Papers

We develop a novel framework to engineer persistent oscillatory modes in Markovian open quantum systems governed by a time-independent Lindblad master equation. We show that oscillatory modes can be created when the Hamiltonian and jump operator can be expressed in the same block-diagonal form. A key feature of the framework is that the dissipator of the Lindblad master equation are generally non-zero. We identify the weak and strong conditions, where the onset of the oscillatory modes is dependent and independent of the parameters of the system, respectively. Our method extends beyond the typical decoherence-free subspace approach, in which the dissipator is zero. We demonstrate the applicability of this framework using various models, showing how carefully tailored system-environment interactions can produce sustained coherent oscillations.

Quantum networks require interfaces translating memory photons to telecom wavelengths while controlling spatial modes; tasks performed by separate components today. We present a programmable alternative: a structured pump writes a virtual Bragg grating enabling simultaneous spatio-spectral conversion and real-time controlling of emission. Using a LiNbO$_3$ whispering-gallery resonator, we demonstrate 93% spatial coupling and bidirectional conversion between 736\,nm and 1347\,nm. This reconfigurable interface eliminates cascaded losses and hardware modifications.

We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is based on the cluster expansion method. We obtain fully polynomial-time approximation schemes for both the probability of intersection and the dimension of intersection for commuting projectors. For general projectors, we provide two algorithms: a fully polynomial-time approximation scheme under a global inclusion-exclusion stability condition, and an efficient affine approximation under a spectral gap assumption. As corollaries of our results, we obtain efficient algorithms for approximating the number of satisfying assignments of conjunctive normal form formulae and the dimension of satisfying subspaces of quantum satisfiability formulae.

Cosmological perturbations generated during inflation exhibit striking quantum features, including entanglement and high circuit complexity. Yet their observational signatures remain effectively indistinguishable from classical stochastic variables. We quantify this tension by showing that quantum inflationary perturbations are continuous variable stabilizer states with vanishing quantum magic, a necessary resource for universal quantum computation as measured by Wigner negativity. Consequently, despite their quantum origins and description, these states can be efficiently simulated using classical algorithms. We further show that the Wigner negativity arising from primordial non-Gaussianity is suppressed not only by the non-linearity parameter $f_{NL}$, but also by the exponential squeezing of the perturbations. Viewing the early universe as a "high complexity, low magic" regime provides another perspective of what it means for the origin of structure in the universe to be "quantum."

This article (I) considers the known optimal control model of a quantum information transfer along a spin chain with controlled external parabolic magnetic field, with an arbitrary length. The article adds certain lower and upper pointwise constraints on controls, adds the problem of keeping the signal at the last spin, considers various classes of controls. For these problems under piecewise continuous controls, the projection-type linearized Pontryagin maximum principle, gradient projection method's constructions in its one- and two- and three-step forms were adapted by analogy with [Morzhin O.V., Pechen A.N. J. Phys. A: Math. Theor., 2025]. Moreover, an example with a genetic algorithm's successful use under a special class of controls is given.

We analyze entanglement generated by the Schwinger effect using a mode-by-mode formalism for scalar and spinor QED in constant backgrounds. Starting from thermal initial states, we derive compact, closed-form results for bipartite entanglement between particle-antiparticle partners in terms of the Bogoliubov coefficients. For bosons, thermal fluctuations enhance production but suppress quantum correlations: the logarithmic negativity is nonzero only below a (mode-dependent) critical temperature $T_c$. At fixed $T$, entanglement appears only above a critical field $E_{\text{entang}}$. For fermions, we observe a qualitatively different pattern: the fermionic logarithmic negativity is non-vanishing at finite temperature, and is monotonically suppressed by thermal noise. As a function of the electric field, it is non-monotonic, featuring a temperature-independent optimal field strength $E_*$ and decreasing on both sides of the maximum. We give quantitative estimates for analog experiments, where our entanglement criteria convert directly into concrete temperature and electric field constraints. These findings identify realistic regimes where the quantum character of Schwinger physics may be tested in the laboratory.

