Papers

Manifesting across all time, mass and length scales, nonlinearities lie at the core of numerous physical phenomena. Next-generation quantum applications, such as quantum sensing, require the combination of nonlinearity with non-classical correlations. This necessitates the search for an experimental platform which enables a nonlinear response at ultra-low excitation levels in a system with practical sensing potential and quantum compatibility. Here, we report the observation and theoretical modeling of nonlinear dynamics in a mechanical system driven at the single-excitation level. We achieve this using a cavity-optomechanical platform with large single-photon coupling rates and a nonlinear microwave resonator. Specifically, the large Kerr nonlinearity of our superconducting microwave circuit reduces the threshold for the observation of nonlinear dynamics by four orders of magnitude, making this regime experimentally accessible at the few-photon level. The parameter-based quantitative predicative power of the theoretical description underlines our deep understanding of the physics involved and that this device concept paves the way for experiments with non-classical microwave drive schemes.

The most elementary non-Hermitian quantum square-well problem with real spectrum is considered. The Schroedinger equation is required discrete and endowed with PT-symmetric Robin (i.e., two-parametric) boundary conditions. Some of the rather enigmatic aspects of impact of the variability of the parameters on the emergence of the Kato's exceptional-point (EP) singularities is clarified. In particular, the current puzzle of the apparent absence of the EP degeneracies at the odd-matrix dimensions in certain simplified one-parametric cases is explained. A not quite expected existence of a multi-band spectral structure in another simplified one-parametric family of models is also revealed.

We present a method to extract the photon indistinguishability error from Hong-Ou-Mandel interference measurements, accounting for the combined effects of loss and multiphoton noise that contaminate the single-photon Hilbert space. Our analysis resolves apparent inconsistencies in previous interpretations of such measurements. The reported method applies to a wide range of single-photon sources, including quantum dots.

Quantum Phase Estimation (QPE) is a cornerstone algorithm for fault-tolerant quantum computation, especially for electronic structure calculations of chemical systems. Optimal simulation relies on a complex trade-offs across many parameters including Hamiltonian simulation techniques, basis sets, and the fermion-to-qubit encodings. Here, we characterize the trade-offs and quantify the quantum resource costs of the sorted-list encoding as a particle-conserving, low-qubit alternative to the Jordan-Wigner encoding. We identify specific regimes, across different simulation techniques and basis sets, where the sorted-list encoding would be favorable compared to existing methods. Our findings are further supported through numerical benchmarks of real-world chemical systems. We found the sorted-list encoding to be a viable alternative to the Jordan-Wigner encoding for the compact molecular orbital basis when the electron-filling ratio is low, which typically occurs when high-precision results are required. In the plane-wave basis, we found similar asymptotic gate and qubit scaling between the sorted-list and the first-quantized encoding, although the first-quantized encoding still retains lower constant factors.

We investigate how much quantum distributed algorithms can outperform classical distributed algorithms with respect to the message complexity (the overall amount of communication used by the algorithm). Recently, Dufoulon, Magniez and Pandurangan (PODC 2025) have shown a polynomial quantum advantage for several tasks such as leader election and agreement. In this paper, we show an exponential quantum advantage for a fundamental task: routing information between two specified nodes of a network. We prove that for the family of “welded trees" introduced in the seminal work by Childs, Cleve, Deotto, Farhi, Gutmann and Spielman (STOC 2003), there exists a quantum distributed algorithm that transfers messages from the entrance of the graph to the exit with message complexity exponentially smaller than any classical algorithm. Our quantum algorithm is based on the recent "succinct" implementation of quantum walks over the welded trees by Li, Li and Luo (SODA 2024). Our classical lower bound is obtained by “lifting” the lower bound from Childs, Cleve, Deotto, Farhi, Gutmann and Spielman (STOC 2003) from query complexity to message complexity.

