Here we show that shadow tomography can generate an efficient and exact ansatz for the many-fermion wave function on quantum devices. We derive the shadow ansatz—a product of transformations applied to the mean-field wave function—by exploiting a critical link between measurement and preparation. Each transformation is obtained by measuring a classical shadow of the residual of the contracted Schrödinger equation (CSE), the many-electron Schrödinger equation (SE) projected onto the space of two electrons. We show that the classical shadows of the CSE vanish if and only if the wave function satisfies the SE and, hence, that randomly sampling only the two-electron space yields an exact ansatz regardless of the total number of electrons. We demonstrate the ansatz's advantages for scalable simulations—fewer measurements and shallower circuits—by computing ${\mathrm{H}}_3$ on simulators and a quantum device.

We study the time-optimal robust control of a two-level quantum system subjected to field inhomogeneities. We apply the Pontryagin maximum principle and we introduce a reduced space onto which the optimal dynamics is projected down. This reduction leads to a complete analytical derivation of the optimal solution in terms of elliptic functions and elliptic integrals. Necessary optimality conditions are then obtained for the original system. These conditions are verified numerically and lead to the optimal control protocol. Various examples, ranging from state-to-state transfer to the generation of a NOT gate, illustrate this study. The connection with other geometric optimization approaches that have been used to solve this problem is also discussed. Finally, we show how this method can be combined with numerical optimization algorithms to design robust control for higher-dimensional quantum systems, as illustrated by a Bose-Einstein condensate in an optical lattice.

The fragmentation dynamics of $\mathrm{NC}\mathrm{C}{\mathrm{N}}^{2+}\mathrm{and}{\mathrm{NCCN}}^{3+}$ produced by 1-keV electron impact have been investigated using the ion momentum imaging technique. Five two-body and two three-body fragmentation channels are identified including two isomerization pathways. The reaction coordinates of isomerization channels were investigated by quantum chemistry calculation. By measuring the momentum vectors of the fragment ions, the kinetic energy release distributions have been determined. With the help of the Dalitz plot, Newton diagram, and native-frame method, we investigated the fragmentation mechanisms of the three-body fragmentation channels. It is found that the channel ${\mathrm{NCCN}}^{3+}\to {\mathrm{N}}^{+}+{\mathrm{N}}^{+}+{\mathrm{C}}_2^{+}$ only dissociates via the concerted mechanism, while channel ${\mathrm{NCCN}}^{3+}\to {\mathrm{C}}^{+}+{\mathrm{N}}^{+}+{\mathrm{CN}}^{+}$ presents two sequential fragmentation processes with $\mathrm{C}{\mathrm{N}}^{2+}$ and ${\mathrm{C}}_2{\mathrm{N}}^{2+}$ as intermediate moieties in addition to the concerted fragmentation.

In the theoretical study of electron-molecule collisions, resonant processes such as vibrational excitation and dissociative electron attachment and recombination are difficult to model due to the breakdown of common techniques such as the adiabatic-nuclei approximation. For this reason, it is useful to have an exactly solvable model so that the validity of different theories can be tested, such as the two-dimensional model introduced by Houfek et al. [Phys. Rev. A 73, 032721 (2006)] and extended to charged targets by Hvizdoš et al. [Phys. Rev. A 97, 022704 (2018)]. We have applied the convergent close-coupling method, a well-established approach for solving a variety of scattering problems, to this two-dimensional model problem. Dissociative attachment and recombination are treated within the same formalism, and the direct and resonant contributions to vibrational excitation are both fully accounted for as a result of solving the close-coupling equations. To accurately model these processes at all energies, the two-center approach is used, in which the states of the dissociated fragments are explicitly included in the expansion of the wave function of the scattering system. Cross sections for vibrational excitation, dissociative attachment, and direct dissociation are calculated for NO-like and ${\mathrm{F}}_2$-like targets, and excellent agreement is found with existing results. Cross sections for vibrational excitation and dissociative recombination are calculated for a ${\mathrm{H}}_2^{+}$-like target, and despite challenges with modeling the many resonances of the cross section, we find reasonably good agreement with existing results.

