Describing systems of superconducting atoms coupled to a continuum of photonic modes at multiple separated locations in a waveguide, waveguide quantum electrodynamics (QED) with giant atoms has emerged as a promising platform for realizing quantum interconnect. Such systems have been reported to exhibit rich phenomena that differ from those of natural atoms. Going beyond the widely used Born-Markov and Wigner-Weisskopf approximations, we investigate the non-Markovian dynamics of one and two giant atoms interacting with a waveguide formed by an array of coupled resonators. We discover that the diverse dynamical behaviors of the giant atoms are intrinsically determined by the energy spectrum of the composite system consisting of the giant atoms and the photonic modes in the waveguide. As long as one or more bound states are present in the energy spectrum, their excited-state probabilities, respectively, tend to stable finite values and lossless Rabi-like oscillations with frequencies proportional to the differences of the bound-state eigenenergies. Our result provides an insightful guideline for suppressing the decoherence of giant atoms and facilitates the development of quantum interconnect devices using giant-atom waveguide QED.

Nitrogen-vacancy (NV) centers in nanodiamonds are promising platforms for nanoscale quantum sensing in biological and condensed-matter environments, but their performance is often limited by charge-state instability and strain-induced spectral fluctuations. Using spin-state-dependent emission measurements, we demonstrate that controlled optical excitation can stabilize the local charge environment surrounding the NV centers in nanodiamonds, thereby improving sensing stability. We observe that spin-state-dependent spectral emission linewidth and splitting saturate as a function of excitation laser power density, which correlates with a reduction in charge fluctuations across nanodiamonds with varied sizes and impurity concentrations. To elucidate these measurements, we develop a macroscopic theoretical model that reproduces the ensemble-averaged response of large NV populations without requiring explicit simulation of microscopic charge dynamics. Furthermore, we introduce incoherent sensing protocols that exploit environmental noise to achieve sensitivity of $\mu \text{T}/\sqrt{\text{Hz}}$, even in regimes of strong spin decoherence. These results provide a practical route to enhancing the robustness of NV-based quantum sensors and an optically addressable platform for physically unclonable imaging tags relevant to quantum security and anticounterfeiting applications.

Contextuality, as a distinguishing feature of quantum mechanics, can be revealed by state-independent contextual (SI-C) sets and the corresponding inequalities. Optimal SI-C inequalities have been studied in [Phys. Rev. Lett. 109, 250402 (2012)] for the ideal scenario. By taking the SI-C set with 13 rays as an example, we investigate the optimal SI-C inequalities under experimental imperfections, characterized by detection inefficiency and the detection error of the outcome flip. We first discover all the extremal symmetric optimal inequalities. Then our results identify the thresholds of detection efficiency and rate of detection error for those optimal symmetric inequalities in the heralded and unheralded scenarios. By incorporating measurement disturbance terms, we extend noncontextuality inequalities to capture the disturbance caused by imperfect detection efficiency in sequential measurements. As it turns out, the detection efficiency should be no less than 0.94741 in the heralded scenario and 0.98244 in the unheralded scenario. Our findings provide valuable insights for designing robust experimental tests of quantum contextuality in realistic settings.

We propose a scalable and deterministic protocol for growing large multiqubit states starting from two-qubit nonmaximally entangled pure states, where the bipartite entanglement in the resultant state is higher than the maximum of the available entangled qubit pairs. This is achieved via a truncation of the Hilbert space corresponding to a subsystem of qubits to a space that hosts a single qubit, brought about by a multiqubit measurement assisted by the graph basis. We prove its equivalence to a repetitive two-qubit measurement-based protocol, and demonstrate realization of the required two-qubit measurement via a two-qubit parity measurement, thereby establishing the implementability of the protocol. We derive lower and upper bounds of the bipartite entanglement concentrated after a given number of rounds of measurements, where the entanglement of the available qubit pairs are notnecessarily equal. We further discuss the effect of possible imperfections that may arise in the protocol and its robustness towards such imperfections. We demonstrate the usefulness of our proposal by applying it to create generalized Greenberger-Horne-Zeilinger states on arbitrary number of qubits, thereby underlining the possibility of creating maximally entangled qubit pairs via qubit-local projection measurements.

