We compute the reduced electric-dipole matrix elements $\langle n{S}_{1/2}\left|\right|D\left|\right|n^{\prime }{P}_J\rangle$ with $n=6,7$ and $n^{\prime }=6,7,...,12$ in cesium using the most complete to date ab initio relativistic coupled-cluster method which includes singles, doubles, perturbative core triples, and valence triples. Our results agree with previous calculations at the linearized single double level but also show large contributions from nonlinear singles and doubles as well as valence triples. We also calculate the normalized ratio ${\xi }_{n,n^{\prime }}\equiv (1/\sqrt{2})\langle n{S}_{1/2}\left|\right|D\left|\right|n^{\prime }{P}_{1/2}\rangle /\langle n{S}_{1/2}\left|\right|D\left|\right|n^{\prime }{P}_{3/2}\rangle$ which is important for experimental determination of matrix elements. The ratios ${\xi }_{6,n}$ display large deviations from the nonrelativistic limit which we associate with Cooper-like minima. Several Appendices are provided where we document the procedure for constructing finite basis sets and our implementation of the random-phase approximation and Brueckner-orbitals method.

We report measurements of the positronium (Ps) $2{}^{3}S_1\to 2{}^{3}P_2$ interval in which atoms traveling in free space were irradiated with microwave radiation generated using a horn antenna. Previous measurements of this transition, performed using atoms in waveguides, exhibited asymmetric and shifted line shapes. In the free-space measurements we report here, much smaller line-shape asymmetry was observed, but with large frequency shifts that varied with the orientation of the horn antenna. Our observations are supported by line-shape simulations and demonstrate that variations in the microwave radiation field distribution can perturb measured line shapes and give rise to apparent frequency shifts without necessarily causing large asymmetries; this effect can explain previous measurements in which an apparent discrepancy with predictions from quantum electrodynamics was ob- served [L. Gurung, T. J. Babij, S. D. Hogan, and D. B. Cassidy, Phys. Rev. Lett. 125, 073002 (2020)].

The ability to track and control the dynamics of a quantum system is the key to quantum technology. Despite its central role, the quantitative reconstruction of the dynamics of a single quantum system from the macroscopic data of the associated observable remains a problem. We consider this problem in the context of weak measurements of a single nuclear carbon spin in a diamond with an electron spin as a meter at room temperature, which is a well-controlled and understandable bipartite quantum system. In this work, based on a detailed theoretical analysis of the model of the experiment, we study the relationship between the statistical properties of the macroscopic readout signal of the spin of a single electron and the quantum dynamics of the spin of a single nucleus, which is characterized by a parameter associated with the strength of the measurement. We determine the parameter of measurement strength in separate experiments and use it to reconstruct the quantum correlation. We control the validity of our approach applying the Leggett-Garg test.

The dynamics of interacting quantum systems in the presence of disorder is studied and an exact representation for disorder-averaged quantities via Itô stochastic calculus is obtained. The stochastic integral representation affords many advantages, including amenability to analytic approximation, potential applicability to interacting systems, and compatibility with tensor network methods. The integral may be expanded to produce a series of approximations, the first of which already includes all diffusive corrections and, further, is manifestly completely positive. The addition of fluctuations leads to a convergent series of systematic corrections. As examples, expressions for the density of states and spectral form factor for the Anderson model are obtained.

We propose an approach for the optimization of the charging of harmonic oscillators (quantum batteries) coupled to a harmonic oscillator (charger), driven by a laser field. We demonstrate that energy transfer limitations can be significantly mitigated in the presence of catalyst systems, mediating between the charger and quantum batteries. We show that these catalyst systems, either qubits or harmonic oscillators, enhance the amount of energy transferred to quantum batteries, while they themselves store almost no energy. It eliminates the need for optimizing the frequency of the charging laser field whose optimal value in the bare setting depends on the coupling strengths between the charger and the batteries.

Nature allows one to explore a manifold of remarkable quantum effects. Most prominently, quantum entanglement can be observed in many-particle systems, between multiple quantized fields, and in hybrid combinations thereof. This diversity, however, also leads to contradicting conclusions about what truly constitutes entanglement in any given physical scenario. By explicitly allowing various perspectives, we rigorously consider different notions of entanglement in the context of first and second quantization. By providing instructive examples, we show that particle entanglement and field entanglement are actually distinct phenomena that can occur and be observed independently of each other. This conclusion not only affects our fundamental understanding but has direct implications for quantum technology which can harness those independent forms of entanglement in practical scenarios.

