Papers

We provide a general theoretical derivation of the phase sensitivity achieved by SU(1,1) interferometers under homodyne detection. The general expressions obtained accommodate arbitrary input states and include internal and external losses. In this systematic review, both full SU(1,1) interferometers with two parametric amplifiers and the truncated interferometers with only one parametric amplifier are examined. We investigate scenarios involving both single-output ports and joint homodyne detection, and consider parametric amplifiers with equal gains or with a boosted gain second amplifier. Our analytical formulation provides physical insight and understanding of the improvements in the sensitivity, which are shown to originate from noise reduction and/or signal amplification, depending on the configurations and practical implementations. Surprisingly, the configuration with single-output mode detection and parametric amplifiers with equal gains exhibits the highest robustness to very high internal losses. We finally apply this framework to a ubiquitous $|\alpha,0\rangle$ input two-mode coherent probe state. This approach permits the comparison of different strategies and the optimization of the interferometer performance in the presence of losses. In particular, we determine which amplification and detection configurations provide the best performance, depending on the level of losses. This exemplifies how this general analytical approach provides a powerful tool to design quantum-enhanced interferometers and achieve optimal sensitivity with selected probe states and homodyne detection.

Minimising EPR consumption is the dominant objective when routing a quantum circuit on a distributed quantum computer (DQC). We present dSABRE, a SABRE-style router for multi-core processors that, on each iteration of a lookahead-driven loop, first resolves any intra-core front-layer gates by SWAP scoring and only falls back to scoring inter-core teleportation candidates when the intra-core front is empty. Three mechanisms drive the improvement over the state of the art: a five-term gate-centric teleportation score that generalises the local SWAP heuristic to the inter-core setting, whose explicit capacity-penalty term keeps the scorer from teleporting into saturated cores; a proactive congestion-relief pass that redistributes idle qubits out of high-demand cores before deadlock; and a BFS-layer construction of the inter-core extended set that respects DAG dependencies layer by layer rather than mixing wires in topological order. Across 18 MQT-Bench circuits at 25, 36, and 64 logical qubits, dSABRE reduces geometric-mean EPR consumption by 41-44% over TeleSABRE and by 16-68% over the gate-teleportation-based pytket-dqc, using standard Qiskit SabreLayout for the initial layout. A large-circuit QFT sweep at 100-360 qubits confirms scalability. Code and online appendices are available at https://github.com/ebony72/dsabre.

We demonstrate how the relative phase between the multiple time periodic driving can decide the emergence and the favorable localization direction of non-Hermitian skin modes. For the static non-Hermitian quantum chain with parity time symmetry, non-Hermitian skin effects (NHSEs) can be prohibited. As the dynamical driving is turned on, NHSEs get artificially reactivated, where the relative phase can serve as the controlling switch by breaking the temporal symmetry constraints. Meanwhile, a change of relative phase can also alter the spatial structures of the long-time averaged effective Hamiltonian, which will consequently lead to the variation of skin localization direction for systems of higher dimensions. Our formalisms can be generally realized in diverse optical and mechanical platforms, and will pave the way for realizing tunable skin density profiles.

Photon blockade is vital for single-photon generation, but current schemes with conventional and unconventional photon blockade face critical limitations like the purity-brightness trade-off, hindering the generation of high-performance single-photons. To overcome these limitations, we introduce a fundamentally new photon blockade mechanism by utilizing three-body interactions between a single photonic mode and two qubits. This kind of interaction intrinsically cuts off the excitation path to the two-photon state, resulting in a perfect photon blockade effect. The mechanism operates across a broad parameter range, free from the constraints of strong coupling or weak driving. Remarkably, it breaks the purity-brightness trade-off, enabling the simultaneous achievement of extreme purity and high brightness, both significantly outperforming previous mechanisms. Furthermore, this approach demonstrates robustness against thermal noise and avoids unwanted oscillations in the time-delayed correlation function. This work provides a path for generating high-purity, high-brightness, and robust single-photon sources, a key resource for quantum technologies.