The quantum approximate optimization algorithm (QAOA) is among the leading candidates for achieving quantum advantage on near-term processors. While typically implemented with a transverse-field mixer (XM-QAOA), the Grover-mixer variant (GM-QAOA) offers a compelling alternative due to its global search capabilities. This work investigates the application of GM-QAOA to higher-order unconstrained binary optimization (HUBO) problems, also known as polynomial unconstrained binary optimization, which form a general class of combinatorial optimization problems involving multivariable interactions. We present a comprehensive numerical study demonstrating that GM-QAOA, unlike XM-QAOA, exhibits monotonic improvement in performance with circuit depth and achieves superior results for HUBO problems within a layerwise optimization framework. An important component of our approach is an analytical framework for modeling GM-QAOA dynamics, which enables a classical approximation of the optimal parameters and helps reduce the optimization overhead. Our resource-efficient parametrized version of GM-QAOA nearly matches the performance of the version optimized using the layerwise approach while being significantly less demanding, making it a highly effective approach for complex optimization tasks. These findings highlight the potential of GM-QAOA and provide a practical pathway for its implementation on current quantum hardware.

We numerically investigate the two-dimensional Bose-Hubbard model with local onsite disorder, where the competition between disorder and short-range interactions leads to the emergence of a Bose glass (BG) phase between the Mott insulator (MI) and superfluid (SF) phases. In order to analyze the inhomogeneous system we employ real-space bosonic dynamical mean-field theory (RBDMFT) and perform an ensemble average over disorder realizations. To distinguish the MI from the BG phase, we compare the Edwards-Anderson order parameter and the compressibility with the energy-gap condition. To identify the insulator to SF transition, we apply a percolation analysis to the condensate order parameter. In qualitative accordance with the theorem of inclusions we always find an intermediate BG phase between the SF and MI. However, the quantitative comparison indicates significant deviations between the MI to BG phase boundary expected in the thermodynamic limit and the one obtained for a finite system size. Additionally, RBMDFT is capable of reliably calculating spectral information throughout the phase diagram. Analyzing the spectral function reveals evidence for analytically predicted damped localized modes in the dispersion relation in the strong-coupling regime.

In recent years, ultracold atomic gases confined in curved geometries have attracted considerable theoretical interest. This is motivated by recent realizations of bubble traps in microgravity conditions, which open the possibility of investigating quantum many-body physics beyond the conventional flat-space paradigm. The theoretical interest up to now was mainly focused on Bose gases and their phenomenology, and the study of Fermi gases has been left behind. In this paper, we investigate a two-component repulsive Fermi gas constrained to the surface of a sphere at finite temperature. We first analyze the noninteracting case, showing how the intrinsic geometrical features of the spherical surface give rise to a shell structure and modify the low-temperature thermodynamics compared to the flat two-dimensional gas. Repulsive interactions are then considered through an effective path-integral approach within a Hartree-Fock mean-field approximation, enabling us to derive the grand canonical potential and to regularize the associated Matsubara summation. We then investigate the stability of the spin-balanced state and obtain the finite-temperature Stoner criterion for fermions on a sphere, highlighting the interplay between the repulsive interactions and shell effects.

In this paper we consider a two-component gas of fermions on the BCS side of the BCS-BEC crossover at zero temperature. We use a momentum-dependent interaction that reproduces the $s$-wave scattering phase shifts of a contact interaction up to a momentum cutoff that is scaled with the Fermi momentum. Using a diagrammatic formulation of Bogoliubov many-body perturbation theory, suitably augmented by self-consistency conditions, we obtain the Hartree shift and the pairing gap to third order. In the weak-coupling regime, our results are not only well converged but also agree with the well-established Gor'kov-Melik-Barkhudarov corrections for the gap and the Galitskii result for the Hartree shift. Near the unitary regime, our results for the Nambu-Gor'kov self-energy are less converged, but there is still reasonable agreement with experiments as well as with quantum Monte Carlo results. Perspectives for improvements and applications of this approach to neutron matter are discussed.

