Papers

In this work, we investigate the Kitaev honeycomb model employing the recently developed Clifford Circuits Augmented Matrix Product States (CAMPS) method. While the model in the gapped phase is known to reduce to the toric code model - whose ground state is entirely constructible from Clifford circuits - we demonstrate that the very different gapless quantum spin liquid (QSL) phase can also be significantly disentangled with Clifford circuits. Specifically, CAMPS simulations reveal that approximately two-thirds of the entanglement entropy in the isotropic point arises from Clifford-circuit contributions, enabling dramatically more efficient computations compared to conventional matrix product state (MPS) methods. Crucially, this finding implies that the Kitaev QSL state retains significant Clifford-simulatable structure, even in the gapless phase with non-abelian anyon excitations when time reversal symmetry is broken. This property not only enhances classical simulation efficiency significantly but also suggests substantial resource reduction for preparing such states on quantum devices. As an application, we leverage CAMPS to study the Kitaev-Heisenberg model and determine the most accurate phase boundary between the anti-ferromagnetic phase and the Kitaev QSL phase in the model. Our results highlight how Clifford circuits can effectively disentangle the intricate entanglement of Kitaev QSLs, opening avenues for efficiently simulating related and similar strongly correlated models.

Flat-band lattices hosting compact localized states are highly sensitive to external modulation, and the tailored design of a perturbation to imprint specific features becomes relevant. Here we show that periodic driving in the high-frequency regime transforms the all-flat-band diamond chain into one featuring two tunable quasi-flat bands and a residual flat band pinned at $E=0$. The interplay between lattice geometry and the symmetries of the driven system gives rise to drive-induced tunneling processes that redefine the interference conditions and open a controllable route to escaping Aharonov-Bohm caging. Under driving, the diamond chain effectively acquires the geometry of a dimerized lattice, exhibiting charge oscillations between opposite boundaries. This feature can be exploited to generate two-particle entanglement that is directly accessible experimentally. The resulting drive-engineered quasi-flat bands thus provide a versatile platform for manipulating quantum correlations, revealing a direct link between spectral fine structure and dynamical entanglement.

The Quantum Approximate Optimization Algorithm (QAOA) is widely studied for combinatorial optimization and has achieved significant advances both in theoretical guarantees and practical performance, yet for general combinatorial optimization problems the expected performance and classical simulability of fixed-round QAOA remain unclear. Focusing on Max-Cut, we first show that for general graphs and any fixed round $p\ge2$, exactly evaluating the expectation of fixed-round QAOA at prescribed angles is $\mathrm{NP}$-hard, and that approximating this expectation within additive error $2^{-O(n)}$ in the number $n$ of vertices is already $\mathrm{NP}$-hard. To evaluate the expected performance of QAOA, we propose a dynamic programming algorithm leveraging tree decomposition. As a byproduct, when the $p$-local treewidth grows at most logarithmically with the number of vertices, this yields a polynomial-time exact evaluation algorithm in the graph size $n$. Beyond Max-Cut, we extend the framework to general Binary Unconstrained Combinatorial Optimization (BUCO). Finally, we provide reproducible evaluations for rounds up to $p=3$ on representative structured families, including the generalized Petersen graph $GP(15,2)$, double-layer triangular 2-lifts, and the truncated icosahedron graph $C_{60}$, and report cut ratios while benchmarking against locality-matched classical baselines.

Bilayer graphene is a maturing material platform for gate-defined quantum dots that hosts long-lived spin and valley states. Implementing solid-state qubits in bilayer graphene requires a fundamental understanding of such confined electronic systems. In particular, states of two and three carriers, for which the exchange interaction between particles plays a crucial role, are a cornerstone for qubit readout and manipulation. Here we report on the spectroscopy of few-carrier states in bilayer graphene quantum dots, using circuit quantum electrodynamics (cQED) techniques that offer substantially improved energy resolution compared to standard transport techniques. Measurements using a superconducting high-impedance resonator capacitively coupled to the double quantum dot reveal dispersive features of two and three electron states, enabling the detection of Pauli spin and valley blockade and the characterization of the spin-orbit gap at zero magnetic field. The results deepen our understanding of few-carrier spin and valley states in bilayer graphene quantum dots and demonstrate that cQED techniques are a powerful state-selective probe for semiconductor nanostructures.

