All elementary particles in nature can be classified as fermions with half-integer spin and bosons with integer spin. Within quantum electrodynamics (QED), even though the spin of the Dirac particle is well defined, there exist open questions on the quantized description of spin of the gauge field particle—the photon. Using quantum field theory, we discover the quantum operators for the spin angular momentum (SAM) ${\mathit{S}}_M=(1/c)\int d^{3}x\mathit{\pi }\times \mathit{A}$ and orbital angular momentum (OAM) ${\mathit{L}}_M=-(1/c)\int d^{3}x{\pi }^{\mu }\mathit{x}\times \mathbf{\nabla }{A}_{\mu }$ of the photon, where ${\pi }^{\mu }$ is the conjugate canonical momentum of the gauge field $A^{\mu }$. We also reveal a perfect symmetry between the angular momentum commutation relations for Dirac fields and Maxwell fields. We derive the well-known OAM and SAM of classical electromagnetic fields from the above-defined quantum operators. Our work shows that the spin and OAM operators commute, which is important for simultaneously observing and separating the SAM and OAM. The correct commutation relations of orbital and spin angular momentum of the photon has applications in quantum optics, topological photonics as well as nanophotonics and can be extended in the future for the spin structure of nucleons.

Estimation of a global parameter defined as a weighted linear combination of unknown multiple parameters can be enhanced by using quantum resources. Advantageous quantum strategies may vary depending on the weight distribution, requiring the study of an optimal scheme achieving a maximal quantum advantage for a given sensing scenario. In this work, we propose a Heisenberg-limited distributed quantum phase sensing scheme using Gaussian states for an arbitrary distribution of the weights with positive and negative signs. The proposed scheme exploits entanglement of Gaussian states only among the modes assigned with equal signs of the weights, but separates the modes with opposite weight signs. We show that the estimation precision of the scheme exhibits the Heisenberg scaling in the mean photon number and it can be achieved by injecting two single-mode squeezed states into the respective linear beam-splitter networks and performing homodyne detection on them in the absence of loss. Interestingly, the proposed scheme is proven to be optimal for Gaussian probe states with zero displacement. We also provide an intuitive understanding of our results by focusing on the two-mode case, in comparison with the cases using non-Gaussian probe states. We expect this work to motivate further studies on quantum-enhanced distributed sensing schemes considering various types of physical parameters with an arbitrary weight distribution.

In ultracold-atom experiments, data often comes in the form of images which suffer information loss inherent in the techniques used to prepare and measure the system. This is particularly problematic when the processes of interest are complicated, such as interactions among excitations in Bose-Einstein condensates (BECs). In this paper, we describe a framework combining machine learning (ML) models with physics-based traditional analyses to identify and track multiple solitonic excitations in images of BECs. We use an ML-based object detector to locate the solitonic excitations and develop a physics-informed classifier to sort solitonic excitations into physically motivated subcategories. Lastly, we introduce a quality metric quantifying the likelihood that a specific feature is a longitudinal soliton. Our trained implementation of this framework, soldet, is publicly available as an open-source python package. soldet is broadly applicable to feature identification in cold-atom images when trained on a suitable user-provided dataset.

For decades, searches for exotic spin interactions have used increasingly precise laboratory measurements to test various theoretical models of particle physics. However, most searches have focused on interaction length scales of $\gtrsim 1\mathrm{mm}$, corresponding to hypothetical boson masses of $\lesssim 0.2\mathrm{meV}$. Recently, quantum sensors based on nitrogen-vacancy (NV) centers in diamond have emerged as a promising platform to probe spin interactions at the micrometer scale, opening the door to explore new physics at this length scale. Here, we propose experiments to search for several hypothetical interactions between NV electron spins and moving masses. We focus on potential interactions involving the coupling of NV spin ensembles to both spin-polarized and unpolarized masses attached to vibrating mechanical oscillators. For each interaction, we estimate the sensitivity, identify optimal experimental conditions, and analyze potential systematic errors. Using multipulse quantum sensing protocols with NV spin ensembles to improve sensitivity, we project constraints that are a $\gtrsim$5-orders-of-magnitude improvement over previous constraints at the micrometer scale. We also identify a spin-polarized test mass, based on hyperpolarized ${}^{13}\mathrm{C}$ nuclear spins in a thin diamond membrane, which offers a favorable combination of high spin density and low stray magnetic fields. Our analysis is timely in light of a recent preprint by Rong et al. (arXiv:2010.15667) reporting a surprising nonzero result of micrometer-scale spin-velocity interactions.