Sampling noisy intermediate-scale quantum devices is a fundamental step that converts coherent quantum-circuit outputs to measurement data for running variational quantum algorithms that utilize gradient and Hessian methods in cost-function optimization tasks. This step, however, introduces estimation errors in the resulting gradient or Hessian computations. To minimize these errors, we discuss tunable numerical estimators, which are the finite difference (including their generalized versions) and scaled parameter-shift estimators [introduced in Phys. Rev. A 103, 012405 (2021)], and propose operational circuit-averaged methods to optimize them. We show that these optimized numerical estimators offer estimation errors that drop exponentially with the number of circuit qubits for a given sampling-copy number, revealing a direct compatibility with the barren-plateau phenomenon. In particular, there exists a critical sampling-copy number below which an optimized difference estimator gives a smaller average estimation error in contrast to the standard (analytical) parameter-shift estimator, which exactly computes gradient and Hessian components. Moreover, this critical number grows exponentially with the circuit-qubit number. Finally, by forsaking analyticity, we demonstrate that the scaled parameter-shift estimators beat the standard unscaled ones in estimation accuracy under any situation, with comparable performances to those of the difference estimators within significant copy-number ranges, and are the best ones if larger copy numbers are affordable.

Fault-tolerant quantum error correction provides a strategy to protect information processed by a quantum computer against noise which would otherwise corrupt the data. A fault-tolerant universal quantum computer must implement a universal gate set on the logical level in order to perform arbitrary calculations to in principle unlimited precision. In this paper we characterize the recent demonstration of a fault-tolerant universal gate set in a trapped-ion quantum computer [Postler et al., Nature (London) 605, 7911 (2022)] and identify aspects to improve the design of experimental setups to reach an advantage of logical over physical qubit operation. We show that various criteria to assess the break-even point for fault-tolerant quantum operations are within reach for the ion trap quantum computing architecture under consideration. Furthermore, we analyze the influence of crosstalk in entangling gates for logical state preparation circuits. These circuits can be designed to respect fault tolerance for specific microscopic noise models. We find that an experimentally informed depolarizing noise model captures the essential noise dynamics of the fault-tolerant experiment that we consider, and crosstalk is negligible in the currently accessible regime of physical error rates. For deterministic Pauli state preparation, we provide a fault-tolerant unitary logical qubit initialization circuit, which can be realized without in-sequence measurement and feed-forward of classical information. Additionally, we show that nondeterministic state preparation schemes, i.e., repeat until success, for logical Pauli and magic states perform with higher logical fidelity over their deterministic counterparts for the current and anticipated future regime of physical error rates. Our results offer guidance on improvements of physical qubit operations and validate the experimentally informed noise model as a tool to predict logical failure rates in quantum computing architectures based on trapped ions.

We theoretically study how a scattered electron can entangle molecular spin qubits (MSQs). This requires solving the inelastic transport of a single electron through a scattering region described by a tight-binding interacting Hamiltonian. We accomplish this using a Green's-function solution. We can model realistic physical implementations of MSQs by parametrizing the tight-binding Hamiltonian with first-principles descriptions of magnetic anisotropy and exchange interactions. We find that, for two-MSQ systems with inversion symmetry, projective measurement of the spin degree of freedom of the scattered electron offers probabilistic control of the degree of entanglement between the MSQs.

The ring-breaking dynamics of ${\mathrm{C}}_6{\mathrm{H}}_6$ in its three dimers $[{\left({\mathrm{C}}_6{\mathrm{H}}_6\right)}_2,$ ${\mathrm{C}}_6{\mathrm{H}}_6\mathrm{Ar},$ and ${\mathrm{C}}_6{\mathrm{H}}_6\mathrm{Kr}]$ are investigated by performing three-body coincidence measurements after interaction with a strong femtosecond laser. The measurements enabled the observation of three ring-breaking channels, resulting in products of ${\mathrm{C}}_1{\mathrm{H}}_3^{+}+{\mathrm{C}}_5{\mathrm{H}}_3^{+},$ ${\mathrm{C}}_2{\mathrm{H}}_3^{+}+{\mathrm{C}}_4{\mathrm{H}}_3^{+},$ and ${\mathrm{C}}_3{\mathrm{H}}_3^{+}+{\mathrm{C}}_3{\mathrm{H}}_3^{+}$ with the neighbor ions. Additionally, kinetic energies from intra- and intermolecular fragmentation are extracted. By using the neighbor ion as a reference, it is found that the lifetimes of corresponding dissociation states have a significant impact on the final angular distributions of the fragments. The vibration excitation of molecules induced by neighboring ions during the repelling process alters the relative ratio between the three observed ring-breaking channels. By examining the ring-breaking dynamics of aromatic molecules in different environments, this study provides valuable insights into molecular fragmentation in complex systems.