Strong-field high-harmonic generation (HHG) is conventionally described semiclassically, with the driving laser treated as a classical field. This approximation becomes insufficient in nanoscale interaction geometries, where extreme spatial confinement raises the vacuum-field amplitude to the ~10^-2 level relative to the driving-field amplitude. When the quantum fluctuations of the driving field are redistributed between conjugate quadratures by squeezing, they can be directly imprinted onto macroscopic HHG observables. To model this interaction, we employ a Wigner phase-space approach that maps the quantum-optical driver onto a stochastic ensemble of time-dependent Schrodinger equation realizations. Although each realization remains classically simulable, the sub-vacuum quadrature covariance structure of squeezed states cannot be reproduced by any field admitting a non-negative Glauber-Sudarshan P-representation. Within this single-mode Gaussian framework, we show that amplitude squeezing suppresses the shot-to-shot variance of the HHG cutoff below the standard quantum limit (SQL). To leading order in the vacuum-to-driver ratio, the normalized cutoff variance decays exponentially with the squeezing parameter, independent of the absolute vacuum-field amplitude and therefore robust against uncertainties in the effective nanoscale mode volume. A subleading phase-noise contribution from the anti-squeezed quadrature produces a variance minimum near r_opt ~ 1.6, providing a concrete experimental target. These results establish the HHG cutoff variance ratio as a nonlinear, self-calibrating Heisenberg witness in which sub-SQL scaling directly reflects the redistribution of quantum uncertainty in the driving field.

We propose a three-cavity scheme to realize full control of the emitter-cavity coupling strength in cavity quantum electrodynamics (cQED). The involvement of coupled oscillators gives rise to transient dynamics comprising multiple spectral components, which significantly increases the numerical cost to resolve the fluorescence spectrum in the time domain. A generalized sensor method is hence developed to simplify the calculation process for the characterization of nonstationary quantum dynamics. Multi-modal spectroscopy reveals the emergence, splitting, and disappearance of supermodes in real time. Based on the depletion of the zero-energy supermode, ultrafast switching of Rabi oscillations is demonstrated for time-domain multi-modal spectroscopy. These results exhibit a consistent picture from the spectral control of multiple oscillators to the quantum observation in ultrafast dynamics, which establishes the sensor method as a powerful theoretical tool for the ultrafast spectroscopy of cQED systems.

Dynamic link prediction is important for modeling evolving interactions in social, communication, financial, and transportation networks. Classical temporal graph models capture changes over time, but they may struggle to represent rapidly evolving node-edge interactions in large dynamic graphs. We propose A2QTGN (Adaptive Amplitude Quantum-Integrated Temporal Graph Network), a hybrid quantum-classical framework that introduces adaptive amplitude encoding as a temporal embedding layer within a Temporal Graph Network. Unlike fixed quantum embeddings, the proposed module maps temporally varying node features into quantum states and selectively refreshes their amplitude representations according to the magnitude of feature change. This allows the framework to preserve stable node information, emphasize meaningful temporal variations, and reduce redundant quantum re-encoding. Across five Temporal Graph Benchmark datasets, A2QTGN achieves test area under the curve (AUC) values of up to 0.9957 and mean reciprocal rank (MRR) values of up to 0.7832, including the highest MRR among the compared baselines on tgbl-review and tgbl-flight. Ablation results further show that the adaptive quantum embedding is central to the model performance: on a 25k-event subset of tgbl-wiki, it improves test accuracy by 13.36 percentage points over always updating and by 22.44 percentage points over using no updates. The trained model is also evaluated using noisy simulations based on an IBM quantum device, followed by a smaller real-device experiment. The results show that adaptive quantum embeddings can provide effective temporal representations for dynamic link prediction while remaining executable under current quantum hardware constraints.

Remote quantum batteries require directional and controllable energy transfer between spatially separated quantum nodes, yet most existing protocols rely on direct charger-battery Hamiltonian couplings. Here we propose a phase-tunable waveguide-QED architecture for remote quantum-battery charging, in which a driven charger and a remote battery are coupled solely via engineered waveguide-mediated interference, without any direct local interaction. We systematically compare four configurations: two-giant-emitter and giant-small-emitter hybrids, each with open or mirror-terminated waveguides. By engineering the propagation and coupling phases, the waveguide-mediated coherent exchange interaction and collective dissipation can be balanced to suppress the backward channel while retaining a finite forward channel, thereby realizing cascaded-like unidirectional charging. Our analysis shows that nonreciprocity and storage efficiency can be independently engineered, offering design flexibility for different quantum network scenarios. The giant-small-emitter mirror-terminated configuration simultaneously achieves perfect nonreciprocity and battery-dominated storage, while both giant-small-emitter configurations exhibit distance-insensitive directionality. Extending the scheme to quadratic driving, we show that anomalous second moments render the battery state non-passive, making ergotropy a performance metric distinct from stored energy. These results establish phase-tunable waveguide networks as a versatile platform for remote quantum-energy transfer and provide design principles for directional and work-extractable energy storage in quantum networks.