Quantum theory departs from classical probabilistic theories in foundational ways. These departures–termed quantumness here–power quantum information and computation. This thesis charts the role of discrete structures in assessing quantumness, synthesizing elements of my postdoctoral research through this lens. After an introduction to the necessary background concepts, I present my work under three broad categories. First, I present work on contextuality that extensively relies on (undirected) graphs and hypergraphs as the discrete structures of interest; more specifically, it relies on invariants associated with them. This work includes Kochen-Specker (KS) contextuality and its operationalization to generalized contextuality, expressed via (hyper)graph-theoretic frameworks. I also present work on KS-contextuality in multiqubit systems and an application of generalized contextuality to a one-shot communication task, both of which rely on hypergraphs. Second, I present work on causality, where the discrete structures of interest are directed graphs. This includes work on indefinite causal order, specifically its connections to the gap between local operations and classical communication (LOCC) and separable operations (SEP), and a device-independent notion of nonclassicality–termed antinomicity–that generalizes Bell nonlocality without global causal assumptions. Finally, I present work on the incompatibility of quantum measurements, its connection to Bell nonlocality, and its role in discriminating between quantum and almost quantum correlations in the single-system setting. The discrete structures of interest here are hypergraphs that model joint measurability relations between quantum measurements. I conclude with a summary and an overview of work that is not covered in this thesis.

We introduce a framework for scalable and broadband free-space phase-matched four-wave mixing in ring resonators. This method for four-wave mixing reduces the complexity of coupling an emitter to a quantum network by combining the spatial and spectral interfaces between them into one nonlinear optical process. The device is compliant with current heterogeneous integration capabilities and has a bandwidth of 165 nm for efficient spatio-spectral conversion. We outline a fabrication-ready diamond-on-insulator pathway towards modular unit cells that natively bridge visible color centers to the infrared spectrum for scalable quantum networks. We also present and analyze an end-to-end framework for considering single-photon coupling efficiency from a color center to a quantum network. This framework represents a step forwards in analyzing and reducing system-scale losses in a spin-photon interface.

Speeding up the relaxation dynamics of many-body quantum systems is important in a variety of contexts, including quantum computation and state preparation. We demonstrate that such acceleration can be universally achieved via transient stochastic resetting. This means that during an initial time interval of finite duration, the dynamics is interrupted by resets that take the system to a designated state at randomly selected times. We illustrate this idea for few-body open systems and also for a challenging many-body case, where a first-order phase transition leads to a divergence of relaxation time. In all scenarios, a significant and sometimes even exponential acceleration in reaching the stationary state is observed, similar to the so-called Mpemba effect. The universal nature of this speedup lies in the fact that the design of the resetting protocol only requires knowledge of a few macroscopic properties of the target state, such as the order parameter of the phase transition, while it does not necessitate any fine-tuned manipulation of the initial state.

We develop a bottom-up, statistics-first framework in which the full probabilistic content of an operational theory is encoded in its matrix of conditional outcome probabilities of events (COPE). Within this setting, five model classes (preGPTs, GPTs, quasiprobabilistic, ontological, and noncontextual ontological) are unified as constrained factorizations of the COPE matrix. We identify equirank factorizations as the structural core of GPTs and noncontextual ontological models and establish their relation to tomographic completeness. This yields a simple, model-agnostic criterion for noncontextuality: an operational theory admits a noncontextual ontological model if and only if its COPE matrix admits an equirank nonnegative matrix factorization (ENMF). Failure of the equirank condition in all ontological models therefore establishes contextuality. We operationalize rank separation via two complementary methods provided by the linear-algebraic framework. First, we use ENMF to interpret noncontextual ontological models as nested polytopes. This allows us to establish that the boxworld operational theory is ontologically contextual. Second, we apply techniques from discrete mathematics to derive a lower bound on the ontological dimensionality of COPE matrices exhibiting sparsity patterns, and use this bound to establish a new proof that a discrete version of qubit theory exhibits ontological contextuality. By reframing contextuality as a problem in matrix analysis, our work provides a unified structure for its systematic study and opens new avenues for exploring nonclassical resources.

Quantum resource theories provide a unified framework for characterizing useful quantum phenomena subject to physical constraints, but are notoriously hard to assess in experimental systems. In this letter, we introduce a unified protocol for quantifying the resource-generating power of arbitrary quantum evolutions applicable to multiple resource theories. It is based on deep thermalization, which has recently gained attention for its role in the emergence of quantum state designs from partial projective measurements. Central to our approach is the use of projected ensembles, recently employed to probe deep thermalization, together with new twirling identities that allow us to directly infer the resource-generating powers of the underlying dynamics. These identities further reveal how resources build up and thermalize in generic quantum circuits. Finally, we show that quantum resources themselves undergo deep thermalization at the subsystem level, offering a complementary and another experimentally accessible route to infer the resource-generating powers. Our work connects deep thermalization to resource quantification, offering a new perspective on the essential role of various resources in generating state designs and on efficient estimation of quantum resources in experiment.