In this work, we formulate the problem of achieving in minimum time perfect chiral resolution with bounded control fields as an optimal control problem on two noninteracting spins $1/2$. We assume the same control bound for the two Raman fields (pump and Stokes) and a different bound for the field directly connecting the two lower-energy states. Using control theory, we show that the optimal fields can only take the boundary values or be zero, with the latter corresponding to singular control. Subsequently, using numerical optimal control and intuitive arguments, we identify some three-stage symmetric optimal pulse sequences for relatively large values of the ratio between the two control bounds and analytically calculate the corresponding pulse timings as a function of this ratio. For smaller values of the bound ratio, numerical optimal control indicates that the optimal pulse sequence loses its symmetry and the number of stages increases in general. In all cases, the analytical or numerical optimal protocol achieves a faster perfect chiral resolution than other pulsed protocols, mainly because of the simultaneous action of the control fields. The present work is expected to be useful in the wide spectrum of applications across the natural sciences in which enantiomer separation is a crucial task.

The simulation of vibrational energy transport and quantum thermodynamics with trapped ions requires good methods for the estimation of temperatures. One valuable tool for this purpose is based on the fit of dark resonances in the fluorescence spectrum. However, this fit demands numerical simulations of the coupled electronic-motional dynamics which usually involve a trade-off between accuracy and speed. Here, we discuss several techniques with simplified dynamical equations for the simulation of the spectrum of a trapped ion that undergoes thermal motion, identifying the advantages and limitations of each method. We start with a three-level model to provide a better insight into the approximations involved, and then move on to tackle the experimentally relevant case of an eight-level calcium ion. We observe that mimicking the effect of thermal motion by means of additional dephasing is computationally very convenient, but can lead to significant errors in the estimation of the temperature. Nevertheless, this can be counteracted by a proper calibration, supporting the use of dark resonances as a practical thermometer.

We propose an efficient method for dissipative generation of magnonic cat states in a cavity-magnon-qubit hybrid system by exploiting a two-magnon driving and dissipation mechanism. When both the magnon and qubit are driven, a coherent nonlinear two-magnon interaction is induced, wherein the qubit and the magnon mode exchange energy through magnon pairs. The dissipation of the qubit is exploited to steer the magnon mode into a quantum superposition of distinct coherent states, where the magnon mode evolves into either an even or odd cat state, depending on the parity of the magnon initial state. For the case where the magnon initial state is a superposition state, e.g., of $|0\rangle$ and $|1\rangle$, the magnon mode can evolve into a weighted mixture of the even and odd cat states. We also find that magnon squeezed states may emerge during the short-time evolution, showcasing the capability of our mechanism in preparing diverse magnon nonclassical states. Magnonic cat and squeezed states are macroscopic quantum states and have applications in macroscopic quantum studies and quantum sensing, e.g., in the dark-matter search using ferromagnetic axion haloscopes.

Noiseless quantum amplifiers are probabilistic quantum devices that enhance the amplitude of coherent states without adding any noise, which has far reaching applications in quantum optics and quantum information processing. Here, we report on an experimental implementation of an advanced noiseless quantum amplifier for coherent states of light that is based on the conditional addition of two photons followed by the conditional subtraction of two photons. We comprehensively characterize the noiselessly amplified coherent states via quantum state tomography and analyze the amplification gain and noise properties of the amplifier. We observe very good agreement between the experiment and theoretical predictions. Our work reveals that sequences of multiple photon additions and subtractions represent an efficient and experimentally feasible alternative to multiplexing that was originally proposed to boost the performance of noiseless quantum amplifiers. Beyond noiseless quantum amplification, our experiment represents a significant step forward towards engineering complex quantum operations on traveling light beams by coherent combinations of various sequences of multiphoton additions and subtractions.

We analytically derive transfer probabilities and efficiencies for an artificial light-harvesting photosynthetic system, which consists of a ring coupled to a central acceptor. For an incident photon pair, we find near-perfect single excitation transfer efficiency with negligible double excitation transfer in the weak-coupling regime. In the strong-coupling regime, single excitation transfer efficiency was greater than $90\%$, while the double excitation efficiency was approximately $50\%$. We have found that the three main factors which determine high transfer efficiencies are large acceptor probabilities, long acceptor decay times, and strong photon-ring coupling. A possible implementation of the theoretical framework to bio-inspired solar energy devices is also discussed.