Improving our understanding of electron dynamics is essential for advancing energy transfer, optoelectronics, light harvesting systems and quantum computing. Recent developments in attosecond x-ray sources provide the fundamental possibility of observing these dynamics with atomic-scale resolution. However, connecting a time-resolved signal to dynamics is challenging due to the broad bandwidth of an attosecond probe pulse. This makes exploring the capabilities of different attosecond imaging techniques crucial. Here, we propose attosecond momentum-resolved resonant inelastic x-ray scattering as a prominent technique for tracking ultrafast dynamics. We demonstrate that the scattering signal contains an information about the instantaneous distribution of charge density across the scattering atoms. To illustrate this, we consider scattering from an $\alpha$-sexithiophene molecule, in which coupled electron-hole dynamics are excited.

The precise measurement of the leptonic CP-violating phase $\delta_{CP}$ remains one of the major open challenges in neutrino physics, as current experiments achieve only very limited accuracy. We address this issue through the lens of quantum estimation theory. A distinctive feature of neutrino oscillation experiments is that they cannot freely optimize the probe or measurement, since both are constrained by the production and detection of flavor eigenstates. We therefore examine whether the large uncertainty in $\delta_{CP}$ originates from intrinsic reasons, either of the neutrino quantum state or of flavor measurements, or if it instead stems from experimental limitations. By comparing quantum and classical Fisher information, we demonstrate that the limited sensitivity to $\delta_{CP}$ originates primarily from the information content of flavor measurements. Furthermore, we show that targeting the second oscillation maximum, as in the ESS$\nu$SB proposal, substantially enhances $\delta_{CP}$ information compared to experiments centered on the first maximum.

We present the experimental implementation of a three-time-bin phase-encoded Twin-Field Quantum Key Distribution (TF-QKD) protocol using a Sagnac-based star-topology plug-and-play architecture. The proposed encoding method leverages the relative phases of three consecutive time bins to encode two bits per signal. The Sagnac loop configuration enables self-compensation for both phase and polarisation drifts, eliminating the need for active stabilisation. However, field deployments are subject to rapid phase fluctuations caused by external vibrations, which can degrade interference visibility. We used the first time bin for real-time phase-fluctuation monitoring. Although this monitoring reduces the effective key generation rate, the system achieved a secure key rate of approximately 1.5e-5 bits per pulse, with a corresponding visibility of up to 87% over a 50 km asymmetric optical fibre channel. These results demonstrate the practicality, stability, and scalability of the proposed three-time-bin TF-QKD protocol for real-world quantum communication networks.

We propose a model of binary random number generator (RNG) based on a Brillouin optomechanical system. The device uses a hard excitation mode in a Brillouin optomechanical system, where thermal noise induces spontaneous transitions between two stable states in the hard excitation mode. We demonstrate the existence of an amplitude criterion for observing these transitions and show that the probability distribution of their occurrence in the non-generating and generating states can be precisely controlled by the amplitude of an external pump wave. At the same time, the use of a low-intensity seed wave allows for the control of the transition times between states. We demonstrate that the proposed random number generator successfully passes the standard tests NIST SP 800-22. The obtained result opens a way for development of an all-optical integrated True RNG, generating a sequence of random bits with equal probability.

The configuration space, i.e. the Hilbert space, of compound quantum systems grows exponentially with the number of its subsystems: its dimensionality is given by the product of the dimensions of its constituents. Therefore a full quantum treatment is rarely possible analytically and can be carried out numerically for fairly small systems only. Fortunately, in order to obtain interesting physics, approximations often very well suffice. One of these approximations is given by the cumulants expansion, where expectation values of products of operators are approximated by products of expectation values of said operators, neglecting higher-order correlations. The lowest order of this approximation is widely known as the mean field approximation and used routinely throughout quantum physics. Despite its ubiquitous presence, a general criterion for applicability and convergence properties of higher order cumulants expansions remains to be found. In this paper, we discuss two problems in quantum electrodynamics and quantum information, namely the collective radiative dissipation of a dipole-dipole interacting chain of atoms and the factorization of a bi-prime by annealing in an adiabatic quantum simulator. In the first case we find smooth, convergence behavior, where the approximation performs increasingly better with higher orders, while in the latter going beyond mean field turns out useless and, even for small system sizes, we are puzzled by numerically challenging and partly non-physical solutions.

