As a branch of quantum machine learning, quantum reinforcement learning (QRL) aims to solve complex sequential decision-making problems more efficiently and effectively than its classical counterpart by exploiting quantum resources. However, in the noisy intermediate-scale quantum (NISQ) era, its realization is challenged by the ubiquitous noise-induced decoherence. Here, we propose a noise-resilient QRL scheme for a quantum eigensolver with a two-level system as an agent. By investigating the nonMarkovian decoherence effect on the QRL for solving the eigenstates of the agent-environment interaction Hamiltonian, we find that the formation of a bound state in the energy spectrum of the total agent-noise system restores the QRL performance to that in the noiseless case. Providing a universal physical mechanism to suppress the decoherence effect on quantum machine learning, our result lays the foundation for designing NISQ algorithms and offers a guideline for their practical implementation.

Quantum steering ellipsoids (QSEs) provide a geometric representation, within the Bloch picture, of all possible states to which one qubit can be steered through measuring another correlated qubit. However, in realistic settings, quantum systems are inevitably coupled to their environment, resulting in decoherence and degradation of the QSEs. Here, by investigating how local dissipative environments coupled to each qubit affect the quantum steering, we find that the geometry of each party's QSEs is closely tied to the non-Markovian effect and the formation of a bound state in the energy spectrum of the total qubit-environment system. The bound state provides the ability and the non-Markovian effect provides the dynamical way for preserving the QSEs. We systematically examine the characteristics of QSEs under three distinct scenarios, i.e., two-sided bound states, one-sided bound states, and no bound state, revealing a diverse range of steering types. Our work establishes quantum reservoir engineering as a tunable strategy for protecting and controlling quantum steering in open systems, offering a practical pathway toward robust steering-based quantum technologies.

The bulk-boundary correspondence (BBC), which relates topological invariants to boundary modes, is well understood for linear systems but remains an open question in the presence of nonlinearity, where multigap topologies make the BBC obscure and the topological description troublesome. We address this by developing an auxiliary-system formalism that enables topological classification of nonlinear-eigenvalue systems. In the two-dimension (2D) case, we show that two fixed eigenvalues can harbor first-order gapless boundary modes and second-order corner modes. Stacking this 2D system along the third dimension (3D) reveals distinct hybrid-order realizations. Under uniform stacking, the corner states in the xy plane transform into hinge states along the z axis, yielding a 3D second-order phase, while the gapless boundary states become side-surface states, yielding a 3D first-order phase. For dimerized stacking, these states are further confined to the two ends of the z axis, yielding a 3D third-order phase, and localized at the hinges, yielding a 3D second-order phase. Our results establish a multiband bulk-boundary correspondence and identify stacking engineering as a versatile platform for exploring hybrid-order topological phases in nonlinear systems.

As a crucial resource in the field of quantum metrology, spin squeezing can facilitate highly precise measurements that surpass the limitations imposed by classical physics. However, the quantum advantages of spin squeezing can be significantly compromised by decoherence, thereby impeding its practical implementation. Here, by investigating the influence of local dissipative environment on spin squeezing beyond the conventional Born-Markov approximation, we find a mechanism to protect spin squeezing from decoherence and show that robust spin squeezing can be achieved in the steady state. We outline an experimental proposal to verify our prediction in a trapped-ion platform. Overcoming the challenges set by decoherence on spin squeezing, our work provides a guideline for realizing high-precision sensing in realistic environments.

Quantum steering ellipsoid (QSE) provides a faithful representation of a two-qubit state. When extended to tripartite systems, the steerability from a trusted party to different receivers is subject to volume monogamy relations, which only constrain the total steerability but cannot individually eliminate the steerability of an untrusted third party, leaving a potential channel for information leakage via steering. Here, we show that this residual steerability can be completely suppressed by selectively engineering bound states in local qubit-environment subsystems, without compromising the steerability between trusted parties. Specifically, when bound states are formed in the subsystems formed by the trusted parties and their environments but absent in the untrusted one, the untrusted party's QSE volume decays to zero, while the trusted party's QSE volume remains finite. Our results establish selective bound-state engineering as a mechanism for extreme volume monogamy, with potential applications in secure quantum communication with an untrusted third party.

