We investigate strategies for reaching the ultimate limit on the precision of frequency estimation when the number of probes used in each run of the experiment is fixed. That limit is set by the quantum Cramér-Rao bound (QCRB), which predicts that the use of maximally entangled probes enhances the estimation precision, when compared with the use of independent probes. However, the bound is only achievable if the statistical model used in the estimation remains identifiable throughout the procedure. This in turn sets different limits on the maximal sensing time used in each run of the estimation procedure, when entangled and independent probes are used. When those constraints are taken into account, one can show that, when the total number of probes and the total duration of the estimation process are counted as fixed resources, the use of entangled probes is, in fact, disadvantageous when compared with the use of independent probes. In order to counteract the limitations imposed on the sensing time by the requirement of identifiability of the statistical model, we propose a time-adaptive strategy, in which the sensing time is adequately increased at each step of the estimation process, calculate an attainable error bound for the strategy, and discuss how to optimally choose its parameters in order to minimize that bound. We show that the proposed strategy leads to much better scaling of the estimation uncertainty with the total number of probes and the total sensing time than the traditional fixed-sensing-time strategy. We also show that, when the total number of probes and the total sensing time are counted as resources, independent probes and maximally entangled ones have now the same performance, in contrast to the nonadaptive strategy, where the use of independent is more advantageous than the use of maximally entangled ones.

Dissipative state engineering is a general term for a protocol which prepares the ground state of a complex many-body Hamiltonian using engineered dissipation or engineered environments. Recently, it was shown that a version of this protocol, where the engineered environment consists of one or more dissipative qubit ancillas tuned to be resonant with the low-energy transitions of a many-body system, resulted in the combined system evolving to reasonable approximation to the ground state. This potentially broadens the applicability of the method beyond nonfrustrated systems, to which it was previously restricted. Here we argue that this approach has an intrinsic limitation because the ancillas, seen as an effective bath by the system in the weak-coupling limit, do not give the detailed balance expected for a true zero-temperature environment. Our argument is based on the study of a similar approach employing linear coupling to bosonic ancillas. We explore overcoming this limitation using a recently developed open quantum systems technique called pseudomodes. With a simple example model of a one-dimensional quantum Ising chain, we show that detailed balance can be fixed, and a more accurate estimation of the ground state obtained, at the cost of two additional unphysical dissipative modes and the extrapolation error of implementing those modes in physical systems.

Two-particle response functions are a centerpiece of both experimental and theoretical quantum many-body physics. Yet, due to their size and discontinuity structure, they are challenging to handle numerically. Recently, two advances were made to tackle this problem: first, the overcomplete intermediate representation (OIR), which provides a highly efficient compression of Green's functions in imaginary frequency, and second, partial spectral functions (PSFs), which allow for an efficient evaluation in real frequency. We show that there is a two-to-one correspondence between PSFs and OIR coefficients and exploit this fact to construct the OIR for three-or-more-particle propagators. We then use OIR to fit and compress imaginary-frequency data obtained from the numerical renormalization group (NRG), reaching a compression ratio of more than 400. Finally, we attempt to match the OIR data to partial Green's functions from NRG. Due to the overcompleteness, we achieve only qualitative agreement.

Due to the linearity of quantum operations, it is not straightforward to implement nonlinear transformations on a quantum computer, making some practical tasks like a neural network hard to achieve. In this paper, we define a task called nonlinear transformation of complex amplitudes and provide an algorithm to achieve this task. Specifically, we construct a block encoding of complex amplitudes from a state preparation unitary. This allows us to transform the complex amplitudes by using quantum singular value transformation. We evaluate the required overhead in terms of input dimension and precision, which reveals that the algorithm depends on the roughly square root of input dimension and achieves an exponential speedup on precision compared with previous work. We also discuss its possible applications to quantum machine learning, where complex amplitudes encoding classical or quantum data are processed by the proposed method. In this paper, we provide a promising way to introduce the highly complex nonlinearity of the quantum states, which is essentially missing in quantum mechanics.