Hall viscosity is a quantized nondissipative stress response of a fractional quantum Hall (FQH) fluid to adiabatic geometric deformations. Despite strong theoretical interest, its experimental observation in the FQH state has remained elusive, making it a demanding target for realization on current IBM quantum hardware. In this letter, we employ a quasi-one-dimensional model of an FQH state coupled to a background metric to probe the geometric response under a metric quench. We design and implement a quantum-circuit protocol that realizes a Hilbert-space-truncated version of the model and extracts the Hall viscosity from the geometric response encoded in the wave-function dynamics on the IBM quantum hardware. While the truncation prevents us from accessing the fully quantized value of Hall viscosity, the hardware data closely track analytical and numerical predictions within this regime.

The Kondo effect, a hallmark of many-body physics, emerges from the antiferromagnetic coupling between localized spins and conduction fermions, leading to a correlated many-body singlet state. Here we propose to use the mixed-dimensional (mixD) bilayer Hubbard geometry as a platform to study Kondo lattice physics with current ultracold atom experiments. At experimentally feasible temperatures, we predict that key features of the Kondo effect can be observed, including formation of the Kondo cloud around a single impurity and the competition of singlet formation with Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions for multiple impurities, summarized in the Doniach phase diagram. Moreover, we show that the mixD platform provides a natural bridge between the Doniach phase diagram of the Kondo lattice model, relevant to heavy-fermion materials, and the phase diagram of cuprate superconductors as described by a single-layer Zhang-Rice type $t$-$J$ model: It is possible to continuously tune between the two regimes by changing the interlayer Kondo coupling. Our findings demonstrate that the direct connection between high-temperature superconductivity and heavy-fermion physics can be experimentally studied using currently available quantum simulation platforms.

We study the photon emission by charged spinless particles with phase vortices and an orbital angular momentum (OAM) projection in longitudinal electric and magnetic fields within the scalar QED. A realistic wave packet of an electron or ion accelerated by a radio-frequency wave locally feels a constant and spatially homogeneous field, which allows us to develop an effective model for losing the angular momentum of the vortex particle due to photon emission. For the fields typical for accelerator facilities, we find that an effective lifetime of the vortex state greatly exceeds the acceleration time. This proves that the acceleration of vortex electrons, ions, muons, and so forth to relativistic energies is possible in conventional linacs, as well as in the wake-field accelerators with higher field gradients, the OAM losses due to the photon emission are mostly negligible, and that the vortex quantum state is highly robust against these losses.

We analyze two simple models derived from a quantum-mechanical particle on an elliptical path. The first Hamiltonian operator is non-Hermitian but equivalent to an Hermitian operator. It exhibits the same two-fold degeneracy as the particle on a circular path. More precisely, the spectrum is $E_{n}=n^{2}E_{1},\ n=0,\pm 1,\pm 2,\ldots $, $E_{1}>0$. The second Hamiltonian operator is Hermitian and does not exhibit such degeneracy. In this case the nth excited energy level splits at the nth order of perturbation theory. Both models can be described in terms of symmetry point groups with one-dimensional irreducible representations but the non-Hermitian example exhibits an additional symmetry that explains the two-fold degeneracy. The Schrödinger equation for the first example is exactly solvable.

We give an efficient 0.8395-approximation algorithm for the EPR Hamiltonian. Our improvement comes from a new nonlinear monogamy-of-entanglement bound on star graphs and a refined parameterization of a shallow quantum circuit from previous works. We also prove limitations showing that current methods cannot achieve substantially better approximation ratios, indicating that further progress will require fundamentally new techniques.

Non-Hermitian Hamiltonians enrich quantum physics by extending conventional phase diagrams, enabling novel topological phenomena, and realizing exceptional points with potential applications in quantum sensing. Here, we present an experimental photonic platform capable of simulating a non-unitary quantum walk generated by a peculiar type of non-Hermitian Hamiltonian, largely unexplored in the literature. The novelty of this platform lies in its direct access to the reciprocal space, which enables us to scan the quasi-momentum across the entire Brillouin zone and thus achieve a precise tomographic reconstruction of the underlying non-Hermitian Hamiltonian, indicated by the comparison between theoretical predictions and experimental measurements. From the inferred Hamiltonian, it is possible to retrieve complex-valued band structures, resolve exceptional points in momentum space, and detect the associated parity-time symmetry breaking through eigenvector coalescence. Our results, presented entirely in quasi-momentum space, represent a substantial shift in perspective in the study of non-Hermitian phenomena.