The superposition of coherent states has attracted extensive and intensive attention, exemplified by intriguing instances such as Schrödinger cat states and compass states. In this study, we derive analytical expressions of the Wigner functions and phase-space displacement sensitivity of circular states, which are superpositions of coherent states distributed equidistantly on a circle. The visualization of these phase-space functions exhibits fascinating quantum kaleidoscopic patterns, and intuitively reveals the internal coherence and symmetric structure in these states. Moreover, we unveil the inherent sub-Planck structure of circular states in terms of the zeros of sensitivity functions.

The dispersive regime of $n$-photon qubit-oscillator interactions is analyzed using Schrieffer-Wolff perturbation theory. Effective Hamiltonians are derived up to the second order in the perturbation parameters. These effective descriptions reveal higher-order qubit-oscillator cross-Kerr and oscillator self-Kerr terms. The cross-Kerr term combines a qubit Pauli operator with an $n$-degree polynomial in the oscillator photon number operator, while the self-Kerr term is an $(n-1)$-degree polynomial in the oscillator photon number operator. In addition to the higher-order Kerr terms, a qubit-conditional $2n$-photon squeezing term appears in the effective non-rotating-wave-approximation Hamiltonian. Furthermore, perturbation theory is applied to the case of multiple qubits coupled to a shared oscillator. A photon-number-dependent qubit-qubit interaction emerges in this case, which can be leveraged to tune the effective multiqubit system parameters using the oscillator state. Results for the converse setup of multiple oscillators and a single qubit are also derived. In this case, a qubit-conditional oscillator-oscillator nonlinear interaction is found. The spectral instabilities plaguing multiphoton qubit-oscillator models are carefully treated by introducing stabilizing higher-order terms in the Hamiltonian. The stabilizing terms preserve low-photon subspaces, avoid negative infinite energies, and facilitate reliable numerical calculations used to validate analytical predictions. The effective descriptions developed here offer a simple and intuitive physical picture of dispersive multiphoton qubit-oscillator interactions that can aid in the design of implementations harnessing various nonlinear effects.

Correlated quantum systems can exhibit thermodynamic behaviors that defy classical expectations, with anomalous energy flow (AEF) against temperature gradients serving as a paradigmatic example. While AEF has been shown to arise from the consumption of initial quantum correlations, little is known about whether AEF can occur without correlation depletion, or if analogous anomalous transport exists for conserved quantities—dubbed charges—other than energy. Here, we develop a general global-local thermodynamic approach to describe charge exchange between arbitrary correlated quantum systems. For energy-conserving systems, we analytically rule out AEF in initially uncorrelated states, even with the involvement of quantum catalysts, thereby complementing existing studies. In contrast, in systems with multiple conserved charges, we uncover a mechanism for AEF that requires no initial correlations but is instead induced by a drag effect from normal flows of nonenergy charges. Furthermore, by treating all conserved charges on equal footing, we generalize AEF to a broader concept of anomalous charge flow, applicable to any conserved charge. We confirm theoretical expectations with numerical examples. These findings deepen our understanding of nonequilibrium quantum thermodynamics and open new avenues for controlling transport phenomena in correlated quantum systems.

Quantum computing (QC) and quantum Monte Carlo (QMC) represent state-of-the-art quantum and classical computing methods, respectively, for understanding many-body quantum systems. However, straightforward integration of the two methods may encounter significant challenges, such as exponential sampling cost and inefficient walker propagation. Here, we propose an efficient hybrid quantum-classical algorithm that integrates the two methods, overcoming these limitations while leveraging their strengths in representing and manipulating quantum states. To measure the effectiveness of the hybrid approach, we first introduce nonstoquasticity indicators (NSIs) and their theoretical upper bounds, which quantify the severity of the sign problem, a major limitation of QMC. Next, we present a hybrid QC-QMC method where the walkers are represented by quantum states prepared by a shallow quantum circuit. Although the Hamiltonian in the quantum state walker basis is not sparse, we offer an efficient and scalable approach to implement walker propagation using a quantum computer. From the QMC perspective, our algorithm significantly mitigates the sign problem in the quantum state walker basis. From the QC perspective, integrating QMC increases the expressivity of shallow quantum circuits, enabling more accurate computations that are traditionally achievable only with much deeper quantum circuits. Our method has immediate applications in tackling complex quantum many-body problems. We numerically test and verify it for the ${\mathrm{N}}_2$ molecule (12 qubits) and the Hubbard model (16 qubits), observing a significant suppression of the sign problem (which exponentially decreases with circuit depth) and a notable improvement in calculation accuracy (which is about two to three orders compared to variational quantum algorithms). Our work paves the way to solving practical problems with intermediate-scale and early fault-tolerant quantum computers, with broad applications in chemistry, condensed matter physics, and materials.

