operators to implement quantum teleportation in any system with well-defined set of measurements in a relevant entangled basis. We illustrate it with a collective spin model and demonstrate its versatility by applying it to teloportation of single and multiple qubit states, coherent and Dicke states, and for systems with prior distributions and unequal dimensions. All cases display significant regimes of quantum advantage over corresponding classical schemes with no entanglement. The algorithm offers the flexibility to choose a balance between target fidelity and computational cost.

Postulating a minimal discrete quantum of action $S=\hbar$ and a simple rule for the growth of an oriented graph, we construct a strict hierarchy of temporal layers $C N$ with discrete periods $\tau_N=N\hbar/E$. Each layer is specified by its configuration space, symplectic structure, update rule, and emergent symmetry. At $C1$ the state is represented by a single oriented edge with $U(1)$ phase $e^{i E t/\hbar}$. The transition $C1 \to C2$ splits the edge into two independent flows, which yields canonical pairs $(x_a,p_a)$, local $U(1)$ invariance, and an effective $(2{+}1)$ metric with signature $(+--)$. The closure $C2 \to C3$ produces $SU(3)$ connections and an Einstein-Yang-Mills type action. We show that these structures follow from discrete-action principles, and that stochastic graph growth naturally provides mechanisms for decoherence and spontaneous symmetry breaking.

In this paper, we propose a novel approach for optimizing the linear layer used in symmetric cryptography. It is observed that these matrices often have circulant structure. The basic idea of this work is to utilize the property to construct a sequence of transformation matrices, which allows subsequent heuristic algorithms to find more efficient implementations. Our results outperform previous works for various linear layers of block ciphers. For Whirlwind M0 , we obtain two implementations with 159 XOR counts (8% better than Yuan et al. at FSE 2025) and depth 17 (39% better than Shi et al. at AsiaCrypt 2024) respectively. For AES MixColumn, our automated method produces a quantum circuit with depth 10, which nearly matches the manually optimized state-of-the-art result by Zhang et al. at IEEE TC 2024, only with 2 extra CNOTs.

The paper considers the propagation of Laguerre-Gaussian beams in a turbulent gas medium. As demonstrated by numerical modelling and the decomposition of Laguerre-Gaussian modes according to the basis of orthogonal Zernike polynomials, disparities in the stability of Laguerre-Gaussian modes with differing radial and azimuthal numbers are evident. The demonstration is made of the minimization of the distortion of the transverse beam profile with an increase in the radial number.

Bound states in the continuum (BICs) are spatially localized modes embedded in the spectrum of extended states, typically stabilized by symmetry or interference. While extensively studied in single-particle and linear systems, the many-body regime of BICs remains largely unexplored. Here, we demonstrate that giant atoms, quantum emitters coupled nonlocally to structured waveguides, can host robust doublon BICs, i.e., two-photon bound states stabilized by destructive interference and interactions. We first analyze a driven two-photon emission process and show how doublon BICs arise and mediate decoherence-free interaction between distant atoms. We then demonstrate that these many-body BICs also emerge under natural, undriven dynamics via a virtual two-photon emission process in three-level giant atoms. Our results reveal an interference-based mechanism for stabilizing many-body localization in open quantum systems, with potential applications in quantum simulation, non-ergodic dynamics, and protected quantum information processing.

The deterministic control of light-matter interactions at the level of single particles and on subwavelength scales is central to quantum optics and hybrid integrated quantum technologies. However, combining cold atom research with nanophotonic devices in a fully controllable platform remains a major experimental challenge. Here, we demonstrate the deterministic coupling of an ultracold atomic lattice to light propagating in suspended on-chip photonic circuits. These capabilities open avenues to address scalability challenges in neutral-atom quantum computers and simulators, enabling fast optical readout, efficient and subwavelength non-diffracting interaction zones, and genuine compatibility with integrated solid-state photon sources, detectors, and stop-band modulators. Beyond controllable quantum matter, the platform also enables in-situ imaging of evanescent fields of light and nanoscale structures, including prospects for three-dimensional scanning microscopy with non-invasive single-atom probes for quantum sensing applications.

The integer factorization problem (IFP) underpins the security of RSA, yet becomes efficiently solvable on a quantum computer through Shor's algorithm. Regev's recent high-dimensional variant reduces the circuit size through lattice-based post-processing, but introduces substantial space overhead and lacks practical implementations. Here, we propose a qubit reuse method by intermediate-uncomputation that significantly reduces the space complexity of Regev's algorithm, inspired by reversible computing. Our basic strategy lowers the cost from \( O(n^{3/2}) \) to \( O(n^{5/4}) \), and refined strategies achieve \( O(n \log n) \)which is a space lower bound within this model. Simulations demonstrate the resulting time-space trade-offs and resource scaling. Moreover, we construct and compile quantum circuits that factor \( N = 35 \), verifying the effectiveness of our method through noisy simulations. A more simplified experimental circuit for Regev's algorithm is executed on a superconducting quantum computer, with lattice-based post-processing successfully retrieving the factors. These results advance the practical feasibility of Regev-style quantum factoring and provide guidance for future theoretical and experimental developments.

By employing supersymmetric quantum mechanics, we present a general algorithm to construct supersymmetric partner potentials and hence derive exact stationary solutions of the inhomogeneous nonlinear Schrödinger equation (INLSE). This is possible due to the connection between the INLSE and the nonlinear Schrödinger equation (NLSE), which can be established from a treatment based on Lie point symmetries and is related with Schrödinger equation, under certain conditions. As an illustrative example, we construct exact solutions for the INLSE through a Pösch-Teller potential with a single bound state.

The linear and phase insensitive absorption of a single quanta via coherent interactions with a saturable system, even a single ground state qubit, is sufficient to deterministically generate quantum non-Gaussian states in an oscillator, even stimulated merely by increasing thermal oscillator energy. However, the resultant states only approach Fock states and therefore do not exhibit quantum coherence. Here we overcome this limitation using a minimal step: a nonlinear phase-insensitive absorption process added to the linear one. The coherent addition of such individually passive processes allows coherence to emerge and increase in phase space without an external drive and with minimal interaction requirements. The coherence of quantum non-Gaussian states emerges because the linear and nonlinear absorption processes are not mutually passive. In the simplest case rotationally symmetric Wigner functions of the oscillator Fock states convert their many negative regions to an extremely complex asymmetric structure in sharp contrast to the rotational symmetry of those obtained by the individual interactions. We extend this case to include an unsaturable absorber (oscillator) and analyse switching between linear and nonlinear absorptions, suitable for broad classes of experiments.