A key technical requirement of any future quantum network is the ability to distribute quantum-entangled resources between two spatially separated points at a high rate and high fidelity. Entanglement distribution protocols based on satellite platforms, which transmit and receive quantum resources directly via free-space optical propagation, are therefore excellent candidates for quantum networking, since the geometry and loss characteristics of satellite networks feasibly allow for up to continental-scale ($\sim10^3$ km) over-the-horizon communication without the infrastructure, cost, or losses associated with equivalent fibre-optic networks. In this work, we explore two network topologies commonly associated with quantum networks - entanglement distribution between two satellites in low-Earth orbit mediated by a third satellite and entanglement distribution between two ground stations mediated by a satellite in low-Earth orbit, and two entanglement distribution schemes - one where the central satellite is used as a relay, and the other where the central satellite is used to generate and distribute the entangled resource directly. We compute a bound on the rate of distribution of distillable entanglement achieved by each protocol in each network topology as a function of the network channels for both single-rail discrete- (DV) and continuous-variable (CV) resources and use or non-use of probabilistic noiseless linear quantum amplification (NLA). In the case of atmospheric channels we take into account the turbulent and optical properties of the free-space propagation. We determine that for the triple-satellite network configuration, the optimal strategy is to perform a distributed NLA scheme in either CV or DV, and for the ground-satellite-ground network the optimal strategy is to distribute a DV resource via the central satellite.

In quantum theory on curved backgrounds, Heisenberg's uncertainty principle is usually discussed in terms of ensemble variances and flat-space commutators. Here we take a different, preparation-based viewpoint tailored to sharp position measurements on spacelike hypersurfaces in general relativity. A projective localization is modeled as a von Neumann-Lüders projection onto a geodesic ball $B_\Sigma(r)$ of radius $r$ on a Cauchy slice $(\Sigma,h)$, with the post-measurement state described by Dirichlet data. Using DeWitt-type momentum operators adapted to an orthonormal frame, we construct a geometric, coordinate-invariant momentum standard deviation $\sigma_p$ and show that strict confinement to $B_\Sigma(r)$ enforces an intrinsic kinetic-energy floor. The lower bound is set by the first Dirichlet eigenvalue $\lambda_1$ of the Laplace-Beltrami operator on the ball, $\sigma_p \ge \hbar\sqrt{\lambda_1}$, and is manifestly invariant under changes of coordinates and foliation. A variance decomposition separates the contribution of the modulus $|\psi|$ from phase-gradient fluctuations and clarifies how the spectral geometry of $(\Sigma,h)$ controls momentum uncertainty. Assuming only minimal geometric information, weak mean-convexity of the boundary yields a universal, scale-invariant Heisenberg-type product bound, $\sigma_p r \ge \pi\hbar/2$, depending only on the proper radius $r$.

We study symmetry preserving adiabatic and Floquet dynamics of one-dimensional systems. Using quasiadiabatic evolution, we establish a correspondence between adiabatic cycles and invertible defects generated by spatially truncated Thouless pump operators. Employing the classification of gapped phases by module categories, we show that the Thouless pumps are classified by the group of autoequivalences of the module category. We then explicitly construct Thouless pump operators for minimal lattice models with $\text{Vec}_G$, Rep($G$), and Rep($H$) symmetries, and show how the Thouless pump operators have the group structure of autoequivalences. The Thouless pump operators, together with Hamiltonians with gapped ground states, are then used to construct Floquet drives. An analytic solution for the Floquet phase diagram characterized by winding numbers is constructed when the Floquet drives obey an Onsager algebra. Our approach points the way to a general connection between distinct Thouless pumps and distinct families of Floquet phases.

We present a sample- and time-efficient algorithm to learn any bosonic Fock state acted upon by an arbitrary Gaussian unitary. As a special case, this algorithm efficiently learns states produced in Fock state BosonSampling, thus resolving an open question put forth by Aaronson and Grewal (Aaronson, Grewal 2023). We further study a hierarchy of classes of states beyond Gaussian states that are specified by a finite number of their higher moments. Using the higher moments, we find a full spectrum of invariants under Gaussian unitaries, thereby providing necessary conditions for two states to be related by an arbitrary (including active, e.g. beyond linear optics) Gaussian unitary.