Information units are progressively approaching the fundamental physical limits of integration density, including in terms of extremely small sizes, multistates and probabilistic traversal. However, simultaneously encompassing all of these characteristics in a unit remains elusive. Here, via real-time in situ electrical monitoring, we clearly observed stochastic alterations of multiple conductance states in Sc2C2@C88. The true random bit sequence generated exhibited an autocorrelation function whose confidence interval fell within ±0.02, demonstrating high-quality randomness. The alterations of multiple conductance states are controllable, that is, whose probability distributions could traverse from 0 to 1, enabling us to factorize 551 into its prime factors. Furthermore, we proposed a matrix-chain multiplication scheme and experimentally verified the multiplication of two 4 × 4 state-transition matrices with a small maximum error of <0.05. Combined with theoretical calculations, the stochastic but controllable multistates are probably attributed to the rich energy landscape, which could be stepwise changed by the electric field. Our findings reveal extremely small multilevel probabilistic bit for matrix multiplication, which pave the way for ultra-compact intelligent electronic devices.

The advancement of magnonics has facilitated the utilization of hybrid magnetic systems in quantum technologies. A hybrid magnetic lattice (HML), comprising an array of superconducting loops and magnetic particles, has been devised as a quantum bus to disseminate quantum resources among magnetic quantum entities (MQEs) serving as nodes of a quantum network. However, the HML also exerts a decoherence effect on the MQEs, which has the potential to impair its practical performance. By studying the non-Markovian dynamics of two MQEs comprised of either nitrogen-vacancy centers or magnon modes coupled to two independent HMLs, we propose a Floquet-engineering scheme by applying periodic driving on the MQEs to overcome the unwanted effect. It is revealed that the decoherence can be suppressed and a significant degree of entanglement can be maintained in the steady state, provided that a FBS exists within the quasienergy spectrum of the total system of each periodically driven MQE and its HML. This result enhances our ability to control hybrid magnetic systems and is beneficial for the application of HML in quantum networks.

As a key component of quantum networks, the quantum router distributes quantum information among different quantum nodes. The silicon-vacancy (SiV) center in diamond offers a promising platform for quantum technology due to its strong strain-induced coupling with phonons. However, the development of a practical quantum router faces the challenges of achieving long-range entanglement and suppressing decoherence. Here, we propose a non-Markovian quantum router based on a diamond waveguide embedded with an array of SiV centers as the quantum nodes. Unlike conventional channel-switching methods, our design enables parallel quantum-state transfer from a single input node to multiple target nodes, analogous to a classical WiFi router. We demonstrate that persistent entanglement and suppressed decoherence of the SiV centers over long distances are achievable when bound states are present in the energy spectrum of the total system formed by the SiV centers and the phonon waveguide. Our scheme enriches the implementation of quantum routing and prompts the development of solid-state quantum networks.

The parametric amplification enabled by two-photon driving constitutes a versatile platform for advanced quantum technologies. We present an optimized scheme for implementing quantum batteries (QBs) based on a superconducting circuit system, where a two-photon-driven LC resonator serves as the charger and an array of transmon qubits functions as the battery. Our results show that two-photon parametric driving exponentially enhances the effective cavity-qubit coupling, which in turn gives rise to near-degenerate energy-level structures and highly entangled quantum states. This significantly enhances the charging power and enables rapid energy transfer from the charger to the battery. Moreover, the engineered squeezed cavity mode and the associated quantum correlations effectively suppress environmentally induced decoherence, thereby delaying energy leakage and facilitating stable energy storage. The proposed scheme remains robust against practical experimental imperfections, such as parameter disorder and environmental noise, preserving its performance advantages. The work provides a feasible platform for realizing high-power, high-stability QBs and highlights the potential of parametric control in quantum energy technologies.