Spatially structured dissipation organizes driven quantum matter beyond Hamiltonian control. We show that a dissipation gradient combined with a Stark-induced detuning ramp selects a nonlinear resonance slice in a two-dimensional driven-dissipative Bose-Hubbard lattice, producing a pinned density front in generalized Gross-Pitaevskii simulations. The underlying resonance condition fixes the front position, while its Airy-like profile obeys a width scaling set by tunneling stiffness and the effective detuning slope. Treating the front as an emergent interface explains how tuning the selected resonance toward the minimum-loss side yields Peierls-Nabarro depinning steps, discrete transverse pattern locking, spatiotemporal chaos, and minimum-loss localization. Center-of-mass and generalized-imbalance diagnostics map these outcomes into a dynamical phase diagram as detuning-ramp slope and dissipation-gradient strength vary. The results suggest structured dissipation as a mechanism for reconfigurable transport barriers and nonequilibrium interfaces in programmable bosonic lattices.

Different quantum error correction schemes trade off overhead, error suppression, and hardware connectivity. Code concatenation can relax these tradeoffs by using an outer code whose non-local connectivity is supplied by logical operations of an inner code rather than directly by hardware. Prior works showed that this can reduce memory overhead for local low-rate inner codes such as the surface code. Here, we study concatenation over non-local, high-rate inner codes. Such inner codes experience correlated errors among the many logical qubits in a single codeblock. We handle this by treating each block as a single logical Galois qudit, enabling concatenation with algebraic outer codes with excellent parameters and, crucially, list decoders. In particular, we consider a memory system formed by concatenating quantum Reed-Solomon outer codes over the gross code. For fault-tolerant syndrome extraction, we develop a Galois qudit Shor scheme using "time-like" Reed-Solomon protection against measurement errors. Interestingly, a lightweight fault tolerance scheme, that would fail for qubits, works well for large-alphabet qudits, suggesting a very different theory of fault tolerance for such qudits. The whole protocol is optimised via improved bicycle instruction logical error rates, novel compilation strategies, and recent decoder post-selection rules. At uniform $10^{-3}$ physical noise, the concatenated gross code reaches the teraquop regime, which it previously could not access, with a lower space overhead than the $288$-qubit two-gross code, while offering several advantages from the engineering standpoint. Beyond our main case study, we believe the core ideas of Galois qudits, quantum Reed-Solomon outer codes, and list decoding, will prove generically powerful and highly transferable ideas across high-rate quantum architectures.

Waveguide cavity quantum electrodynamics (QED) with atomic mirrors is a growing research area of quantum optics and can be applied to quantum information processing. We here study the photon statistics of output fields from a waveguide cavity QED system, in which the waveguide is coupled to quantized mirror atoms and one driven medium atom. Our results show that the photon blockade can occur even for a bad atom cavity with large dissipation and small coupling between the medium atom and the cavity, in contrast to the small dissipation and the strong coupling of the medium atom to the cavity field for the conventional photon blockade or the quantum interference for the unconventional photon blockade in the cavity QED system. Utilizing both the master equation and scattering theories, we derive the condition under which the photon blockade occurs in weakly driven systems. We find that such photon anomalous blockade is due to the quantum Zeno effect and is robust against variations of the medium atom's position within the cavity. Our study paves a way to exploit the photon blockade and single-photon devices via the waveguide cavity QED.

Device-independent quantum secret sharing (DI-QSS) provides high security by eliminating the need to trust devices, yet its practical performance is limited by channel loss and noise. This work extends advantage distillation from two-party quantum key distribution (QKD) to three-party DI-QSS, redesigning the corresponding data interaction and verification procedures. The technique is systematically applied to the basic protocol and three active improvement strategies: noise preprocessing, post-selection, and their combination. This approach enhances noise tolerance, reduces the required global detection efficiency threshold, and significantly extends the maximum secure communication distance. Numerical simulations demonstrate that for the basic protocol over fiber, the maximum secure distance increases from 0.16 km to 1.85 km, and the noise tolerance improves from 10.17% to 28.49%. The results show that generalizing advantage distillation to the three-party setting effectively strengthens the protocol's robustness and practicality, enhancing its adaptability to realistic noise and advancing the development of more reliable quantum secret sharing systems.