We investigate quantum thermometry using a single-qubit probe embedded in a non-Markovian environment, employing the numerically exact hierarchical equations of motion (HEOM) to overcome the limitations of Born-Markov approximations. Through a systematic analysis of the dynamical and steady-state behavior of the quantum signal-to-noise ratio (QSNR) for temperature estimation, we identify several key findings that challenge the conventional expectation that strong coupling necessarily enhances thermometric performance. In non-equilibrium dynamical thermometry, weak system-environment coupling generally yields the optimal QSNR, whereas in the steady-state regime, strong coupling enhances sensitivity only in the ultra-low-temperature limit, while weak coupling significantly improves precision at moderately low temperatures. To optimize performance across coupling regimes, we develop a hybrid computational framework that integrates HEOM with quantum-enhanced particle swarm optimization, enabling precise quantum dynamical control under varying coupling strengths. Our results reveal fundamental constraints and opportunities in quantum thermometry, offering practical strategies for the design of high-performance quantum thermometers operating in realistic open quantum systems.

We derive analytical results for continuous-time quantum walks from a new class of initial states with tunable delocalization. The dynamics are governed by a Hamiltonian with complex hopping amplitudes. We provide closed-form equations for key observables, revealing three notable findings: (1) the emergence of directed quantum transport from completely unbiased initial conditions; (2) a quantum backfire effect, where greater initial delocalization enhances short-time spreading but counterintuitively induces a comparatively smaller long-time spreading after a crossing time $t_{\mathrm{cross}}$; and (3) an exact characterization of survival probability, showing that the transition to an enhanced $t^{-3}$ decay is a fine-tuned effect. Our work establishes a comprehensive framework for controlling quantum transport through the interplay between intermediate initial delocalization and Hamiltonian phase.

We study the problems of state preparation, ground state preparation and quantum state preparation. We propose an analytic approach to a stochastic quantum algorithm which prepares the ground state for $n$-qubit Hamiltonian that is represented by $\text{poly}(n)$ Pauli operators and has an inverse-polynomial gap, requiring only $\text{poly}(n)$ Pauli rotations, measurements, and classical time complexity when $n$ exceeds a threshold, to inverse-polynomial precision given the initial overlap being lower bounded by $\frac{1}{2^n}$. Extending this result, we prove that any $n$-qubit quantum state can be prepared in two regimes: (1) with a constant number of Pauli rotations to constant precision, or (2) with a polynomial number of rotations to inverse-polynomial precision. Our results improve over previous approaches to quantum state preparation in terms of gate complexity, thereby yielding quantum space advantage. As an application, we identify a practical condition under which quadratic unconstrained binary optimization (QUBO) problems can be solved with exponential quantum speedups.

We present the design and characterization of a cryogenic vacuum chamber incorporating mechanical isolation from vibrations, a high numerical-aperture in-vacuum imaging objective, in-vacuum magnetic shielding, and an antenna for global radio-frequency manipulation of trapped ions. The cold shield near 4 K is mechanically referenced to an underlying optical table via thermally insulating supports and exhibits root-mean-square vibrations less than 7.61(4) nm. Using the in-vacuum objective, we can detect 397 nm photons from a trapped $^{40}\mathrm{Ca}^{+}$ ion with 1.77% efficiency and achieve 99.9963(4)% single-shot state-detection fidelity in 50 $\mu$s. To characterize the efficacy of the magnetic shields, we perform Ramsey experiments on the ground state qubit and obtain a coherence time of 24(2) ms, which extends to 0.25(1) s with a single spin-echo pulse. XY4 and XY32 dynamical decoupling sequences driven via the radio-frequency antenna extend the coherence to 0.72(2) s and 0.81(3) s, respectively.

Competition between short- and long-range interactions underpins many emergent phenomena in nature. Despite rapid progress in their experimental control, computational methods capable of accurately simulating open quantum many-body systems with complex long-ranged interactions at scale remain scarce. Here, we address this limitation by introducing an efficient and scalable approach to dissipative quantum lattices in one and two dimensions, combining matrix product operators and time-dependent variational Monte Carlo. We showcase the versatility, effectiveness, and unique methodological advantages of our algorithm by simulating the non-equilibrium dynamics and steady states of spin-$\frac{1}{2}$ lattices with competing algebraically-decaying interactions for as many as $N=200$ sites, revealing the emergence of spatially-modulated magnetic order far from equilibrium. This approach offers promising prospects for advancing our understanding of the complex non-equilibrium properties of a diverse variety of experimentally-realizable quantum systems with long-ranged interactions, including Rydberg atoms, ultracold dipolar molecules, and trapped ions.