A topological insulator is regarded as an ideal candidate for information storage and high-speed lossless electrical transmission devices due to robust topological protected boundary modes. Previous studies revealed that symmetry exerts an unbreakable constraint on the existence, classes, and orders of its boundary modes. It severely limits the controllability and application of a topological insulator. Here, we propose a Floquet-engineering method to break this symmetry-imposed constraint on a topological insulator. By applying periodic driving on a system belonging to a symmetry class that prohibits the existence of first-order topological phases, we find that rich first-order boundary modes are created. Interestingly, exotic hybrid-order topological insulators with coexisting first-order helical boundary modes and second-order corner modes not only in two different quasienergy gaps but also in one single gap are generated easily by periodic driving. Refreshing the prevailing understanding of symmetry constraint on topological phases, our result opens an avenue for the creation of exotic topological insulators without altering symmetries. It greatly expands the scope of the fabricated materials that host topological insulators.

Mechanical qubits offer unique advantages over other qubit platforms, primarily in terms of coherence time and possibilities for enhanced sensing applications, but their potential is constrained by the inherently weak nonlinearities and small anharmonicity of nanomechanical resonators. We propose overcoming this shortcoming by using squeezed-Fock states of phonons in a parametrically driven nonlinear mechanical oscillator. We find that, under two-phonon driving, squeezed-Fock states become eigenstates of a Kerr-nonlinear mechanical oscillator, featuring an energy spectrum with exponentially enhanced and tunable anharmonicity, such that the transitions to higher energy states are exponentially suppressed. This enables us to encode the mechanical qubit within the ground and first excited squeezed-Fock states of the driven mechanical oscillator. This kind of mechanical qubit is termed mechanical squeezed-Fock qubit. We also show that our mechanical qubit can serve as a quantum sensor for weak forces, with its resulting sensitivity increased by at least one order of magnitude over that of traditional mechanical qubits. The proposed mechanical squeezed-Fock qubit provides a powerful quantum phonon platform for quantum sensing and information processing.

Going beyond the conventional classification rule of Altland-Zirnbauer symmetry classes, PT symmetric topological phases are classified by (PT)^2=1 or -1. The interconversion between the two PT-symmetric topological classes is generally difficult due to the constraint of (PT)^2. Here, we propose a scheme to control and interconvert the PT-symmetric topological classes by Floquet engineering. We find that it is the breakdown of the ℤ_2 gauge, induced by the π phase difference between different hopping rates, by the periodic driving that leads to such an interconversion. Relaxing the system from the constraint of (PT)^2, rich exotic topological phases, e.g., the coexisting PT-symmetric first-order real Chern insulator and second-order topological insulators not only in different quasienergy gaps, but also in one single gap, are generated. In contrast to conventional Floquet topological phases, our result provides a way to realize exotic topological phases without changing symmetries. It enriches the family of topological phases and gives an insightful guidance for the development of multifunctional quantum devices.

Levitated mesoscopic particles hold the promise of revolutionizing gravity sensing by using quantum effects. However, conventional quantum gravimeters based on such systems fail to harness the intrinsic large-mass advantage of the particles, because their commonly utilized auxiliary quantum systems counteract the role of mass as a resource. To overcome this limitation, we propose a quantum gravimetry by directly using the mechanical qubit (QM) formed by a levitated particle as the gravity sensor. Without resorting to the auxiliary quantum system, our scheme enables a straightforward readout of the particle's motion under gravitational influence. The obtained sensitivity behaves as a m^-1/2-scaling with the mass m. We also generalize our scheme to the mechanical cat qubit as the gravity sensor. The sensitivity further scales as N^-1/2 with the mean phonon number N. In the experimentally realizable parameter regime, a sensitivity on the order of 0.1 µGal/√(Hz) can be achieved, which outperforms the traditional schemes by two orders of magnitude. Reaching the double standard quantum limits with m and N simultaneously, our scheme provides a feasible route toward compact high-sensitivity quantum gravimetry.

Exploiting quantum effects for energy storage, quantum batteries (QBs) offer compelling advantages over conventional ones in terms of superior energy density, ultrafast charging, and high conversion efficiency. However, their realization is hampered by decoherence, which causes incomplete charging, rapid self-discharging, and reduced extractable work. Here, we propose a QB architecture based on a chiral magnonic platform. It comprises two yttrium iron garnet (YIG) spheres, one serving as the charger and the other as the QB, coupled to a waveguide. The unique chiral coupling between magnons and the guided electromagnetic fields breaks inversion symmetry, inducing both nonreciprocal energy flow and coherent interference between the charger and QB. Their synergy endows our QB with a 34-fold increase in energy capacity and a 55-fold boost in extractable work compared to its achiral counterpart in an experimentally accessible regime. Our scheme harnesses the decoherence from the electromagnetic fields and turns its destruction into an asset, which enables the robustness and wireless-like remote charging features of the QB. Our analysis reveals that these extraordinary capabilities stem from quantum coherence. By establishing chirality as a useful quantum resource, our work paves a viable path toward the realization of QBs.

