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Superconducting qubits have emerged as a premier platform for large-scale quantum computation, yet the fidelity of state readout is often hindered by random noise and crosstalk, especially in multi-qubit systems. While neural networks trained on labeled data have shown promise in reducing crosstalk effects during readout, their current capabilities are limited to binary discrimination of joint-qubit states due to architectural constraints. Here we introduce a time-resolved modulated neural network capable of full-state tomography for individual qubits, enabling detailed time-resolved measurements like Rabi oscillations. This scalable approach, with a dedicated module per qubit, mitigated readout error by an order of magnitude under low signal-to-noise ratios and substantially reduced variance in Rabi oscillation measurements. This advancement bolsters quantum state discrimination with neural networks, and propels the development of next-generation quantum processors with enhanced performance and scalability.

The nonclassicality of a macroscopic single-mode optical superposition state is potentially convertible into entanglement, when the state is mixed with the vacuum on a beam splitter. Considering light beams with polarization degree of freedom in Euclidean space as coherent product states in a bipartite Hilbert space, we propose a method to convert the two orthogonal polarizations into simultaneous entanglement and classical nonseparability through nonclassicality in the superpositions of coherent and displaced Fock states. Equivalent Bell state emerges from the resulted superpositions and the proportion of mixed entanglement and nonseparablity is determined by the displacement amplitudes along the polarization directions. We characterize the state nonclassicality via features in Wigner distributions and propose an experimental method for generating these states and measuring them via homodyne tomography.

Modern cryptographic protocols rely on sophisticated hash functions to generate quasi-unique numbers that serve as signatures for user authentication and other security verifications. The security could be compromised by finding texts hash-mappable to identical numbers, forming so-called collision attack. Seeding a disturbance vector in the hash mapping to obtain a successful collision is that a major focus of cryptography study in the past two decades to improve hash protocols. We propose an algorithm that takes advantage of entangled quantum states for concurrent seeding of candidate disturbance vectors, out of which the one entailing collision is selected through a combination of quantum search, phase gating, diffusion gating, and information feedbacks from classical computing machinery. The complexity reduction is shown to be on the order of $\mathcal{O}(2^{n/2+1})$ where $n$ is the number of qubits encoding addresses. We demonstrate the practicality of the proposed by an implementation scheme based on degenerate optical parametric oscillators.

Recent experimental evidences point to two-level defects, located in the oxides and on the interfaces of the Josephson junctions, as the major constituents of decoherence in superconducting qubits. How these defects affect the qubit evolution with the presence of external driving is less well understood since the semiclassical qubit-field coupling renders the Jaynes-Cummings model for qubit-defect coupling undiagonalizable. We analyze the decoherence dynamics in the continuous coherent state space induced by the driving and solve the master equation endowed with an extra decay-cladded driving term via a Fokker-Planck equation. The solutions for diffusion propagators as Gaussian distributions show four distinct dynamic phases: four types of convergence paths to limit cycles of varying radius by the distribution mean, which are determined by the competing external driving and the defect decays. The qubit trajectory resulted from these solutions is a super-Poissonian over displac ed Fock states, which reduces to a Gibbs state of effective temperature decided by the defect at zero driving limit. Further, the Poincare map shows the dependence of the rate of convergence on the initial state. In other words, the qubit evolution can serve as an indicator of the defect coupling strength through the variation of the driving strength as a parameter.

A scheme to encode arbitrarily long integer pairs on degenerate optical parametric oscillations multiplexed in time is proposed. The classical entanglement between the polarization directions and the phases of the oscillating pulses, regarded as two computational registers, furnishes the integer correlations within each pair. We show the major algorithmic steps, modular exponentiation and discrete Fourier transform, of Shor's quantum factoring algorithm can be executed in the registers as pulse interferences under the assistance of external logics. The factoring algorithm is thus rendered equivalent to a semi-classical optical-path implementation that is scalable and decoherence-free. The sought-after multiplicative order, from which the prime factors are deduced, is identified from a two-dimensional fringe image generated by four-hole interference measured at the end of the path.