Quantum error mitigation (QEM) is typically viewed as a suite of practical techniques for today's noisy intermediate-scale quantum devices, with limited relevance once fault-tolerant quantum computers become available. In this work, we challenge this conventional wisdom by showing that QEM can continue to provide substantial benefits in the era of quantum error correction (QEC), and in an even more efficient manner than it does on current devices. We introduce a framework for logical-level QEM that leverages soft information naturally produced by QEC decoders, requiring no additional data, hardware modifications, or runtime overhead beyond what QEC protocols already provide. Within this framework, we develop and analyze three logical-level QEM techniques: post-selection and runtime abort policies, probabilistic error cancellation, and zero-noise extrapolation. Our techniques reduce logical error rates by more than 100x while discarding fewer than 0.1% of shots; they also provide in situ characterization of logical channels for QEM protocols. As a proof of principle, we benchmark our approach using a surface-code architecture and two state-of-the-art decoders based on tensor-network contraction and minimum-weight perfect matching. We evaluate logical-level QEM on random Clifford circuits and molecular simulation algorithms and find that, compared to previous approaches relying on QEC only or QEC combined with QEM, we can achieve up to 87.4% spacetime overhead savings. Our results demonstrate that logical-level QEM with QEC decoder soft information can reliably improve logical performance, underscoring the efficiency and usefulness of QEM techniques for fault-tolerant quantum computers.

Random number generation is fundamental for many modern applications including cryptography, simulations and machine learning. Traditional pseudo-random numbers may offer statistical unpredictability, but are ultimately deterministic. On the other hand, True Random Number Generation (TRNG) offers true randomness. One way of obtaining such randomness are quantum systems, including quantum computers. As such the use of quantum computers for TRNG has received considerable attention in recent years. However, existing studies almost exclusively consider IBM quantum computers, often stop at using simulations and usually test only a handful of different TRNG quantum circuits. In this paper, we address those issues by presenting a study of TRNG circuits on Odra 5 a real-life quantum computer installed at Wrocław University of Science and Technology. It is also the first study to utilize the IQM superconducting architecture. Since Odra 5 is available on-premises it allows for much more comprehensive study of various TRNG circuits. In particular, we consider 5 types of TRNG circuits with 105 circuit subvariants in total. Each circuit is used to generate 1 million bits. We then perform an analysis of the quality of the obtained random sequences using the NIST SP 800-22 and NIST SP 800-90B test suites. We also provide a comprehensive review of existing literature on quantum computer-based TRNGs.

In this work, we present a practical and efficient framework for verifying entangled states when only a tomographically incomplete measurement setting is available-specifically, when access to observables is severely limited. We show how the experimental estimation of a small number of observables can be directly exploited to construct a large family of entanglement witnesses, enabling the efficient identification of entangled states. Moreover, we introduce an optimization approach, formulated as a semidefinite program, that systematically searches for those witnesses best suited to reveal entanglement under the given measurement constraints. We demonstrate the practicality of the approach in a proof-of-principle experiment with photon-polarization qubits, where entanglement is certified using only a fraction of the full measurement data. These results reveal the maximal usefulness of incomplete measurement settings for entanglement verification in realistic scenarios.

We demonstrate deterministic preparation of arbitrary two-component product states of fermionic $^6$Li atoms in an 8$\times$8 optical tweezer array, achieving motional ground-state fidelities above $98.5\,\%$. Leveraging the large differential magnetic moments for spin-resolution, with parallelized site- and number-resolved control, our approach addresses key challenges for low-entropy quantum state engineering. Combined with high-fidelity spin-, site-, and density-resolved readout within a single $20\,\mathrm{\mu s}$ exposure, and $3\,\mathrm{s}$ experimental cycles, these advances establish a fast, scalable, and programmable architecture for fermionic quantum simulation.