Topological phases are a novel class of physical phases, distinct from those defined by Landau symmetry-breaking theory and characterized by order parameters. The phase transitions of topological phases are typically unrelated to symmetry breaking, their properties being described by topological invariants. The important characteristic of topological phases is their topological protection: as long as the band structure remains open, continuous variations or perturbations of the Hamiltonian will not alter the topological properties of the system. Their uniqueness lies in boundary states being linked to topological invariants and exhibiting distinctive transport properties. Despite rapid advances in this field, material limitations persist, making the control of topological properties an urgent challenge. To address this challenge, Floquet engineering offers novel approaches. By introducing time as a tunable variable, this method transforms systems into periodic time-dependent regimes, thereby enabling precise control over topological properties and providing practical pathways for applications. This paper primarily explores novel topological phases induced by periodic driving in diverse systems, including phase transitions between distinct topological phases, topological phases governed by major topological invariants, and hybrid-order topological phases.

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 and 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.

The discovery of topological phases has ushered in a new era of condensed matter physics and revealed a variety of natural and artificial materials. They obey the bulk-boundary correspondence (BBC), which guarantees the emergence of boundary states with nonzero topological invariants in the bulk. Widespread attention has been paid to extending topological phases to nonlinear and non-Hermitian systems. However, the BBC and topological invariants of non-Hermitian nonlinear systems remain largely unexplored. Here, we establish a complete BBC and topological characterization of the topological phases in a class of non-Hermitian nonlinear-eigenvalue systems by introducing an auxiliary system. We restore the BBC broken by non-Hermiticity via employing the generalized Brillouin zone on the auxiliary system. Remarkably, we discover that the interplay between non-Hermiticity and nonlinearity creates an exotic complex-band topological phase that coexists with the real-band topological phase. Our results enrich the family of nonlinear topological phases and lay a foundation for exploring novel topological physics in metamaterial systems.

Abstract Going beyond the conventional classification rule of Altland-Zirnbauer symmetry classes, P T symmetric topological phases are classified by ( P T ) 2 = 1 or − 1 . The interconversion between the two P T -symmetric topological classes is generally difficult due to the constraint of ( P T ) 2 . Here, we propose a scheme to control and interconvert the P T -symmetric topological classes by Floquet engineering. We find that it is the removal of the Z 2 gauge degree of freedom, induced by the π phase difference between different hopping rates, by the periodic driving that leads to such an interconversion. Relaxing the system from the constraint of ( P T ) 2 , rich exotic topological phases, e.g. the coexisting P T -symmetric first-order real Chern insulator and second-order topological insulator not only in different quasienergy gaps, but also in one single gap, are generated. In contrast to conventional Floquet topological phases, our result provides a way to realize exotic topological phases without changing symmetries. It enriches the family of topological phases and gives an insightful guidance for the development of multifunctional quantum devices.

It was recently found that, going beyond the tendfold Altland-Zirnbauer symmetry classes and violating the bulk-boundary correspondence of the usual topological phases, PT-invariant systems support a real Chern insulator with the so-called boundary criticality, which forbids the transition between different orders of topological phases accompanied by the closing and reopening of the bulk-band gap. Here, we fnd that the periodic driving can break the boundary criticality of a PT-invariant system. Setting free from the the boundary criticality, diverse first- and second-order topological phases absent in the static case are found in both the zero and Pi/T modes. The application of our result in the three-dimensional PT-invariant system permits us to discover exotic second-order Dirac and nodal-line semimetals with coexisting surface and hinge Fermi arcs. Enriching the family of the topological phases in PT-invariant systems, our result provides us a useful way to explore novel topological phases.