When considered as orthogonal bases in distinct vector spaces, the unit vectors of polarization directions and the Laguerre-Gaussian modes of polarization amplitude are inseparable, constituting a so-called classical entangled light beam. Equating this classical entanglement to quantum entanglement necessary for computing purpose, we show that the parallelism featured in Shor's factoring algorithm is equivalent to the concurrent light-path propagation of an entangled beam or pulse train. A gedanken experiment is proposed for executing the key algorithmic steps of modular exponentiation and Fourier transform on a target integer $N$ using only classical manipulations on the amplitudes and polarization directions. The multiplicative order associated with the sought-after integer factors is identified through a four-hole diffraction interference from sources obtained from the entangled beam profile. The unique mapping from the fringe patterns to the computed order is demonstrated through simulations for the case $N=15$.

Classical entanglement refers to non-separable correlations between the polarization direction and the polarization amplitude of a light field. The degree of entanglement is quantified by the Schmidt number, taking the value of unity for a separable state and two for a maximally entangled state. We propose two detection methods to determine this number based on the distinguishable patterns of interference between four light sources derived from the unknown laser beam to be detected. The second method being a modification of the first one has the interference fringes form discernable angles uniquely related to the entangled state. The maximally entangled state corresponds to fringes symmetric about the diagonal axis at either 45{\deg} or 135{\deg} direction while the separable state corresponds to fringes symmetric either about the X- or Y-axis or both simultaneously. States with Schmidt number between unity and two have fringes of symmetric angles between these two extremes. The detection methods would be beneficial to constructing transmission channels of information contained in the classically entangled states.

The generation of GHZ states calls for simultaneous excitation of multiple qubits. The peculiarity of such states is reflected in their nonzero distributed entanglement which is not contained in other entangled states. We study the optimal way to excite three superconducting qubits through a common cavity resonator in a circuit such that the generation of distributed entanglement among them could be obtained at the highest degree in a time-controllable way. A non-negative measure quantifying this entanglement is derived as a time function of the quadripartite system evolution. We find that this measure does not stay static but obtains the same maximum periodically. When the qubit-resonator couplings are allowed to vary, its peak value is enhanced monotonically by increasing the greatest coupling strength to one of the qubits. The period of its peak to peak revival maximizes when the couplings become inhomogeneous, thus qubit excitation becoming asynchronous, at a relative ratio of 0.35. The study demonstrates the role of asynchronous excitations for time-controlling multi-qubit systems, in particular in extending entanglement time.

We proposed a spectroscopic method that extends Ramsey's atomic spectroscopy to detect the transition frequency of a qubit fabricated on a superconducting circuit. The method uses a multi-interval train of qubit biases to implement an alternate resonant and dispersive couplings to an incident probe field. The consequent absorption spectrum of the qubit has a narrower linewidth at its transition frequency than that obtained from constantly biasing the qubit to resonance while the middle dispersive evolution incurs only a negligible shift in detected frequency. Modeling on transmon qubits, we find that the linewidth reduction reaches 23% and Ramsey fringes are simultaneously suppressed at extreme duration ratio of dispersion over resonance for a double-resonance scheme. If the scheme is augmented by an extra resonance segment, a further 37% reduction can be achieved.

Microwave pulses are used ubiquitously to control and measure qubits fabricated on superconducting circuits. Due to continual environmental coupling, the qubits undergo decoherence both when it is free and during its interaction with the microwave pulse. As quantum logic gates are executed through pulse-qubit interaction, we study theoretically the decoherence-induced effects during the interaction, especially the variations of the pulse, under a dissipative environment with linear spectral distribution. We find that a transmissible pulse of finite width adopts an asymmetric multi-hump shape, due to the imbalanced pumping and emitting rates of the qubit during inversion when the environment is present. The pulse shape reduces to a solitonic pulse at vanishing dissipation and a pulse train at strong dissipation. We give detailed analysis of the environmental origin from both the perspectives of envelope and phase of the propagating pulse.

The primordial model of quantum computation was introduced over thirty years ago and the first quantum algorithms have appeared for over twenty years. Yet the exact architectures for quantum computer seem foreign to an undergraduate student major in computer science or engineering, even though the mass media has helped popularize the terminologies in the past decade. Despite being a cutting-edge technology from both the theoretical and the experimental perspectives, quantum computation is indeed imminent and it would be helpful to give the undergraduate students at least a skeleton understanding of what a quantum computer stands for. Since instruction-set architectures originated from classical computing models are familiar, we propose analogously a set of quantum instructions, which can be composed to implement renowned quantum algorithms. Albeit the similarity one can draw between classical and quantum computer architectures, current quantum instructions are fundamentally incommensurable from their classical counterparts because they lack the innate capability to implement logical deductions and recursions. We discuss this trait in length and illustrate why it is held responsible that current quantum computers not be considered general computers.