Quantum optical frequency combs generated using optical nonlinearities in integrated photonic resonators provide a versatile paradigm that leverages multiple spectral modes to generate complex quantum states of light. Nevertheless, the maximum number of spectral modes generated by integrated resonators is severely limited by dispersion, which drastically reduces the brightness of the comb lines that are further away from the pumped mode. Here we theoretically propose and numerically demonstrate an inverse-designed ring resonator that can generate highly multimodal, dispersion-free quantum combs with uniformly bright and equally spaced comb lines. More specifically, we utilize a superposition of periodic modulations of the ring resonator waveguide to couple the clockwise and counterclockwise propagating modes of the ring, thereby creating frequency splittings that balance dispersion. Using phase-controlled bidirectional pumping, we show that this approach can be used to generate both discrete-variable quantum combs of entangled photon pairs and continuous-variable quantum combs of two-mode squeezed light. Moreover, this approach is material agnostic and applicable to resonators operating in both anomalous and normal dispersion regimes. Our design closely follows the inverse-designed classical combs and optical parametric oscillators that have been recently implemented using similar modulated ring resonators and is therefore readily implementable using existing fabrication technology. These results provide a practical pathway to highly multimodal and bright quantum comb sources for frequency-encoded quantum communication and computation protocols.

Coupling between quantum and classical systems is consistent, provided the evolution is linear in the state space, preserves the split of systems into quantum and classical degrees of freedom, and preserves probabilities. The evolution law must be a completely positive and norm preserving map. We prove that if the dynamics is memoryless there are two classes of these dynamics, one which features finite jumps in the classical phase space and one which is continuous. We derive the most general form of the dynamics. This is achieved by applying the complete positivity conditions using a Cauchy-Schwarz inequality applicable to classical-quantum systems. The key technical result is a generalization of the Pawula theorem.

This paper introduces a logic structure for reversible quantum circuit synthesis. Our synthesis method aims to minimize the quantum cost of reversible quantum circuits with decoders. In this method, multivalued input, binary output (MVI) functions are utilized as a mathematical concept only, but the circuits are binary. We introduce the concept of “MultiValued Input Fixed Polarity Reed-Muller” forms. Our decoder-based circuit uses three logical levels in contrast with commonly used methods based on Exclusive-or Sum of Products (ESOP) with two levels (AND-XOR expressions), realized by Toffoli gates. In general, the high number of input qubits in the resulting Toffoli gates is a problem that greatly impacts the quantum cost. Using decoders decreases the number of input qubits in these Toffoli gates. We present two practical algorithms for three-level circuit synthesis by finding the MVI–Fixed-Polarity Reed-Muller (MVI-FPRM): product-matching and the newly developed butterfly diagrams. The best MVI-FPRM forms are factorized and reduced to approximate MultiValued Input Generalized Reed-Muller (MVI-GRM) forms. Analytically, various multi-output binary functions, such as comparators, are tested using both the proposed methods and the ESOP approach, and they are evaluated using two cost metrics. The evaluation shows that our method generally has a smaller cost value than that of the ESOP-based approach. Notably, the results demonstrate that our method becomes increasingly effective with comparators of greater sizes.

Quantum state tomography is the fundamental physical task of learning a complete classical description of an unknown state of a quantum system given coherent access to many identical samples of it. The complexity of this task is commonly characterized by its sample complexity: the minimal number of samples needed to reach a certain target precision of the description. While the sample complexity of quantum state tomography has been well studied, the memory complexity has not been investigated in depth. Indeed, the bottleneck in the implementation of naïve sample-optimal quantum state tomography is its massive quantum memory requirements. In this work, we propose and analyze a quantum state tomography algorithm which retains sample-optimality but is also memory-efficient. Our work is built on a form of unitary Schur sampling and only requires streaming access to the samples.