Superconducting parametric amplifiers (SPAs) are critical components for ultralow-noise qubit readout in quantum computing, addressing the critical challenge of amplifying weak quantum signals without introducing noise that degrades coherence and computational fidelity. Unlike classical amplifiers, SPAs can achieve or closely approach quantum-limited performance, specifically the Standard Quantum Limit (SQL) of half a photon of added noise for phase-preserving amplification. The core principle of SPAs relies on parametric amplification, where energy is transferred from a strong pump tone to a weak input signal through non-dissipative nonlinear mixing processes. This is enabled by intrinsic nonlinearities in superconducting materials, primarily kinetic inductance in thin films (e.g., NbTiN, Al) and, more significantly, the Josephson effect in Josephson junctions. These nonlinear elements facilitate frequency mixing (three-wave or four-wave mixing) and can operate in phase-preserving or phase-sensitive amplification modes, with the latter allowing for noise squeezing below the SQL. This chapter emphasizes the significant role of resonator design in determining critical SPA performance metrics such as gain, bandwidth, and noise characteristics. It details both lumped-element (LC) and distributed-element (coplanar waveguide, CPW) resonators, discussing their unique properties, suitability for different frequency ranges, and the importance of achieving high-quality factors (Q) for efficient energy storage and minimal loss. A practical design and simulation of a meandered quarterwavelength CPW resonator coupled to a feed line is presented, illustrating how precise control over geometric parameters optimizes resonant frequency, coupling strength, and quality factor for high-fidelity qubit state discrimination.

Scaling quantum networks to continental distances requires physical infrastructure capable of overcoming both exponential attenuation and severe phase decoherence. While the concept of the vacuum beam guide (VBG) has recently emerged as a promising low-loss solution, we move beyond it by proposing a stringent and conservative physical-layer architectural blueprint anchored by empirical data and methods from Advanced LIGO, particularly regarding its interferometric stability in dynamic environments. To evaluate its system-level viability, we benchmark this architecture against various protocols across quantum communication, metrology, and computation. Ultimately, we identify no fundamental technical blockers to scaling this infrastructure.

Fast coherent state transport is essential to quantum computation and quantum information processing. While an adiabatic transport of atomic qubits guarantees a high fidelity of the state preparation, it requires a long timescale that defies efficient quantum operations. Here, we propose an adaptable and fast bang-bang-bang (BBB) protocol, utilizing a combination of forwardand backward-moving trap potentials, to expedite the coherent state transport. This protocol approaches the quantum speed limit under a harmonic trap potential, surpassing the performance by the forward-moving-only potential protocols. We further showcase the advantage of applying squeezed coherent state evolution under a deeper potential followed by a weaker one, where a design of symmetric squeezing potential transports promotes an even shorter timescale for genuine state preparation. Our protocols outperform conventional forward-moving-only methods, providing new insights and opportunities for rapid state transport and preparation, ultimately advancing the capabilities of quantum control and quantum operations.

Quantum computing is a promising technology that accelerates the partial differential equations solver for practical problems. The reconstruction of solutions (i.e., the readout of quantum states) remains a crucial problem, although numerous efficient quantum algorithms have been proposed. In this paper, we propose and compare several efficient readout methods in the real and the Fourier space. The Fourier space readout (FSR) and the proposed approximate real space readout (ARSR) methods are currently the most efficient and practical ones for the purpose of reconstructing continuous real-valued functions. In contrast, the quantum amplitude estimation (QAE) based methods (especially in the Fourier space) are favorable for mid-term/far-term quantum devices. Besides, we apply the methods for benchmark solutions in computational fluid dynamics (CFD) and demonstrate great improvements compared to the conventional sampling method for large grid numbers. Equipped with efficient readout methods, we further show that a 2D Burgers' equation can be solved efficiently without using the expensive strategy of linearization. It suggests the potential quantum advantages for some practical applications on mid-term quantum devices.