Transformers have gained popularity in machine learning due to their application in the field of natural language processing. They manipulate and process text efficiently, capturing long-range dependencies among data and performing the next word prediction. On the other hand, gate-based quantum computing is based on controlling the register of qubits in the quantum hardware by applying a sequence of gates, a process which can be interpreted as a low level text programming language. We develop a transformer model capable of transpiling quantum circuits from the qasm standard to other sets of gates native suited for a specific target quantum hardware, in our case the set for the trapped-ion quantum computers of IonQ. The feasibility of a translation up to five qubits is demonstrated with a percentage of correctly transpiled target circuits equal or superior to 99.98%. Regardless the depth of the register and the number of gates applied, we prove that the complexity of the transformer model scales, in the worst case scenario, with a polynomial trend by increasing the depth of the register and the length of the circuit, allowing models with a higher number of parameters to be efficiently trained on HPC infrastructures.

We introduce a quantum algorithm for computing the Ollivier Ricci curvature, a discrete analogue of the Ricci curvature defined via optimal transport on graphs and general metric spaces. This curvature has seen applications ranging from signaling fragility in financial networks to serving as basic quantities in combinatorial quantum gravity. For inputs given as a point cloud with pairwise distances, we show that our algorithm can achieve an exponential speedup over the best-known classical methods for two particular classes of problem. Our work is another step toward quantum algorithms for geometrical problems that are capable of delivering practical value while also informing fundamental theory.

Scaling fault tolerant quantum computers, especially cryogenic systems based on the surface code, to millions of qubits is challenging due to poorly-scaling data processing and power consumption overheads. One key hurdle is the design of real-time quantum error correction (QEC) decoders, which demands high data rates for error processing; this is particularly apparent in systems with cryogenic qubits and room temperature (RT) decoders. In response, cryogenic predecoding using lightweight logic has been proposed to handle sparse errors in the cryogenic domain. However, prior work only accounts for a subset of error sources in real-world quantum systems with limited accuracy, often degrading performance below useful levels in practical scenarios. Moreover, prior reliance on SFQ logic precludes detailed architecture-technology co-optimization. To address these limitations, this paper introduces Pinball, a comprehensive design in cryogenic CMOS of a QEC predecoder for the surface code tailored to realistic, circuit-level noise. By accounting for error generation and propagation through QEC circuits, our design achieves higher predecoding accuracy, outperforming logical error rates (LER) of the current state-of-the-art (SOTA) cryogenic predecoder by nearly six orders of magnitude. Remarkably, despite operating under much stricter power and area constraints, Pinball also reduces LER by 32.58x and 5x, respectively, compared to SOTA RT predecoder and RT ensemble configurations. By increasing cryogenic coverage, we also reduce syndrome bandwidth up to 3780.72x. Through co-design with 4 K-characterized 22nm FDSOI technology, we achieve peak power consumption under 0.56 mW. Voltage/frequency scaling and body biasing enable 22.2x lower typical power consumption, yielding up to 67.4x total energy savings. Assuming a 1.5 W 4 K power budget, our predecoder supports up to 2,668 logical qubits at d=21.

We study the problem of certifying local Hamiltonians from real-time access to their dynamics. Given oracle access to $e^{-itH}$ for an unknown $k$-local Hamiltonian $H$ and a fully specified target Hamiltonian $H_0$, the goal is to decide whether $H$ is exactly equal to $H_0$ or differs from $H_0$ by at least $\varepsilon$ in normalized Frobenius norm, while minimizing the total evolution time. We introduce the first intolerant Hamiltonian certification protocol that achieves optimal performance for all constant-locality Hamiltonians. For general $n$-qubit, $k$-local, traceless Hamiltonians, our procedure uses $O(c^k/\varepsilon)$ total evolution time for a universal constant $c$, and succeeds with high probability. In particular, for $O(1)$-local Hamiltonians, the total evolution time becomes $\Theta(1/\varepsilon)$, matching the known $\Omega(1/\varepsilon)$ lower bounds and achieving the gold-standard Heisenberg-limit scaling. Prior certification methods either relied on implementing inverse evolution of $H$, required controlled access to $e^{-itH}$, or achieved near-optimal guarantees only in restricted settings such as the Ising case ($k=2$). In contrast, our algorithm requires neither inverse evolution nor controlled operations: it uses only forward real-time dynamics and achieves optimal intolerant certification for all constant-locality Hamiltonians.

We investigate theoretically the ability of an optical centrifuge - a laser pulse whose linear polarization is rotating at an accelerated rate, to control molecular rotation in the regime when the rigid-rotor approximation breaks down due to coupling between the vibrational and rotational degrees of freedom. Our analysis demonstrates that the centrifuge field enables controlled excitation of high rotational states while maintaining relatively low spread along the vibrational coordinate. We contrast this to the rotational excitation by a linearly polarized Gaussian pulse of equal spectral width and pulse energy which, although comparable to the centrifuge-induced rotation, is unavoidably accompanied by a substantial broadening of the vibrational wavepacket.

