Subskin modes are distinct from conventional skin modes because they localize not at the system's edge but rather below the edge. Unlike skin modes, where a substantial number of them can accumulate at the boundaries of a system due to the non-Hermitian skin effect, subskin modes are typically limited in number to one or a few, and emerge only when the size of the system and the couplings are related in a very specific way. Nonlinear interactions can lift the restrictions on the couplings for the formation of these modes. The findings reveal the potential of subskin modes for practical applications and new research in non-Hermitian systems.

Nonadiabatic holonomic quantum computation is a promising approach for implementing quantum gates that offers both efficiency and robustness against certain types of errors. A key element of this approach is a geometric constraint known as the parallel transport condition. According to the principle of covariance, this condition must be appropriately modified when changing reference frames. In this paper, we detail how to adjust the parallel transport condition when transitioning from the laboratory frame to a rotating reference frame. Furthermore, building on gauge invariance considerations, we develop a framework for nonadiabatic holonomic quantum computation with projective gates. The parallel transport condition of this framework effectively addresses the problem of global dynamical phases inherent in conventional nonadiabatic holonomic quantum computation. We extend the isoholonomic inequality, which provides a fundamental bound on the efficiency of protocols used to implement holonomic quantum gates, to encompass projective quantum gates. We also determine a minimum execution time for projective holonomic quantum gates and show that this time can be attained when the codimension of the computational space is sufficiently large.

In holonomic quantum computation, quantum logic gates are realized by cyclic parallel transport of the computational space. The resulting quantum gate corresponds to the holonomy associated with the closed path traced by the computational space. The isoholonomic inequality for gates establishes a fundamental lower bound on the path length of such cyclic transports, which depends only on the spectrum of the holonomy, that is, the eigenvalues of the implemented quantum gate. The isoholonomic inequality also gives rise to an estimate of the minimum time required to execute a holonomic quantum gate, underscoring the central role of the inequality in quantum computation. In this paper, we show that when the codimension of the computational space is sufficiently large, any quantum gate can be implemented using a parallel transporting Hamiltonian in a way that saturates the isoholonomic inequality and the corresponding time estimate. We call such implementations tight. The treatment presented here is constructive and lays the foundation for the development of efficient and optimal implementation strategies in holonomic quantum computation.

Quantum entanglement constitutes a pivotal resource, serving as a fundamental cornerstone within the field of quantum information science. In recent years, the study of vortex light entanglement has garnered widespread attention due to its unique structure and inherent advantages; however, the majority of these investigations are primarily focused on discrete variable systems. In this paper, we present a theoretical framework for generating vortex optical entanglement in coherently prepared media, employing continuous-variable analysis and leveraging Raman scattering as an alternative to the conventional spontaneous parametric down-conversion method. The entanglement arises from the quantum correlation between the two light fields, induced by atomic coherence. Using numerical simulations, we thoroughly explore the impact of various tunable system parameters on the degree of entanglement, ultimately identifying the optimal conditions for maximal entanglement. Our findings offer a reference framework for vortex light entanglement, with potential implications across quantum teleportation, quantum key distribution, quantum computing, high-dimensional quantum information, and other related fields.

A quadrillion-dimensional Hilbert space hosted by a quantum processor with over 50 physical qubits has been expected to be powerful enough to perform computational tasks ranging from simulations of many-body physics to complex financial modeling. Despite a few examples and demonstrations, it is still unclear how we can utilize such a large Hilbert space as a computational resource, particularly how a simple and small quantum system could solve nontrivial computational tasks. This paper shows a simple Ising model capable of performing such nontrivial computational tasks in a quantum neural network model. An Ising spin chain as small as ten qubits can solve a practical image classification task with high accuracy. To evaluate the mechanism of its computation, we examine how the symmetries of the Hamiltonian would affect its computational power. We show how the interplay between complexity and symmetries of the quantum system dictates the performance as quantum neural network.