Macrorealism posits that a system possesses definite properties at all times and that we can discover these properties, in principle, without disturbing the system's subsequent behavior. The Leggett-Garg inequalities are derived under these assumptions and are readily violated by standard quantum mechanics, thereby providing a scheme to test whether demonstrably macroscopic systems can exhibit quantum coherence. Unfortunately, Leggett-Garg tests suffer from the difficult to avoid clumsiness loophole: the difficulty of proving that sequential measurements have not inadvertently disturbed the system. The recently uncovered Tsirelson inequality is derived from the simple dynamical assumption of uniform precession, obeyed by many classical systems, and requires only single-time measurements. However, Tsirelson inequality violations could be explained by a macrorealistic system that merely breaks the dynamical assumption, rather than genuine quantum behavior. By carrying out a quantum-mechanical analysis of the Tsirelson inequality in the harmonic oscillator, we develop a protocol to rule out this possibility by assessing generalized conditions of uniform precession. We show that various measures of uniform precession, some of which are related to Leggett-Garg quantities, are satisfied well enough that the presence of quantum-mechanical interference terms must be implied. We derive several incidental mathematical results relating to violating states of Tsirelson's inequality, concerning dwell time, crossing number, and probability currents, and also consider a group-theoretic analysis of the Tsirelson operator.

The amplitude encoding of an arbitrary $n$-qubit state vector requires $\mathrm{\Omega }\left(2^n\right)$ gate operations, owing to the exponential dimension of the Hilbert space. We can, however, form dimensionality-reduced representations of quantum states using matrix product states (MPSs). In this article, we illustrate that MPS techniques enable the preparation of quantum states representative of functions with complexity up to low-degree piecewise polynomials via shallow-depth quantum circuits with accuracy exceeding 99.99%. We extend these results to the approximate amplitude encoding of pixel values. We showcase this approach by efficiently preparing a $128\times 128$ ChestMNIST medical image on 14 qubits with fidelity exceeding 99.2% on a circuit with a total depth of just 425 single-qubit rotation and cnot gates.

We report a joint experimental and theoretical study of $K$-shell photoionization of S and F atoms in sulfur hexafluoride, ${\mathrm{SF}}_6$. In our experiment, we employed tunable synchrotron radiation to generate photoelectrons emitted from the $1s$ shells of the S and F atoms with different kinetic energies. Coincident electron- and fragment-ion detection, carried out using cold target recoil-ion momentum spectroscopy, enabled access to polarization-averaged molecular-frame photoelectron angular distributions. In addition, we performed electronic structure calculations within the relaxed-core Hartree-Fock approximation by using a stationary single-center method. The calculations are in good agreement with the experiment. Our results support previous findings on the feasibility of imaging three-dimensional atomic arrangements in molecules using polarization-averaged molecular-frame angular distributions. In particular, we demonstrate that such imaging is possible even at intermediate photoelectron kinetic energies and even for six experimentally undistinguished F $1s$ emitters.

Flat-band lattices supporting compact localized states provide a versatile platform for exploring unconventional transport phenomena in photonic, ultracold atomic, electronic, and other systems. Here, we investigate the transport of path-entangled multiphoton NOON states in a flat-band rhombic lattice and observe intriguing localization-delocalization features that depend on both the phase and photon number of the NOON states. To experimentally emulate photon-number correlations, we develop an intensity correlation measurement protocol using coherent laser light with tunable relative phases. We first apply this protocol to show spatial bunching and antibunching of two-photon NOON states in a one-dimensional waveguide lattice. In the rhombic lattice, we show that for an even (odd) photon number $N$, localization occurs at the $0\left(\pi \right)$ phase of the NOON state with a probability of $2^{1-N}$, which is demonstrated up to eight photons. Our results open an exciting route toward understanding the dynamics of correlated photons in complex photonic networks.

In this work, we consider a parameterized Ising model with long-range symmetric pairwise interactions on a network of spin-$1/2$ particles. The system is designed with symmetric dynamics, allowing for the reduction of the state space to a subspace defined by the set of Dicke states. We propose a method for designing robust electromagnetic amplitude pulses based on a moment quantization approach. The introduced parameter accounts for uncertainties in the electromagnetic field, resulting in a family of distinct Hamiltonians. By employing a discretized moment-based quantization technique, we design a control pulse capable of simultaneously steering an infinite collection of dynamical systems to compensate for parameter variations. This approach benefits from the duality between the infinite-dimensional parameterized system and its finite-dimensional truncated moment dynamics. Simulation results demonstrate the efficacy of this method in achieving states of significant interest in quantum sensing, including the Greenberger-Horne-Zeilinger and $W$ states.