Using the Wei-Norman theory, we obtain a time-dependent complex Riccati equation (TDCRE) as the solution of the time evolution operator (TEO) of quantum systems described by time-dependent (TD) Hamiltonians that are linear combinations of the generators of the $\mathrm{su}(1,1)$, $\mathrm{su}\left(2\right)$, and $\mathrm{so}(2,1)$ Lie algebras. Using a recently developed solution for the time evolution of these quantum systems, we solve the TDCRE recursively as generalized continued fractions, which are optimal for numerical implementations, and establish the necessary and sufficient conditions for the unitarity of the TEO in the factorized representation. The inherited symmetries of quantum systems can be recognized by a simple inspection of the TDCRE, allowing effective quantum Hamiltonians to be associated with it, as we show for the Bloch-Riccati equation whose Hamiltonian corresponds to that of a generic TD system of the Lie algebra $\mathrm{su}\left(2\right)$. As an application, but also as a consistency test, we compare our solution with the analytic one for the Bloch-Riccati equation considering the Rabi frequency driven by a complex hyperbolic secant pulse generating spin inversion, showing an excellent agreement.

The local structure present in Wigner and Husimi phase-space distributions and their marginals are studied and quantified via information-theoretic quantities. Shannon, Rényi, and cumulative residual entropies of the Wigner and Husimi distributions are examined in the ground and excited states of a harmonic oscillator. The entropies of the Wigner function marginals are lower than the corresponding entropies of the Husimi function marginals, which illustrates how the nodal structure present in the Wigner function is lost upon consideration of the Husimi function. Shannon and cumulative residual entropies of the Wigner function yield entropies which are complex valued. Absolute values and real components of these quantities increase with quantum number, displaying a behavior which is consistent with their real-valued Husimi function counterparts. This comportment is also similar to the real-valued Rényi entropies of the Wigner function. The entropies of the Wigner function are observed to be lower than the corresponding Husimi function ones, in agreement with the results for the marginals. The real components of the Wigner function entropies are seen to be closer to the uncertainty relation bound compared to the corresponding Husimi function entropies. These real components are also closer to the bound when contrasted to the entropic sum of the marginal densities. The Rényi or collision entropy of the Wigner function sits exactly on the bound. Related statistical correlation measures show that the position-momentum correlation is larger in the Wigner function compared to the Husimi function and increases with quantum number.

Ground-state preparation for a given Hamiltonian is a common quantum-computing task of great importance and has relevant applications in quantum chemistry, computational material modeling, and combinatorial optimization. We consider an approach to simulate dissipative non-Hermitian Hamiltonian quantum dynamics using Hamiltonian simulation techniques to efficiently recover the ground state of a target Hamiltonian. The proposed method facilitates the energy transfer by repeatedly projecting ancilla qubits to the desired state, rendering the effective non-Hermitian Hamiltonian evolution on the system qubits. To make the method more resource friendly in the noisy intermediate-scale quantum (NISQ) and early fault-tolerant era, we combine the non-Hermitian projection algorithm with multiple variational gadgets, including variational module enhancement and variational state recording, to reduce the required circuit depth and avoid the exponentially vanishing success probability for postselections. We compare our method, the non-Hermitian-variational algorithm, with a pure variational method, the quantum approximate optimization algorithm (QAOA), for solving the 3-SAT problem and preparing the ground state for the transverse field Ising model. As demonstrated by numerical evidence, the non-Hermitian-variational algorithm outperforms QAOA in convergence speed with improved quantum resource efficiency.

Coherence underlies quantum phenomena, yet it is manifest in classical theories; delineating coherence's role is a fickle business. The quadrature coherence scale (QCS) was invented to remove such ambiguity, quantifying quantum features of any single-mode bosonic system without choosing a preferred orientation of phase space. The QCS is defined for any state, reducing to well-known quantities in appropriate limits, including Gaussian and pure states, and perhaps most importantly for a coherence measure, it is highly sensitive to decoherence. Until recently, it was unknown how to measure the QCS; we here report on an initial measurement of the QCS for squeezed light and thermal states of light. This is performed using Xanadu's machine Borealis, accessed through the cloud, which offers the configurable beam splitters and photon-number-resolving detectors essential for measuring the QCS. The data and theory match well, certifying the usefulness of interferometers and photon-counting devices in certifying quantumness.