Using a microscopic master equation to account for the environmental effects, we compute the decoherence culminated during the propagation of a microwave pulse of arbitrary shape through a superconducting qubit. It is shown that the qubit decoherence vanishes and the pulse shape remains absorption-free when the latter adopts a soliton shape with $n\pi$ area. Otherwise, the environmental feedback decelerates the velocity of the soliton envelop and induces an monotonic increase of phase in the microwave. A pulse of non-$n\pi$ area thus ramifies into a transparent part that travels decoherence-free at incident velocity and a slowing part that decays through space. The ramification explains the environmental origin of pulse splitting observed in self-induced transparency.

Magnetic skyrmions have attracted great research interest in recent years due to their exotic physical properties, scientific merit and potential applications in modern technology. Here, we apply a quantum computational method to investigate the spin configurations of Fe$_{0.5}$Co$_{0.5}$Si-Like quasi-two-dimensional ferromagnetic system with co-existence of Dzyaloshinsky-Moriya and Heisenberg exchange interactions. We find that within a weak magnetic field perpendicular to the film plane, skyrmion crystal (SkX) of hexagonal-close-packed pattern can be induced, the spin configurations evolve with applied magnetic field and temperature. This quantum model, if scaled, is able to qualitatively reproduce the experimental results of SkX with long periodicity, especially, when the skyrmion size is around a few nano-meters in diameter, it is expected to be more accurate than the classical ones., Comment: 7 figures

We study the absorption spectrum of a probe field by a {\Lambda}-type three-level system, which is coupled to a quantized control field through the two upper energy levels. The probe field is applied to the ground and the second excited states. When the quantized control field is in vacuum, we derive a threshold condition to discern vacuum induced transparency (VIT) and vacuum induced Autler- Townes splitting (ATS). We also find that the parameter change from VIT to vacuum induced ATS is very similar to that from broken PT symmetry to PT symmetry. Moreover, we find the photon number resolved spectrum in the parameter regime of vacuum induced ATS when the mean photon number of the quantized control field is changed from zero (vacuum) to a finite number. However, there is no photon number resolved spectrum in the parameter regime of VIT even that the quantized control field contains the finite number of photons. Finally, we further discuss possible experimental realization.

Some nonlinear radiations such as superfluorescence can be understood as cooperative effects between atoms. We regard the cooperative radiation as a manifested effect secondary to the intrinsic synchronization among the atoms and propose a time-resolved measure of synchronization on a cavity-coupled dual-qubit system using multipartite concurrence. Comparing the variation of the concurrence over time with that of an asynchronicity measure, we find that the synchronization between the qubits features a time delay characteristic to the initiation of superfluorescent pulses. The delay coincides with the duration for the qubits to establish cooperation and emit the collective radiation, after which the concurrence monotonically increases to a stationary value while the asynchronicity dives to a steady minimum. Furthermore, the establishment of synchronization is determined by the qubit-cavity coupling strength. Asynchronicity shows that synchronization is only possible when the coupling enters strong regime and sustains to a high level when the coupling becomes ultra-strong.

We employ a self-consistent simulation approach based on quantum physics here to study the magnetism of antiferromagnetic skyrmions formed on manolayer nanodisk planes. We find that if the disk is small and the Dzyaloshinsky-Moriya (DM) interaction is weak, a single magnetic vortex may be formed on the disk plane. In such a case, when uniaxial anisotropy normal to the disk plane is further considered, the magnetic configuration remains unchanged, but the magnetization is enhanced in that direction, and reduced in other two perpendicular orientations. Very similarly, a weak external magnetic field normal to the disk plane cannot obviously affect the spin structure of the nanodisk; however, when it is sufficiently strong, it can destroy the AFM skyrmion completely. On the other hand, by increasing DM interaction so that the disk diameter is a few times larger than the DM length, more self-organized magnetic domains, such as vortices and strips, will be formed in the disk plane. They evolve with decreasing temperature, however always symmetric about a geometric axis of the square unit cell. We further find that in this case introducing normal magnetic anisotropy gives rise to the re-construction of AFM single-vortex structure or skyrmion on the disk plane, which provides a way to create and/or stabilize such spin texture in experiment.