Many recent investigations have concluded, based on asymptotic complexity analyses, that quantum computers could accelerate combinatorial optimization (CO) tasks relative to a purely classical computer. However, asymptotic analysis alone cannot support a credible claim of quantum advantage. Here, we highlight the challenges involved in benchmarking quantum and classical heuristics for CO, with a focus on the Sherrington-Kirkpatrick problem. Whereas hope remains that a quadratic quantum advantage is possible, our numerical analysis casts doubt on the idea that current methods exhibit any quantum advantage at all. This doubt arises because even a simple classical approach can match with quantum methods we investigated. We conclude that more careful numerical investigations are needed to evaluate the potential for quantum advantage in CO, and we give some possible future directions for such investigations.

Certified randomness guaranteed to be unpredictable by adversaries is central to information security. The fundamental randomness inherent in quantum physics makes certification possible from devices that are only weakly characterized, i.e., requiring little trust in their implementation. It was recently shown that the amount of certifiable randomness can be improved using the so-called entropy accumulation theorem generalized to prepare-and-measure settings. Furthermore, this approach allows a finite-size analysis which avoids assuming that all rounds are independent and identically distributed. Here, we demonstrate this improvement in semi-device-independent randomness certification from untrusted measurements.

We study the effectiveness of two distinct machine learning techniques, neural networks and random forests, in the quantification of entanglement from two-qubit tomography data. Although we predictably find that neural networks yield better accuracy, we also find that the way the two methods reach their prediction is starkly different. This is seen by the measurements which are the most important for the classification. Neural networks follow the intuitive prediction that measurements containing information about nonlocal coherences are most important for entanglement, but random forests signify the dominance of information contained in occupation measurements. This is because occupation measurements are necessary for the extraction of data about all other density matrix elements from the remaining measurements. The same discrepancy does not occur when the models are used to learn entanglement directly from the elements of the density matrix, so it is the result of the scattering of information and interdependence of measurement data. As a result, the models behave differently when noise is introduced to various measurements, which can be harnessed to obtain more reliable information about entanglement from noisy tomography data.

The manipulation of quantum information in large systems requires precise control of quantum systems that are out of equilibrium. As the size of the system increases, its fragility in response to external perturbations and intrinsic decoherence processes also increases. The degradation of the system response makes accurate measurements a challenging and time-consuming task. However, quantum information lifetime enhancement can be achieved by dynamical decoupling techniques, where an external drive with a frequency much higher than the system's internal evolution renders signal acquisition with decay times greater than 1000-fold. In this study, we demonstrate that the system response during a prethermal period, subject to Floquet control, can be utilized to probe the multiple quantum evolution of dense and highly connected spin systems. This approach exhibits an enhanced sensitivity at a reduced experimental time. The enhanced signal-to-noise ratio achieved enabled the use of numerical inversion strategies to model the evolution of the excited multiple quantum coherences, which describe the number of correlated spins within a cluster. We observed that the increase in the number of correlated spins with multiple quantum evolution is accompanied by an increase in the distribution of spin cluster sizes, which follows a quadratic law.

The collective interaction of electronic excitations with the electromagnetic field in atomic arrays can lead to reduced decay rates, forming subradiant states with applications in quantum information and memories. By including quantized vibrational excitations, we examine the effects of finite trap strength and light-mediated forces on highly subradiant singly excited states for two, three, and many atoms in a one-dimensional waveguide or free space. For waveguide-coupled and tightly trapped atoms, the recoil energy from photon emission can reach a vibrational quantum, even in the Lamb-Dicke regime. For weakly trapped atoms, the vibrational wave packets are shifted or distorted due to induced forces and uneven decay. These effects lead to a time-dependent decay rate, extra vibrational energy transfer, and mixing of different electronic and vibrational states. The resulting entanglement entropy and infidelity can be mitigated by decreasing the induced forces or increasing trap strength. For quantum information storage, these findings suggest optimal array configurations in geometry and polarization. Our results provide insights for quantum memories and atom array experiments.