Decoded Quantum Interferometry (DQI) promises superpolynomial speedups for structured optimization; however, its practical realization is often hindered by significant sensitivity to hardware noise and spectral dispersion. To bridge this gap, we introduce Kernelized Decoded Quantum Interferometry (k-DQI), a unified framework that integrates spectral engineering directly into the quantum circuit architecture. By inserting a unitary kernel prior to the interference step, k-DQI actively reshapes the problem's energy landscape, concentrating the solution mass into a “decoder-friendly” low-frequency head. We formalize this advantage through a novel robustness metric, the noise-weighted head mass $\Sigma_K$, and prove a Monotonic Improvement Theorem, which establishes that maximizing $\Sigma_K$ guarantees higher decoding success rates under local depolarizing noise. We substantiate these theoretical gains in Optimal Polynomial Interpolation (OPI) and LDPC-like problems, demonstrating that kernel tuning functions as a “spectral lens” to recover signal otherwise lost to isotropic noise. Crucially, we provide explicit, efficient circuit realizations using Chirp and Linear Canonical Transform (LCT) kernels that achieve significant boosts in effective signal-to-noise ratio with negligible depth overhead ($\tilde{O}(n)$ to $\tilde{O}(n^2)$). Collectively, these results reframe DQI from a static algorithm into a tunable, noise-aware protocol suited for near-term error-corrected environments.

Virtual maps allow the simulation of quantum operations by combining physical processes with classical post-processing. Recent work on virtual unitary covariant broadcasting has shown, however, that such maps remain impractical for observable estimation tasks due to poor sample efficiency. Here we investigate whether relaxing the symmetry requirements can improve operational performance, focusing on virtual phase-covariant quantum broadcasting for qubits. We show that imposing phase-covariance, flip covariance, permutation invariance, and classical consistency fully determines the structure of the broadcasting map. Within this family, we identify the unique map that minimizes the simulation cost, and we prove that both the simulation cost and the distance to the closest CPTP map are strictly smaller than in the unitary covariant setting. We also demonstrate that the closest physical map is the optimal phase-covariant cloning channel, mirroring the relation between unitary covariant broadcasting and universal cloning. Despite these improvements, the resulting virtual broadcasting map remains sample-inefficient and is therefore still operationally impractical.

Fault tolerance is widely regarded as indispensable for achieving scalable and reliable quantum computing. However, the spacetime overhead required for fault-tolerant quantum computating remains prohibitively large. A critical challenge arises in many quantum algorithms with Clifford + $\varphi$ compiling, where logical rotation gates $R_{Z_L}(\varphi)$ serve as essential components. The Eastin-Knill theorem prevents their transversal implementation in quantum error correction codes and necessitating resource-intensive workarounds through T-gate compilation combined with magic state distillation and injection. In this work, we consider error-structure-tailored fault tolerance, where fault-tolerance conditions are analyzed by combining perturbative analysis of realistic dissipative noise processes with the structural properties of stabilizer codes. Based on this framework, we design 1-fault-tolerant continuous-angle rotation gates in stabilizer codes, implemented via dispersive-coupling Hamiltonians. Our approach could circumvent the need for T-gate compilation and distillation, offering a hardware-efficient solution that maintains simplicity, minimizes physical footprint, and requires only nearest-neighbor interactions. Integrating with recent small-angle-state preparation techniques, we can suppress the gate error to $91|\varphi| p^2$ for small rotation angle (where p denotes the physical error rate). For current achievable hardware parameters ($p=10^{-3}$), this enables reliable execution of over $10^7$ small-angle rotations when $|\varphi|\approx 10^{-3}$, meeting the requirements of many near-term quantum applications. Compared to the 15-to-1 magic state distillation and magic state cultivation approaches, our method reduces spacetime resource costs by factors of 1337.5 and 43.6, respectively, for a Heisenberg Hamiltonian simulation task under realistic hardware assumptions.