Symmetry is fundamental in the description and simulation of quantum systems. Leveraging symmetries in classical simulations of many-body quantum systems can result in significant overhead due to the exponentially growing size of some symmetry groups as the number of particles increases. Quantum computers hold the promise of achieving exponential speedup in simulating quantum many-body systems; however, a general method for utilizing symmetries in quantum simulations has not yet been established. In this work, we present a unified framework for incorporating symmetry group transforms on quantum computers to simulate many-body systems. The core of our approach lies in the development of efficient quantum circuits for symmetry-adapted projection onto irreducible representations of a group or pairs of commuting groups. We provide resource estimations for common groups, including the cyclic and permutation groups. Our algorithms demonstrate the capability to prepare coherent superpositions of symmetry-adapted states and to perform quantum evolution across a wide range of models in condensed-matter physics and ab initio electronic structure in quantum chemistry. Specifically, we execute a symmetry-adapted quantum subroutine for small molecules in first-quantization on noisy hardware and demonstrate the emulation of symmetry-adapted quantum phase estimation for preparing coherent superpositions of quantum states in various irreducible representations of a symmetry group. In addition, we present a discussion of open problems regarding treating symmetries in digital quantum simulations of many-body systems, paving the way for future systematic investigations into leveraging symmetries quantumly for practical quantum advantage. The broad applicability and rigorous resource estimation for symmetry transformations make our framework appealing for achieving provable quantum advantage on fault-tolerant quantum computers, especially for symmetry-related properties.

Superoscillation is a counterintuitive phenomenon for its mathematical feature of faster than Fourier, which has allowed novel optical imaging beyond the diffraction limit. In this article we introduce a superoscillating quantum control protocol realized by sequential selections within the framework of weak measurement, which steers the apparatus (target) by repeatedly applying optimal pre- and postselections to the system (controller). Our protocol accelerates the adiabatic transport of trapped ions and the adiabatic quantum search algorithm at a finite energy cost. We demonstrate the accuracy and robustness of the protocol in the presence of decoherence and fluctuating noise and elucidate the trade-off between fidelity and rounds of selections. Our findings open avenues for quantum-state manipulation and wave-packet control using superoscillation across a range of quantum platforms.

Inverse participation ratios (IPRs) and the related participation entropies quantify the spread of a quantum state over a selected basis of the Hilbert space, offering insights into the equilibrium and nonequilibrium properties of the system. In this work, we propose three quantum algorithms to estimate IPRs on multiqubit and multiqudit quantum devices. The first algorithm allows for the estimation of IPRs in the computational basis by single-qubit measurements, while the second one enables measurement of IPR in the eigenbasis of a selected Hamiltonian, without the knowledge about the eigenstates of the system. Next, we provide an algorithm for IPR in the computational basis for a multiqudit system. We discuss resources required by the algorithms and benchmark them by investigating the one-axis twisting protocol, the thermalization in a deformed PXP model, and the ground state of a spin-1 Affleck-Kennedy-Lieb-Tasaki chain in a transverse field.

To simulate the real- and imaginary-time evolution of a many-electron system on a quantum computer based on the first-quantized formalism, we need to encode molecular orbitals (MOs) into qubit states for typical initial-state preparation. We propose an efficient scheme for encoding an MO as a many-qubit state from a Gaussian-type solution that can be obtained from a tractable solver on a classical computer. We employ the discrete Lorentzian functions (LFs) as a fitting basis set, for which we maximize the fidelity to find the optimal Tucker-form state to represent a target MO. For $n_{\mathrm{prod}}$ three-dimensional LFs, we provide the explicit circuit construction for the state preparation involving $O\left(n_{\mathrm{prod}}\right)$ cnot gates. Furthermore, we introduce a tensor decomposition technique to construct a canonical-form state to approximate the Tucker-form state with controllable accuracy. Rank-$R$ decomposition reduces the cnot gate count to $O\left(R{n}_{\mathrm{prod}}^{1/3}\right).$ We demonstrate via numerical simulations that the proposed scheme is a powerful tool for encoding MOs of various quantum chemical systems, paving the way for first-quantized calculations using hundreds or more logical qubits.