Magic state distillation is a key component of fault-tolerant quantum computation, as it enables the implementation of non-Clifford gates such as the $T$ gate and the $CCZ$ gate via gate teleportation. However, conventional distillation protocols require a large number of logical qubits and introduce substantial spatial and temporal overhead, posing a significant bottleneck for scalable fault-tolerant quantum computation. In this work, we propose a zero-level distillation protocol that efficiently generates a high-fidelity logical $CCZ$ magic state using only physical qubits on a two-dimensional square lattice with nearest-neighbor interactions. Our method leverages the transversal $T/T^\dagger$ operation of the $[[ 8,3,2 ]]$ code to fault-tolerantly encode the state $\overline{CCZ}|+++\rangle$, which is subsequently teleported to three surface-code logical qubits via lattice surgery. To enable teleportation between codes with different distances, we introduce adaptively initialized teleportation (AIT), a tailored initialization procedure for the surface code. Numerical simulations demonstrate that the logical error rate scales as $p_L \simeq 300 \times p^2$ with respect to the physical error rate $p$. For example, the proposed method improves the logical error rate by approximately one and two orders of magnitude at $p = 10^{-3}$ and $p = 10^{-4}$, respectively, compared to conventional seven-$T$-gate approaches. The distillation circuit requires only 22 physical qubits, 3 logical qubits, and a circuit depth of 24, reducing the space-time overhead by a factor of approximately 5-10 compared to previous methods. This result highlights the practicality of $CCZ$-state distillation in early fault-tolerant quantum computation and offers a new direction toward resource-efficient physical-level magic state distillation beyond conventional $T$-state generation.

We develop the quantum theory of the causal formation of a long-range magnetic field generated by an external current that is instantaneously switched on and subsequently kept constant in time. The resulting non-equilibrium quantum state, describing the expanding magnetic field, is obtained exactly and compared with the corresponding quantum magnetostatic state. In contrast to the magnetostatic case, the expanding solution exhibits a propagating shockwave-like front separating regions where the magnetic field has already been formed from those that remain causally disconnected from the source. We show that although the expanding field locally approaches the magnetostatic field behind the shockwave-like front, the associated quantum systems remain distinct at all times. In particular, we obtain manifestly different results for the energy, photon number, and their fluctuations in expanding and magnetostatic field configurations. Our results are first derived for a general external current and then illustrated with a specific example.

A recent Letter by Wadhia et al. reports a realization of a quantum clock using a double quantum dot (DQD) [Phys. Rev. Lett. 135, 200407 (2005)]. This Comment identifies two fundamental issues: (I) the claimed “quantum clock" exhibits only classical behavior and lacks intrinsic temporal correlations between ticks; it is not sufficient for accurate time as a good clock. (II) the thermodynamic analysis misassigns entropy production and conflates amplification with measurement; the reported combined entropy is an engineering dissipation, not a fundamental cost of quantum timekeeping.

Distributed Quantum Computers (DQCs) enable large system sizes by connecting smaller chips via photonic interconnects. DQCs use teleportation to relocate qubits and execute CNOTs between qubits on different chips. But, non-local CNOTs are 4.3-7.7$\times$ slower and 4$\times$ more error-prone than local CNOTs within a chip, which degrades program fidelities. Compilers group CNOTs with overlapping qubits into blocks and collectively optimize teleportations for each block. However, block-level scheduling suffers from two key drawbacks. First, they lack lookahead ability between blocks because they select the best schedule for a block before proceeding. So, they cannot assess the impact of a teleportation on future blocks. Our studies show that naively expanding the lookahead window to include subsequent blocks does not address the issue. Second, they do not schedule future block operations or teleportations they need unless preceding blocks are fully scheduled, introducing delay and latency overheads. We propose IRIS, a DQC compiler that addresses these limitations using two key insights: Utility-driven Lookahead With Multi-Candidate Block Scheduling (UMS) and EPR-Capacity-Aware Early Scheduling (EES). UMS schedules a block by considering only useful future blocks in its lookahead window. A future block has utility if it shares overlapping qubits with the current block being scheduled. UMS also maintains multiple schedules during compilation, allowing it to defer commitment to globally sub-optimal schedules early. EES enables IRIS to schedule future operations and their relocations early if EPR resources are available for teleportations. Our evaluations show that IRIS reduces teleportations by 34% on average and by up to 65%; and latency by 2$\times$ on average and by up to 2.9$\times$ compared to the state-of-the-art DQC compiler.