We prove that the PARITY protocol is optimal for a general class of non-adaptive distillation protocols of all $n$ player nonlocal boxes (NLBs) based on XOR games. The conditional distributions generated by these NLBs are assumed to have trivial local marginals. We also show that already for $n=2$, PARITY is no longer optimal if the local marginals are non-trivial. The OR protocol is shown to perform better and in the process also slightly extend the known correlations that collapse communication complexity. This emphasizes again the need to understand the local properties of nonlocal systems in order to obtain a better characterization of the global behavior. We conclude by showing an equivalence between adaptive distillation protocols that use identical NLBs and PARITY protocol using nonidentical NLBs.

This paper develops a unified framework for quantum wavelet shrinkage, extending classical denoising ideas into the quantum domain. Shrinkage is interpreted as a completely positive trace-preserving process, so attenuation of coefficients is carried out through controlled decoherence rather than nonlinear thresholding. Phase damping and ancilla-driven constructions realize this behavior coherently and show that statistical adaptivity and quantum unitarity can be combined within a single circuit model. The same physical mechanisms that reduce quantum coherence, such as dephasing and amplitude damping, are repurposed as programmable resources for noise suppression. Practical demonstrations implemented with Qiskit illustrate how circuits and channels emulate coefficientwise attenuation, and all examples are provided as Jupyter notebooks in the companion GitHub repository. Encoding schemes for amplitude, phase, and hybrid representations are examined in relation to transform coherence and measurement feasibility, and realizations suited to current noisy intermediate-scale quantum devices are discussed. The work provides a conceptual and experimental link between wavelet-based statistical inference and quantum information processing, and shows how engineered decoherence can act as an operational surrogate for classical shrinkage.

Ultrafast quantum matter experiments have validated predictions from Floquet theory - notably, the dynamical modification of the electronic band structure and the light-induced anomalous Hall effect, via monotonic modulation of the driving amplitude. Here, we demonstrate how new physics is uncovered by leveraging quantum optimal control techniques to design Floquet amplitude modulation profiles. We discover a fundamentally different regime of topological transport, whereby the optimal oscillatory preparation protocol functions as a non-adiabatic topological pump: as a result, ultrahigh time-averaged anomalous Hall conductivities emerge, that reach up to around seventy times the values one would expect from the Chern number of the targeted Floquet state. The optimal protocols achieve >99% fidelity at the topological energy gap closing point - a twenty-fold improvement over standard monotonic approaches in as little as ten Floquet cycles - while unexpectedly generating the predicted ultrahigh conductivities. Our findings demonstrate that optimally prepared non-equilibrium quantum states can access transport regimes not achievable in the corresponding equilibrium system or even by applying conventional Floquet approaches, opening new avenues for ultrafast quantum technologies and topological device applications.

Quantum sensors based on the nitrogen-vacancy (NV) center in diamond are leading platforms for high-sensitivity magnetometry with nanometer-scale resolution. State-of-the-art implementations, however, typically rely on bulky free-space optics or sacrifice spatial resolution to achieve high sensitivities. Here, we realize an integrated platform that overcomes this trade-off by fabricating monolithic whispering-gallery-mode cavities from a diamond chip containing a high density of NV centers and by evanescently coupling excitation to and photoluminescence from the cavity using a tapered optical fiber. Employing a lock-in-amplified Ramsey magnetometry scheme, we achieve a photon-shot-noise-limited DC sensitivity of $58\,\text{nT}/\sqrt{\text{Hz}}$—the best sensitivity reported to date for a nanofabricated cavity-based magnetometer. The microscopic cavity size enables micrometer-scale spatial resolution and low-power operation, while fiber-coupling provides a path to scalable on-chip integration. Arrays of such sensors could enable NV-NMR spectroscopy of sub-nanoliter samples, new magnetic-gradient imaging architectures, and compact biosensing platforms.