Multiphoton dynamics beyond linear optical materials are of significant fundamental and technological importance in quantum information processing. However, it remains largely unexplored in nonlinear waveguide QED. In this work, we theoretically propose a structured nonlinear waveguide in the presence of staggered photon-photon interactions, which supports two branches of gaped bands for doublons (i.e., spatially bound-photon-pair states). In contrast to linear waveguide QED systems, we identify two important contributions to its dynamical evolution, i.e., single-photon bound states (SPBSs) and doublon bound states (DBSs). Most remarkably, the nonlinear waveguide can mediate the long-range four-body interactions between two emitter pairs, even in the presence of disturbance from SPBSs. By appropriately designing system's parameters, we can achieve high-fidelity four-body Rabi oscillations mediated only by virtual doublons in DBSs. Our findings pave the way for applying structured nonlinear waveguide QED in multi-body quantum information processing and quantum simulations among remote sites.

We report high-accuracy calculations of the ground and the lowest eight excited ${}^{2}P^o$ states of the two stable isotopes of the boron atom, ${}^{10}\mathrm{B}$ and ${}^{11}\mathrm{B}$, as well as of the boron atom with an infinite nuclear mass ${}^{\infty }\mathrm{B}$. The nonrelativistic wave function of each of the states is generated in an independent variational calculation by expanding it in terms of a large number, $12000–17000$, of all-electron explicitly correlated Gaussian (ECG) functions whose nonlinear parameters are extensively optimized with a procedure that employs analytic energy gradient determined with respect to these parameters. These highly accurate wave functions are used to compute the fine-structure splittings using the first order of the perturbation theory $(\sim {\alpha }^2)$, where $\alpha$ is the fine-structure constant, which are then corrected for the electron magnetic moment anomaly $(\sim {\alpha }^3)$. As the nonrelativistic Hamiltonian explicitly depends on the mass of the nucleus, the recoil corrections up to the order of ${\alpha }^2$ are automatically accounted for in the fine-structure calculations. Furthermore, the off-diagonal corrections to the fine structure $(\sim {\alpha }^4)$ are estimated using the multireference methods based on one-electron Gaussian orbitals. The results obtained in this paper are considerably more accurate than those available in the literature. Moreover, we report accurate splittings for a number of excited ${}^{2}P^o$ states, for which there have been no reliable experimental or theoretical data at all. The calculated values presented in this paper may serve as a valuable guide for future experimental measurements of the fine structure of the boron atom. As the fine structure of an atom provides a spectral signature that can facilitate atom's detection, our data can also aid the search for trace amounts of boron in the interstellar medium.

Quantum diffusion of hydrogen (H) on palladium (Pd) (111) was studied using two types of path integral simulations: quantum transition state theory (QTST) and ring polymer molecular dynamics (RPMD). The use of an artificial neural network potential trained by density functional theory calculations has made it feasible to perform path integral simulations considering nuclear quantum effects (NQEs) of a many-body Pd-H system with ab initio accuracy. The QTST result has shown a clear non-Arrhenius behavior in the diffusion coefficient $\left(D\right)$ of H below the temperature of 150–200 K due to the NQEs. Comparing the $D$ on Pd surface and bulk Pd, it was found that surface and bulk diffusion are competitive at high temperature. Consistent with this, it was observed in the RPMD simulation at 800 K that a part of the quantum trajectories of H on the surface bifurcates to the Pd subsurface. As the temperature decreases, the surface diffusion becomes much faster than the bulk diffusion. Furthermore, distinct quantum behaviors of H were identified at the surface and within the bulk. The $D$ values obtained from this study using a “flexible” Pd surface model differed considerably from those previously reported using “frozen” Pd surface models, indicating an important contribution from Pd vibrations coupled with H diffusion.