Completeness of the Klein–Gordon oscillator eigenfunctions is proved in one and three spatial dimensions. The proofs establish the closure relations satisfied by the eigenfunctions and are based on standard properties of the Hermite and the generalized Laguerre polynomials, supplemented in three dimensions by the completeness of the spherical harmonics. The scalar nature of the Klein–Gordon field renders the argument strictly simpler than the analogous proof for the Dirac oscillator: no off-diagonal cancellation is required.

In this study, we examine an innovative framework towards implementing quantum decision trees utilizing a laser-driven four-level system. We discuss a diamond-shaped atomic configuration, in which we apply Lie-algebraic formalisms to analyze the dynamics of the system. The system is perturbed by a Stokes pulse, represented as $\beta_j(t)$ (for $j=1,2$), which interacts with the atomic states $|0\rangle, |3\rangle$ and $|1\rangle, |2\rangle$. In addition, a pump laser, denoted as $\alpha_j(t)$, couples the states $|0\rangle, |1\rangle$ and $|2\rangle, |3\rangle$. By employing pulse profiles that possess identical temporal behavior but differ in amplitude, one can effectively redistribute the population from the initial ground state to the other energy levels. This technique facilitates the mimicry of a quantum decision tree. We highlight that the proposed methodology is scalable to N-level systems, enhancing its adaptability and potential utility in quantum computing and various decision-making applications. We introduce a novel framework for implementing quantum decision trees using a four-level laser-driven atomic system. Employing a diamond-shaped energy configuration, we analyze system dynamics through Lie-algebraic methods. Using pulse profiles with identical temporal structures but varying amplitudes, we achieve controlled population redistribution among energy levels, effectively simulating a quantum decision tree. This methodology is scalable to systems of \(N\) levels, offering potential applications in quantum computing and decision-making processes.

Generating usable output-entanglement in continuous variable systems can serve as a viable resource for improving applications in quantum information science. In this work, we show how to generate steady-state output-entanglement in a two-stage conversion setup between optical and microwave photon which employs resonantly coupled magnetic and mechanical excitations, as proposed in Phys. Rev. Applied 18, 044059 (2022). We show that the entanglement can be maximized for the same set of parameters which optimize the frequency-conversion efficiency, and that it can be leveraged for a teleportation-based state-transfer protocol for coherent input-states with fidelity close to unity. We propose an implementation based on an Yittrium Iron Garnet disk of micrometer scale, and use both simulation results and reasonable estimates to assess the performance under optimized conditions. We find a maximum teleportation fidelity of $0.75$ for the proposed setup.

Efficiently realizing logical operations on general stabilizer codes remains a long-standing challenge in fault tolerant quantum computing. While code surgery provides a general framework with provable guarantees by joint logical measurements, existing constructions are largely theoretical and incur substantial ancilla overhead in practice. In this work, we propose GeneCS, a resource-efficient compiler for synthesizing code surgery protocols for arbitrary stabilizer codes. Our approach leverages structure-aware optimizations to eliminate redundancy in graph construction, dynamically balance expansion and congestion, and incorporate code degree constraints. Experimental results show that GeneCS achieves an average reduction of over $85\%$ in ancillary qubits and checks for both single-code and cross-code logical operations, while preserving logical error rates. Moreover, our compiler scales to codes with more than $10^4$ qubits with an amortized compilation time of about one second per instance. These results enable practical logical operations and efficient cross-code communication, thereby supporting the deployment of modern QLDPC codes and heterogeneous quantum architectures.