We investigate the emergence of an exciton condensate and associated collective modes in a bilayer configuration of $\text{MnBi}_2\text{Te}_4$, an antiferromagnetic topological insulator and van der Waals material, recognized for hosting axion physics. Utilizing a minimal low-energy Hamiltonian for the two layer system which is gapped by the intrinsic Néel order, we first employ mean-field theory to establish the conditions for exciton condensation. Our analysis identifies a nonzero, spin-singlet exciton order parameter which is tuned by external displacement field, temperature, and Coulomb attraction. Beyond the mean-field, we explore collective mode fluctuations in the uncondensed phase via many-body perturbation theory and the random phase approximation. From this, we derive the exciton spectral function which allows for a direct comparison between theoretical prediction and experimental observation. We detail how the softening of the collective mode peak is a function of the competition between interlayer detuning and thermal fluctuations. This work elucidates how the unique topological and magnetic environment of $\text{MnBi}_2\text{Te}_4$ offers a tunable platform for the realization and manipulation of exciton condensates and the corresponding collective excitations. Our findings contribute to understanding the interplay of topology and bosonic condensates, which could inspire application in optically accessing topological properties, dissipationless transport, and gate-tunable optoelectronics.

Timing and phase resolution in satellite QKD, kilometre-scale gravitational-wave detectors, and space-borne clock networks hinge on quantum-speed limits (QSLs), yet benchmarks omit relativistic effects for coherent and squeezed probes. We derive first-order relativistic corrections to the Mandelstam-Tamm and Margolus-Levitin bounds. Starting from the Foldy-Wouthuysen expansion and treating $-p^{4}/(8 m^{3} c^{2})$ as a harmonic-oscillator perturbation, we propagate Gaussian states to obtain closed-form QSLs and the quantum Cramér-Rao bound. Relativistic kinematics slow evolution in an amplitude- and squeezing-dependent way, increase both bounds, and introduce an $\epsilon^{2} t^{2}$ phase drift that weakens timing sensitivity while modestly increasing the squeeze factor. A single electron ($\epsilon \approx 1.5\times 10^{-10}$) in a $5.4\,\mathrm{T}$ Penning trap, read out with $149\,\mathrm{GHz}$ quantum-limited balanced homodyne, should reveal this drift within $\sim 15\,\mathrm{min}$ – within known hold times. These results benchmark relativistic corrections in continuous-variable systems and point to an accessible test of the quantum speed limit in high-velocity or strong-field regimes.

The Landau paradigm is a central dogma for understanding phase and phase transitions in condensed matter systems, yet for decades it has been known that a variety of quantum phases exist beyond the framework. Is there a more general framework that provides a systematic understanding of phase and phase transitions in quantum many-body systems? Recent developments of the notion of generalized symmetry and generalized gauging seem to point to a way to generalize the Landau Paradigm. In this essay, we discuss how `beyond Landau' phases and phase transitions can be captured by a generalized Landau paradigm in terms of the breaking of generalized symmetries, often induced by the generalized gauging procedure facilitated through the topological holography formalism. We also discuss what needs to be understood to make the generalized Landau paradigm useful in the study of quantum phase and phase transitions.

We consider the phase space of the Maxwell field as a simplified framework to study the quantisation of holonomies (Wilson line operators) on lightlike (null) surfaces. Our results are markedly different from the spacelike case. On a spacelike surface, electric and magnetic fluxes each form a commuting subalgebra. This implies that the holonomies commute. On a lightlike hypersurfaces, this is no longer true. Electric and magnetic fluxes are no longer independent. To compute the Poisson brackets explicitly, we choose a regularisation. Each path is smeared into a thin ribbon. In the resulting holonomy algebra, Wilson lines commute unless they intersect the same light ray. We compute the structure constants of the holonomy algebra and show that they depend on the geometry of the intersection and the conformal class of the metric at the null surface. Finally, we propose a quantisation. The resulting Hilbert space shows a number of unexpected features. First, the holonomies become anti-commuting Grassmann numbers. Second, for pairs of Wilson lines, the commutation relations can continuously interpolate between fermionic and bosonic relations. Third, there is no unique ground state. The ground state depends on a choice of framing of the underlying paths.