We consider a family of tensor network states defined on regular lattices that come with a natural definition of an adiabatic path to prepare them. This family comprises relevant classes of states, such as injective matrix product and projected entangled-pair states, and some corresponding to classical spin models. We show how uniform lower bounds to the gap of the parent Hamiltonian along the adiabatic trajectory can be efficiently computed using semidefinite programming. This allows one to check whether the adiabatic preparation can be performed efficiently with a scalable effort. We also derive a set of observables whose expectation values can be easily determined and that form a complete set, in the sense that they uniquely characterize the state. We identify a subset of those observables which can be efficiently computed if one has access to the quantum state and local measurements, and analyze how they can be used in verification procedures.

The interplay between dissipation, topology, and sensitivity to boundary conditions has recently attracted tremendous amounts of attention at the level of effective non-Hermitian descriptions. Here we exactly solve a quantum mechanical Lindblad master equation describing a dissipative topological Su-Schrieffer-Heeger (SSH) chain of fermions for both open boundary condition (OBC) and periodic boundary condition (PBC). We find that the extreme sensitivity on the boundary conditions associated with the non-Hermitian skin effect is directly reflected in the rapidities governing the time evolution of the density matrix giving rise to a Liouvillian skin effect. This leads to several intriguing phenomena including boundary sensitive damping behavior, steady state currents in finite periodic systems, and diverging relaxation times in the limit of large systems. We illuminate how the role of topology in these systems differs in the effective non-Hermitian Hamiltonian limit and the full master equation framework.

We simulate the phase diagram and critical behavior of the $q$-state clock model on the square lattice by using the state-of-the-art loop optimization for tensor-network renormalization (loop-TNR) algorithm. The two phase transition points for $q\ge 5$ are determined with very high accuracy. Furthermore, by computing the conformal scaling dimensions for both transition points, we are able to determine the radius $R$ of the compactified boson theories at both transition points with high precision. In particular, the radius $R$ at higher temperature phase transition point is precisely the same as the one predicted by Berezinskii-Kosterlitz-Thouless (BKT) transition. Moreover, we find that the fixed-point tensors at higher temperature transition point also converge to the same one approximately for large enough $q$ and the corresponding operator product expansion (OPE) coefficient of the compactified boson theory can also be read out directly from the fixed-point tensor.

The derivation of ultimate limits to communication over certain quantum repeater networks have provided extremely valuable benchmarks for assessing near-term quantum communication protocols. However, these bounds are usually derived in the limit of ideal devices and leave questions about the performance of practical implementations unanswered. To address this challenge, we quantify how the presence of loss in repeater stations affect the maximum attainable rates for quantum communication over linear repeater chains and more complex quantum networks. Extending the framework of node splitting, we model the loss introduced at the repeater stations and then prove the corresponding limits. In the linear chain scenario we show that, by increasing the number of repeater stations, the maximum rate cannot overcome a quantity, which solely depends on the loss of a single station. We introduce a way of adapting the standard machinery for obtaining bounds to this realistic scenario. The difference is that whilst ultimate limits for any strategy can be derived given a fixed channel, when the repeaters introduce additional decoherence, then the effective overall channel is itself a function of the chosen repeater strategy (e.g., one-way versus two-way classical communication). Classes of repeater strategies can be analysed using additional modeling and the subsequent bounds can be interpreted as the optimal rate within that class.

We consider the instantaneous equilibrium (ieq) transition of an underdamped Brownian particle under arbitrary time-dependent temperature and potential variations and derive analytic results for the temperature and potential protocols for minimal dissipative work. Explicit results for the time-dependent minimal dissipation protocols and the associated energetics are obtained for the cases of pure temperature variation, pure potential parameter (stiffness) variation, and isentropic ieq processes. The minimal dissipation condition enforces the forward and backward protocols to be time-reversal related, with the same minimal dissipative work. Remarkably, it is shown that the minimal dissipation path is also the isentropic ieq transition. The energetics in the mdieq transitions are analyzed in detail with emphasis on the conditions for maximizing the mean work and power that can be extracted. Furthermore, exact results for the overdamped limit are derived, indicating that there is great freedom to choose the minimal dissipation protocols, thus allowing the realization of mdieq transitions in Brownian colloidal systems with relative ease.

The random language model, proposed as a simple model of human languages, is defined by the averaged model of a probabilistic context-free grammar. This grammar expresses the process of sentence generation as a tree graph with nodes having symbols as variables. Previous studies proposed that a phase transition, which can be considered to represent the emergence of order in language, occurs in the random language model. We discuss theoretically that the analysis of the “order parameter” introduced in previous studies can be reduced to solving the maximum eigenvector of the transition probability matrix determined by a grammar. This helps analyze the distribution of a quantity determining the behavior of the order parameter and reveals that no phase transition occurs. Our results suggest the need to study a more complex model such as a probabilistic context-sensitive grammar, in order for phase transitions to occur.