We present a review on quantum metrology and sensing, from its foundations to current applications. Highlights of the review include consideration of both frequentist and Bayesian approaches to parameter estimation; single as well as multiparameter estimation; estimation for different encoding processes comprising unitary as well as noisy channels, quantum thermometry, and channels involving indefinite causal order; different estimation strategies incorporating also recent advances like quantum error correction-aided methods and reservoir engineering; usefulness of quantum Fisher information to detect resources; applications of quantum metrology in diverse arenas covering quantum many-body sensors, sensing protocols in atomic ensembles, atom-photon systems, and continuous-variable systems, quantum imaging, quantum illumination, atomic clocks and atom interferometry, etc; and experimental realizations of quantum sensors in different physical platforms.

We explore the concept of antiflatness to characterize the structural fluctuations within the entanglement spectrum of a quantum state (i.e., the spectrum of its reduced density operator). As a measure of the interplay between entanglement and magic, two fundamental quantum resources, antiflatness provides second-order information about quantum correlations that standard average measures fail to capture. Recognizing that standard majorization theory fundamentally orders states by purity and is structurally blind to spectral fluctuations, we introduce a novel partial ordering known as antiflat majorization, based on the Rényi entropy spread. We define Flatness-Preserving Operations (FPOs), establishing new necessary conditions for state convertibility. Furthermore, we unify different measures of antiflatness-such as Capacity of Entanglement, Linear Rényi spread, and Logarithmic antiflatness-using the frameworks of escort distributions and Bregman divergences. We prove that the Capacity of Entanglement can be expressed as a second derivative of the Kullback-Leibler divergence along the escort trajectory, connecting it with the Quantum Fisher Information. Finally, we demonstrate that absolute maximal antiflatness is not achieved by a single universal state, but rather by a continuous Pareto frontier of extremal states with jump spectra, and we analyze the typicality of these spectral fluctuations using Haar, Bures-Hall and t-doped Clifford random state ensembles.

Frequency crowding is a fundamental limitation in superconducting quantum architectures, particularly in tunable-coupler systems. We present a framework that explicitly models both coherent spectator-induced errors and incoherent lifetime effects through an error budgeting approach. Using this model, we analyze how frequency crowding impacts gate fidelity as module size and connectivity scale, and formulate a constrained optimization problem to assign qubit and coupler frequencies under realistic separation and hardware constraints. We demonstrate scalable frequency allocation strategies that minimize spectator-induced errors. We further show that increasing qubit count and coupling density within a module leads to a fidelity-connectivity tradeoff. To explore the benefits at the system scale, we have developed a noise-aware transpilation approach called FINESSE, which minimizes error by selecting high-fidelity paths that satisfy connectivity via SWAP insertion while jointly optimizing downstream gate execution. We demonstrate this physics-informed architecture-transpilation co-design approach for a SNAIL-based third-order coupler that natively realizes the $\sqrt{iSWAP}$ basis with frequency aware gate fidelities. On SNAIL architectures, FINESSE achieves an average 8.9% reduction in log-infidelity cost and 6.8% reduction in circuit depth vs. SABRE. We also compare results on IBM Brisbane's architecture.

Spin squeezing in atomic ensembles enables atom interferometry with sensitivities below the shot-noise limit, but the associated entanglement is highly susceptible to loss, making imperfections in atom optics a central limitation. Bragg diffraction is an established technique for driving transitions between atomic momentum states and enables large-momentum transfer through higher-order diffraction while preserving the internal state. However, it is intrinsically limited by two competing mechanisms: Short light pulses induce parasitic diffraction into off-resonant orders beyond an effective two-level description, while long pulses face velocity selectivity. We derive analytical expressions in a second-quantized framework for the atom optics and phase uncertainty of a Mach-Zehnder interferometer including these effects. We demonstrate that sub-shot-noise scaling is achieved only in a regime of intermediate pulse duration. Furthermore, we show that deleterious effects of higher-order diffraction are partially mitigated by optimizing the input quantum state.

Dissipative quantum chaos is an emerging theory that is expected to extend the ideas, concepts, and methodology of conventional Hamiltonian quantum chaos from coherent evolution to open quantum dynamics. The new theory should provide a set of tools to distinguish chaotic open quantum systems from integrable ones, as well as quantitative measures of their chaoticity (or, conversely, integrability). The foundations of this theory were laid in the late 1980s, and from the very start it was clear that, like its Hamiltonian predecessor, it had to be based on the spectral properties of the operators governing open quantum evolution. After these first steps, the field remained relatively quiet for many years and it is only over the last decade that the development of dissipative quantum chaos has received a strong boost, as confirmed by a large number of publications on this topic and, very recently, the first experiments performed to test its theoretical predictions. In this chapter, we review these recent developments and outline the basic foundations of dissipative quantum chaos.