In this work we present an improved analysis for decoy-state methods, enhancing both achievable key rates and recovering analytical results for the single intensity scenario. Our primary focus is improving the shortcomings observed in current decoy-state methods, in particular recovering results when employing no decoy intensities. Our methods enable the continuous interpolation across varying numbers of intensity settings. Additionally, we extend decoy-state techniques to encompass scenarios where intensities vary depending on the signal state, thereby relaxing the constraints on experimental implementations. Our findings demonstrate that a minimum of one decoy intensity is sufficient for high asymptotic secret key rates, thereby further softening experimental requirements. We also address inherent imperfections within detection setups like imperfect beamsplitters. We derive provable secure lower bounds on the subspace population estimation, which is required for certain squashing methods such as the flag-state squasher. These analytical bounds allow us to encompass arbitrary passive linear optical setups and, together with intensities varying with each signal state, let us include a broad class of experimental setups.

Giant atoms are quantum emitters that can couple to light at multiple discrete points. Such atoms have been shown to interact without decohering via a one-dimensional waveguide. Here, we study how giant atoms behave when coupled to a two-dimensional square lattice of coupled cavities, an environment characterized by a finite-energy band and band gaps. In particular, we describe the role that bound states in the continuum (BICs) play in how giant atoms avoid decoherence. By developing numerical methods, we are able to investigate the dynamics of the system and show the appearance of interfering BICs within a single giant atom, as well as oscillating BICs between many giant atoms. In this way, we find the geometric arrangements of atomic coupling points that yield protection from decoherence in the two-dimensional lattice. These results on engineering the interaction between light and matter may find applications in quantum simulation and quantum information processing.

Group twirling is crucial in quantum information processing, particularly in randomized benchmarking and randomized compiling. While protocols based on Pauli twirling have been effectively crafted to transform arbitrary noise channels into Pauli channels for Clifford gates—thereby facilitating efficient benchmarking and mitigating worst-case errors—the lack of practical twirling groups for multiqubit non-Clifford gates remains a challenge. To address this gap, we study the issue of finding twirling groups for generic quantum gates, focusing on a widely used circuit structure in randomized benchmarking or randomized compiling. Specifically, for multiqubit controlled phase gates, which are essential in quantum algorithms and directly implementable in practice, we determine optimal twirling groups within the realm of classically replaceable unitary operations. Contrasting with the local Pauli twirling group for Clifford gates, the optimal groups for such gates contain nonlocal operations, highlighting the overhead of tailoring noise in global non-Clifford contexts. We design new benchmarking procedures for multiqubit controlled phase gates based on the optimal twirling groups. Our simulation results show that our scheme can improve the precision and accuracy of benchmarking in small-scale systems.

Materials that exhibit ferroaxial order hold potential for novel multiferroic applications. However, in pure ferroaxials, domains are not directly coupled to stress or static electric field due to their symmetry, limiting the ability to pole and switch between domains—features required for real-world applications. Here we propose a general approach to selectively condense and switch between ferroaxial domains with light. We show that circularly polarized light pulses on resonance with infrared-active phonons manifest helicity-dependent control over ferroaxial domains. Nonlinear contributions to the lattice polarizability play an essential role in this phenomenon. We illustrate the feasibility of our approach using first-principles calculations and dynamical simulations for the archetypal ferroaxial material $\mathrm{RbFe}{\left({\mathrm{MoO}}_4\right)}_2$. Our results are discussed in the context of future pump-probe optical experiments, where polarization, carrier frequency, and fluence threshold are explored.

Compositional structure of host-associated microbiomes is potentially affected by interactions among the microbes and between the microbes and the host. To quantify the relative importance of these contributions to the microbiome composition and variation, here we analyze absolute abundance (count) data for a minimal eight-species native microbiome in the Caenorhabditis elegans intestine. We find that a simple neutral model only considering migration, birth, death, and competition for space among the bacteria can capture the means and variances of bacterial abundance, but not the experimental bacteria-bacteria covariances. We find that either bacteria-bacteria interactions or correlations among bacterial population dynamics parameters induced by the host can qualitatively recapitulate the observed correlations among bacterial taxa. However, both models are underdetermined and not unique, and the combination of both mechanisms likely contributes. This highlights that single time-point measurements on their own are not sufficient to distinguish between two distinct biological mechanisms. Further, we observe that different interactions are required to explain (co)variance data in microbiota associated with different host genotypes, suggesting different community dynamics associated with these host types. Finally, we find that many of these signals are obscured when data are converted to proportions from counts, consistent with a growing literature on the limitations of compositional data for inference of population dynamics. We end with a discussion of the limitations of Lotka-Volterra type assumptions for microbial community data analysis revealed by our results.