We propose a single auxiliary-assisted purification-based framework for quantum error correction, capable of correcting errors that drive a system from its ground-state subspace into excited-state sectors. The protocol consists of a joint time evolution of the system-auxiliary duo under a specially engineered interaction Hamiltonian, followed by a single measurement of the auxiliary in its energy eigenbasis and a subsequent post-selection of one of the measurement outcomes. We show that the resulting purified state always achieves unit fidelity, while the probability of obtaining any energy of the auxiliary other than its ground state energy yields the success rate of the protocol. We demonstrate the power of this proposed method for several low-distance quantum codes, including the three-, four-, and five-qubit codes, and for the one-dimensional isotropic Heisenberg model, subjected to bit-flip, phase-flip, and amplitude-damping noises acting on all qubits. Notably, the protocol expands the class of correctable errors for a given code, particularly in the presence of amplitude-damping noise. We further analyze the impact of replacing the auxiliary qudit with a single auxiliary qubit, and the changes in the performance of the protocol under the realistic scenario where noise remains active during the correction cycle.

The fundamental question of when a static or dynamic system should be deemed intrinsically quantum remains a challenge to address in absolute terms. In this regard, a critical requirement lies in the certification (ideally, in real-time) of the emergence and persistence of genuine quantum features, principally entanglement and quantum superposition. Quantum Non-Demolition Measurements (QNDM) serve as the appropriate instrument for this certification, both from a theoretical and experimental standpoint. In this review paper, we explain, with accessible clarity, how the implementation of QNDM can be directly linked to a necessary and sufficient condition for the presence of genuinely quantum features in the system's state monitored over time in finite-dimensional systems, establishing a conceptual parallel with Leggett-Garg inequalities. Using concrete examples that detail the detection of negative terms in the quasi-probability density function resulting from QNDM, we introduce the core concepts for quantumness certification. As specific examples, we discuss an application where the quantum-to-classical transition due to the interaction with an environment can be tracked by QNDM. Moreover, we argue about the robustness of QNDM protocols in the presence of noise sources and their advantages with respect to standard Leggett-Garg inequalities defined by two-time correlators.

The necessity of random numbers for various tasks, from simulation to cryptography, is crucial and immense. Here we demonstrate CV-QRNG using the CV payload of the SPOQC mission. The homodyne setup for QRNG uses the laser from the payload, in addition to potentially being used as detector in the case of an uplink scenario. Here we quantify the extractable secure randomness from the QRNG setup, that involves homodyne measurement of the vacuum states. The extracted randomness is tested against NIST test suite in addition to formally upper bounding the min-entropy. With the raw key length being $\approx1$ Mb in a given satellite pass, we get a total length of $\approx19.5$ Kb of certified random numbers from the 12-bit ADC.

Photon subtraction and addition are essential non-Gaussian processes in quantum optics, where conventional methods using linear optics and number-resolving detection often suffer from low success probability. Here, we introduce the concept of dynamic stimulated emission, whereby a quantum emitter undergoes stimulated emission with a time-dependent coupling. Despite interacting with a multimode photon field, we show that, for both two- and three-level emitters, their dynamics can mimic that of a single-mode Jaynes-Cummings model. This feature can be used to deterministically add or subtract a photon while maintaining a single propagating optical mode. We provide semi-analytic solutions to this problem for Fock states, enabling deterministic and unconditional photon addition and subtraction with fidelity ${\cal F}>0.996$. Our semi-analytic solutions are provided for both dynamically coupled two-level systems and for three-level systems whose dynamical coupling is controlled by a coherent laser drive. Moving beyond individual Fock states, we further showcase the ability to subtract and add single photons to photon-number superposition states. We show that Schrödinger cat states can be prepared from squeezed vacuum input via cascaded subtraction or cascaded addition. Finally, we show that our photon-addition process can be used to add a photon to any squeezed and displaced state with high success probability and fidelity ${\cal F}>0.99$, thereby potentially converting quantum emitters from single-photon sources to sources of single-photon-added Gaussian states without the need for inline squeezing. Our protocols provide a path towards integrating quantum emitters to construct efficient sources of single-mode non-Gaussian light beyond single photons.