Exchange-only (EO) spin qubits in quantum dots offer an expansive design landscape for engineering scalable device layouts. The study of two-EO-qubit operations, which involve six electrons in six quantum dots, has so far been limited to a small number of possible configurations, and previous works lack analyses of design considerations and implications for quantum error correction. Using a simple and fast optimization method, we generate complete pulse sequences for cx, cz, $i$swap, leakage-controlled cx, and leakage-controlled cz two-qubit gates on 450 unique planar six-dot topologies and analyze differences in sequence length (up to 43% reduction) across topology classes. In addition, we show that relaxing constraints on postoperation spin locations can yield further reductions in sequence length; conversely, constraining these locations in a particular way generates a cxswap operation with minimal additional cost over a standard cx. We integrate this pulse library into the Intel quantum stack and experimentally verify pulse sequences on a Tunnel Falls chip for different operations in a linear-connectivity device to confirm that they work as expected. Finally, we explore architectural implications of these results for quantum error correction. Our work guides hardware and software design choices for future implementations of scalable quantum-dot architectures.

The dynamical and radiative features of an excited system of two identical atoms are analyzed. The metastability of the system, the directionality of its emission, and its internal forces are studied. Closed-form expressions are derived for the time propagator of the system, for the angular distribution of its spontaneous emission, and for its internal dipole forces, both conservative and nonconservative. The latter reveals the presence of nonreciprocal forces, which leads to a net time-dependent force upon the system. We estimate that, for a free binary system of Li Rydberg atoms, the net internal force may cause a displacement of its center of mass as large as 120 nm over a lifetime.

We propose using many-body Ramsey interferometry to measure correlation functions of one-dimensional (1D) integrable systems. The 1D transverse-field Ising model, which is conjectured to equilibrate into nonthermal generalized Gibbs ensemble (GGE) steady states, is studied. It is shown that retarded Green's functions, as opposed to ordinary spin-spin correlators considered previously, convincingly distinguish between the GGE and thermal postquench steady states, justifying the assumption of convergence towards the GGE as the system equilibrates. We also propose the experimental protocol for measuring response functions with Ramsey interferometry, which can be used to distinguish between different postquench phases of the model. Our proposal can be realized with current ultracold atom techniques and opens up the possibility to study dynamics in nonthermal ensembles.

Spin-orbit coupling (SOC) changes the Fermi surface and creates topological states with non-Abelian Majorana zero modes. However, it also drastically suppresses the Cooper pairing with finite momentum and thus the coexistence of Majorana zero modes and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is still challenging to be observed. In this work we introduce more complex interactions to the platform and investigate the unconventional superfluidity of a dipolar fermionic gas in a biwire configuration with the SOC induced by laser-assisted interwire tunneling. Employing a nonlocal self-consistent Bogoliubov–de Gennes formalism, we reveal a complex phase diagram featuring various topological-superfluid phases. In particular, due to the peculiar competition between the long-range dipolar interaction and the SOC, a phase separation structure emerges, exhibiting a stripe FFLO phase core encompassed by the topological-superfluid states. Moreover, the long-range dipolar interaction induces a remarkable oscillatory structure in the resultant Majorana zero modes at the FFLO phase boundary and enables direct manipulation of these zero modes. Finally, we provide an experimental proposal to realize our system and give the method to detect the novel quantum phase. The discovery of the Majorana zero modes at the interface between the FFLO state and the topological phase, along with their unique properties, deepens our understanding of Majorana fermions and enriches the zoo of Majorana quasiparticles.

Oscillators are often employed as a model of radiation fields, which may couple to an atom and play an important role for creating and manipulating nonclassical states in quantum metrology, quantum simulation, and quantum information. Aging transitions in coupled oscillators have been studied extensively in both the classical and quantum contexts. It is well known that the onset of aging transitions can be modulated by the dissipative coupling between oscillators. In this study, we propose an alternative way to modulate the aging transition through coherent couplings between a two-level atom and the oscillators. Our findings reveal that, compared to atom-free systems in both classical and quantum regimes, the atom-oscillator coherent interaction reduces the inactive-to-total oscillator ratio required for aging transitions. Analytical results of the transition for both the classical oscillators and quantum oscillators suggest that the decay rate of the atom and the atom-oscillator coupling strength jointly change the aging transition point. The physics behind the observation is also elucidated in this article. Our research introduces a readily implementable strategy for manipulating aging transitions in more intricate systems, thereby advancing the control and understanding of these critical transitions in quantum technologies.