We introduce a matrix product operator (MPO) encoding of the Magnus expansion and the Dyson series for one-dimensional quantum lattice models with time-dependent Hamiltonians. The MPO construction can be made accurate up to arbitrary order in the time step, it can be applied to both finite and infinite systems, and it can handle long-range interactions. The resulting MPO can be combined with state-of-the-art time evolution algorithms based on matrix product states, allowing for drastic improvements in simulating evolution under time-dependent Hamiltonians. Our MPO construction can also be used for the optimization of quantum circuits in the context of quantum simulation of time-dependent Hamiltonians.

We propose a realizable experiment to test the response of a particle detector prepared in a superposition of locations interacting with a relativistic quantum field. Using a beamsplitter to prepare two superposed branches of a modulated laser probe, these branches are directed to intersect a pancake-shaped Bose-Einstein condensate at two separate locations. The branches are then recombined with another beamsplitter. Heterodyning one of the outputs, the response function corresponding to an Unruh-deWitt detector in a superposition of locations interacting with a (2+1)-dimensional massless scalar field is shown to appear in the difference photocurrent power spectrum. Operating beyond the standard quantum limit using squeezed light, we estimate the signal-to-noise ratio $SNR\gtrsim 10$ for extracting the response function over a broad set of baseband frequencies.

We study algebraic locality principles on a 2+1D closed lattice in the presence of a Gauss law for a non-invertible symmetry. Prior work in arXiv:2509.03589 showed that when enforcing the Gauss law of an invertible symmetry, the principle of "Haag duality" is preserved exactly, and "disjoint additivity" is preserved after appropriate treatment of discreteness artifacts. Here we show that for a large class of non-invertible on-site symmetries, Haag duality is preserved exactly only for sufficiently nice, "cuspless" regions. For cusped regions, we instead have a weak form of Haag duality that requires adding a collar. Our results apply to double models with a purely magnetic constraint, and to the more general framework of constraints induced by the on-site action of a Hopf algebra. In particular, we treat a class of extended string-net models explicitly. We also demonstrate disjoint additivity for double models based on a group, and a weakened form of disjoint additivity in the setting of a general Hopf algebra.

We show that Maxwell theory with a codimension-$1$ Chern-Simons interface supports chiral electromagnetic surface waves on the interface, even when the bulk theory on both sides is conventional vacuum electrodynamics in infinite space. Solving the exact boundary value problem we find that the Chern-Simons interaction acts with opposite sign on the two helicities oriented along the interface, giving rise to one normalizable mode localized on the interface. This mode is a gapless chiral surface photon with linear dispersion and a frequency-independent index of refraction set by the Chern-Simons coefficient. This mode exists despite the absence of ambient material response or geometric confinement.

Quantum purity amplification (QPA) is the task of coherently transforming $n$ copies of a mixed state into high-fidelity copies of a chosen eigenstate. We develop a general theory of QPA for $n$ input copies, $m$ output copies, and arbitrary choices of target eigenstate, local dimension $d$, and input spectrum. We introduce the overhang-removal protocol, derive its all-site and one-site fidelities across output regimes, and show that it is optimal in several regimes, both asymptotically and nonasymptotically. For the asymptotic analysis, we use a path-graph parametrization to show that, when the target eigenvalue has a constant spectral gap $D_{k,\mathrm{min}}$, achieving worst-case all-site error $\varepsilon$ scales as $O(m/(\varepsilon D_{k,\mathrm{min}}^2))$. When $m/n$ approaches a constant, the performance exhibits phase-like regimes, which we characterize explicitly. For the nonasymptotic analysis, we develop a theory of generalized Young diagrams that yields tight sample complexity bounds and provides the first tight dimension-uniform guarantee for optimal QPA. We also provide asymptotically efficient implementations of the overhang-removal protocol. Together, these results establish QPA as a rigorous example of coherent quantum information processing with dimension-uniform sample complexity, supplying the technical foundation for the coherent-incoherent separation developed in the companion work.