This work presents exact solutions of the Kemmer equation for spin-1 particles in $(1+1)$-dimensional Rindler spacetime, motivated by the need to understand vector bosons under uniform acceleration, including non-inertial effects and the Unruh temperature, which distinguish them from spin-0 and spin-1/2 systems. Starting from the free Kemmer field in an accelerated reference frame, we establish eigenvalue equations resembling those of the Klein–Gordon equation in Rindler coordinates. By introducing the Dirac oscillator interaction through a momentum substitution, we derive an exact closed-form spectrum for the Kemmer oscillator, revealing how the acceleration parameter modifies the characteristic length, shifts the discrete energy spectrum, and lifts degeneracies. In the Minkowski limit $a\to 0$, the standard Kemmer oscillator spectrum is recovered, ensuring consistency with flat-spacetime results. These findings provide a tractable framework for analyzing acceleration-induced effects, with implications for quantum field theory in curved spacetime, quantum gravity, and analogue gravity platforms.

In this work, we investigate the microlocal properties of the evolutions of Schrödinger equations using metaplectic Wigner distributions. So far, only restricted classes of metaplectic Wigner distributions, satisfying particular structural properties, have allowed the analysis of microlocal properties. We first extend the microlocal results to all metaplectic Wigner distributions, including the well-known Kohn-Nirenberg quantization, and examine these findings in the framework of Fourier integral operators with quadratic phase. Finally, we analyze the phase space concentration of the (cross) Wigner distribution arising from the interaction of two states, with particular attention to interactions generated by certain Schrödinger evolutions. These contributions enable a more refined study of the so-called ghost frequencies.

In this letter, we introduce a method to synthesize an $n$-qubit Clifford unitary $C$ from the stabilizer tableau of its inverse $C\dag$, using ancilla qubits and measurements. The procedure uses ancillary $|+\rangle$ states, controlled-Paulis, $X$-basis measurements and single-qubit Pauli corrections on the data qubits (based on the measurement results). This introduces a new normal form for Clifford synthesis, with the number of two-qubit gates required exactly equal to the weight of the stabilizer tableau, and a depth linear in $n$.

We develop an approach for understanding the dynamics of open quantum systems by analyzing individual quantum trajectories in the eigenbasis of the Liouvillian superoperator. From trajectory-eigenstate overlaps, we construct a quasiprobability distribution that characterizes the degree of localization of the trajectories in the Liouvillian eigenbasis. Contrary to the common wisdom that late-time dynamics are governed solely by the steady state and the slowest-decaying modes, we show that trajectories can remain well spread over transient eigenstates deep within the bulk of the Liouvillian spectrum even at late times. We demonstrate this explicitly using numerical simulations of interacting spin chains and bosonic systems. Moreover, we find that the delocalization of the trajectory strongly correlates with the purity of the trajectory-averaged steady state, establishing a further link between the trajectory and ensemble pictures of open quantum dynamics.

We investigate how detuning and auxiliary qubits collaboratively enhance quantum synchronization in a dissipative multi-qubit system that is coupled to a structured reservoir. Our findings indicate that while detuning is ineffective in Markovian environments, it emerges as a powerful control parameter in the non-Markovian regime, where environmental memory facilitates long-lived phase coherence. It is shown that adding more auxiliary qubits amplifies this effect by strengthening the collective coupling and enhancing memory, resulting in robust phase locking within the system. Analysis using the Husimi Q-function, synchronization measures, and Arnold tongue structures reveals a detuning-induced enhancement of phase locking, which significantly improves stability compared to the resonance case. These results establish a cooperative control strategy where detuning actively engineers phases, while auxiliary qubits provide the necessary memory for sustained synchronization.

Absorption spectroscopy is a fundamental tool for probing molecular structure. However, performing absorption spectroscopy on individual molecules is challenging due to the low signal-to-noise ratio. Here, we report on a nondestructive absorption spectroscopy on a mid-infrared vibrational transition in a single molecular ion that is co-trapped with an atomic ion. The absorption of a single photon is detected via the momentum transfer from the absorbed photon onto the molecule. This recoil signal is amplified using a non-classical state of motion of the two-ion crystal and subsequently read out via the atomic ion. We characterize the recoil detection method and use it to investigate the interaction between femtosecond laser pulses and the O-H stretching vibration in individual CaOH+ molecular ions. Furthermore, we present the single-photon absorption spectrum obtained for the vibrational transition. This method represents a milestone towards quantum non-demolition measurements of complex polyatomic molecules, providing high-fidelity methods for preparation and measurement of the quantum state of a wide range of molecular species.