The presence of decoherence in quantum computers necessitates the suppression of noise. Dynamically corrected gates via specially designed control pulses offer a path forward, but hardware-specific experimental constraints can cause complications. Existing methods to obtain smooth pulses are either restricted to two-level systems, require an optimization over noise realizations, or limited to piecewise-continuous pulse sequences. In this paper, we present the first general method for obtaining truly smooth pulses that minimizes sensitivity to noise, eliminating the need for sampling over noise realizations and making assumptions regarding the underlying statistics of the experimental noise. We parametrize the Hamiltonian using a neural network, which allows the use of a large number of optimization parameters to adequately explore the functional control space. We demonstrate the capability of our approach by finding smooth shapes, which suppress the effects of noise within the logical subspace as well as leakage out of that subspace.

Simulating electronic structure on a quantum computer requires encoding of fermionic systems onto qubits. Common encoding methods transform a fermionic system of $N$ spin-orbitals into an $N$-qubit system, but many of the fermionic configurations do not respect the required conditions and symmetries of the system so the qubit Hilbert space in this case may have unphysical states and thus cannot be fully utilized. We propose a generalized qubit-efficient encoding (QEE) scheme that requires the qubit number to be only logarithmic in the number of configurations that satisfy the required conditions and symmetries. For the case of considering only the particle-conserving and singlet configurations, we reduce the qubit count to an upper bound of $\mathcal{O}\left(m{log}_{2}N\right)$, where $m$ is the number of particles. This QEE scheme is demonstrated on an ${\mathrm{H}}_2$ molecule in the 6-31G basis set and a $\mathrm{LiH}$ molecule in the STO-3G basis set using fewer qubits than the common encoding methods. We calculate the ground-state energy surfaces using a variational quantum eigensolver algorithm with a hardware-efficient ansatz circuit. We choose to use a hardware-efficient ansatz since most of the Hilbert space in our scheme is spanned by desired configurations so a heuristic search for an eigenstate is sensible. The simulations are performed on IBM Quantum machines and the Qiskit simulator with a noise model implemented from a IBM Quantum machine. Using the methods of measurement error mitigation and error-free linear extrapolation, we demonstrate that most of the distributions of the extrapolated energies using our QEE scheme agree with the exact results obtained by Hamiltonian diagonalization in the given basis sets within chemical accuracy. Our proposed scheme and results show the feasibility of quantum simulations for larger molecular systems in the noisy intermediate-scale quantum (NISQ) era. The number of terms in the Hamiltonian has an upper bound of $\mathcal{O}\left(\frac{N^{2m+1}}{(m-1)!m!}\right)$ for the QEE scheme while it scales as $\mathcal{O}\left(N^4\right)$ for the Jordan-Wigner encoding scheme. Nevertheless, we present several cases where QEE is useful.

In this work, we provide a means to quantify genuine tripartite entanglement in arbitrary (pure and mixed) continuous-variable states as measured by the tripartite entanglement of formation—a resource-based measure quantifying genuine multipartite entanglement in units of elementary Greenberger-Horne-Zeilinger (GHZ) states called gebits. Furthermore, we predict its effectiveness in quantifying the tripartite spatial and energy-time entanglement in photon triplets generated in cascaded spontaneous parametric down-conversion (SPDC), and find that ordinary nonlinear optics can be a substantial resource of tripartite entanglement.

Bose-Hubbard models are simple paradigmatic lattice models used to study dynamics and phases of quantum bosonic matter. We combine the extended Bose-Hubbard model in the hard-core regime with ring-exchange hoppings. By investigating the symmetries and low-energy properties of the Hamiltonian we argue that the model hosts fractonic defect excitations. We back up our claims with exact numerical simulations of defect dynamics exhibiting mobility constraints. Moreover, we confirm the robustness of our results against fracton symmetry breaking perturbations. Finally, we argue that this model can be experimentally realized in recently proposed quantum simulator platforms with big time crystals, thus paving a way for the controlled study of many-body dynamics with mobility constraints.

We theoretically study the ground-state properties and the condensations of exciton-like Cooper pairs and biexciton-like Cooper quartets in an electron-hole system. Applying the quartet Bardeen-Cooper-Schrieffer (BCS) theory to the four-component fermionic system consisting of spin-$\frac{1}{2}$ electrons and spin-$\frac{1}{2}$ holes, we show how Cooper pairs and quartet correlations appear in the equation of state at the thermodynamic limit. The biexciton-like four-body correlations survive even at the high-density regime as a many-body BCS-like state of Cooper quartets. Our results are useful for further understanding of exotic matter in the interdisciplinary context of quantum many-body physics with multiple degrees of freedom.