The supersymmetric connection that exists between the Jaynes-Cummings (JC) and anti-Jaynes Cummings (AJC) models in quantum optics is unraveled entirely. A new method is proposed to obtain the temporal evolution of observables in the AJC model using supersymmetric techniques, providing an overview of its dynamics and extending the calculation to full photon counting statistics. The approach is general and can be applied to determine the high-order cumulants given an initial state. The analysis reveals that engineering the collapse-revival behavior and the quantum properties of the interacting field is possible by controlling the initial state of the atomic subsystem and the corresponding atomic frequency in the AJC model. The substantial potential for applications of supersymmetric techniques in the context of photonic quantum technologies is thus demonstrated.

Understanding deaths and life-death boundaries of cells is a fundamental challenge in biological sciences. In this study, we present a theoretical framework for investigating cell death. We conceptualize cell death as a controllability problem within dynamical systems, and compute the life-death boundary through the development of “stoichiometric rays.” This method utilizes enzyme activity as control parameters, exploiting the inherent property of enzymes to enhance reaction rates without affecting thermodynamic potentials. This approach facilitates the efficient evaluation of the global controllability of models. We demonstrate the utility of our framework using its application to a toy metabolic model, where we delineate the life-death boundary. The formulation of cell death through mathematical principles provides a foundation for the theoretical study of cellular mortality.

In scenarios coined Maxwell's demon, information on microscopic degrees of freedom is used to seemingly violate the second law of thermodynamics. This has been studied in the classical as well as the quantum domain. In this paper, we study an implementation of Maxwell's demon that can operate in both domains. In particular, we investigate information-to-work conversion over the quantum-to-classical transition. The demon continuously measures the charge state of a double quantum dot and uses this information to guide electrons against a voltage bias by tuning the on-site energies of the dots. Coherent tunneling between the dots allows for the buildup of quantum coherence in the system. Under strong measurements, the coherence is suppressed, and the system is well-described by a classical model. As the measurement strength is further increased, the Zeno effect prohibits interdot tunneling. A Zeno-like effect is also observed for weak measurements, where measurement errors lead to fluctuations in the on-site energies, dephasing the system. We anticipate similar behaviors in other quantum systems under continuous measurement and feedback control, making our results relevant for implementations in quantum technology and quantum control.

Nonlinear processes with individual quanta beyond bilinear interactions are essential for quantum technology with bosonic systems. Diverse coherent splitting and merging of quanta in them already manifest in the estimation of their nonlinear coupling from observed statistics. We derive nontrivial but optimal strategies for sensing the experimentally feasible trilinear interactions, served here as basic gates and examples of multimode nonlinear interactions, using nonclassical particlelike Fock states as a probe and feasible measurement strategies. Remarkably, the optimal probing of nonlinear coupling reaches estimation errors scaled down with $N^{-3/2}$ for overall $N$ of quanta in specific and high-quality Fock states in all interacting modes. It can reveal unexplored aspects of nonlinear dynamics relevant to using such nonlinear processes in bosonic experiments with trapped ions and superconducting circuits and opens further developments of quantum technology with them.

We employ quantum state discrimination theory to establish the ultimate limit for spoofing detection in electromagnetic signals encoded with random quantum states. Our analysis yields an analytical expression for the optimal bound, which we prove can be achieved using a pair of coherent states. Notably, the quantum enhancement persists regardless of photon number, thereby removing the previous constraint to single-photon sources. This breakthrough unlocks new experimental possibilities using standard laser sources. Furthermore, we explore the encoding of squeezed states and demonstrate that the detection probability approaches 100% when the spoofer's capability is restricted to coherent-state generation.