An optical field inside a Fabry-Perot cavity would exhibit multistability either when an atomic medium, acting as a classical dielectric, is filled into the cavity or when the cavity becomes optomechanical where one reflecting end becomes movable. An external laser is essential in both cases to drive the cavity mode out of the zero equilibrium state. We study the equilibrium states of an atom-filled optomechanical cavity, where the atoms are considered a collective two-level systems as well as an active component that replaces the role of the driving laser. Multistability is found when the atomic ensemble is lossy, for which the complex atom-photon coupling breaks the \mathcal{PT}-symmetry of the system Hamiltonian and matches in a periodic pattern to the frequencies and the linewidths of the cavity mode and the collective bosonic mode of the atoms. We show an input-output hystersis cycle between the atomic mode and the cavity mode to demonstrate the driving role the atoms replace an extra-cavity laser., Comment: 7 pages

We employ a self-consistent simulation approach based on quantum theory to investigate the physical properties of a pair of ferromagnetic and antiferromagnetic nanotubes. It was observed that under the given conditions, no matter the external magnetic field was absent or applied along the easy longitudinal axis, the spins always ordered in that direction due to the special geometric shape of the tubes and the magnetic uniaxial anisotropy, so that the two sorts of nanosystems exhibit typical ferromagnetic and antiferromagnetic properties, which may find applications in modern technology, in strong contrast to the phenomena observed previously in nanoparticle, where an external magnetic field, applied parallel to the antiferromganetically coupled spins, is able to turn the spins off their original direction to form symmetric pattern around the field direction. This peculiar feature enable us to build up one-dimensional chain models for the two sorts of nanosystems. Considering their fast computational speed and simplicity, these theoretical models were then utilized to investigate the finite size effects of the nanosystems, and perform further analysis for long tubes. Especially, our results obtained with the theoretical models and the numerical approach are exactly identical, verifying the correctness and applicability of the computational methodology.

We give a theoretical study on the magnetic properties of monolayer nanodisks with both Heisenberg exchange and Dzyaloshinsky-Moriya (DM) interactions. In particular, we survey the magnetic effects caused by anisotropy, external magnetic field, and disk size when DM interaction is present by means of a new quantum simulation method based on mean-field theory. This computational approach finds that uniaxial anisotropy and transverse magnetic field enhances the net magnetization as well as increases the transition temperature of the vortex phase while preserving the chiralities of the nanodisks. Whereas, when the strength of DM interaction is sufficiently strong for a given disk size, magnetic domains appear within the circularly bounded region, which vanish and gives in to a single vortex when a transverse magnetic field is applied. The latter confirms the magnetic skyrmions induced by the magnetic field as observed in the experiments.

We give a theoretical study of a double-cavity system in which a mechanical resonator beam is coupled to two cavity modes on both sides through radiation pressures. The indirect coupling between the cavities via the resonator sets up a correlation in the optomechanical entanglements between the two cavities with the common resonator. This correlation initiates an entanglement transfer from the intracavity photon-phonon entanglements to an intercavity photon-photon entanglement. Using numerical solutions, we show two distinct regimes of the optomechanical system, in which the indirect entanglement either builds up and eventually saturates or undergoes a death-and-revival cycle, after a time lapse for initiating the cooperative motion of the left and right cavity modes., Comment: 7 pages

A cavity optomechanical system is initiated by a radiation pressure of a cavity field onto a mirror element acting as a quantum resonator. This radiation pressure can control the thermodynamic character of the mirror to some extent, such as cooling its effective temperature. Here we show that by properly engineering the spectral density of a thermal heat bath that interacts with a quantum system, the evolution of the quantum system can be effectively turned on and off. Inside a cavity optomechanical system, when the heat bath is realized by a multi-mode oscillator modeling of the mirror, this on-off effect translates to infusion or extraction of heat energy in and out of the cavity field, facilitating a four-stroke thermodynamic cycle.

In a circuit quantum eletrodynamic system, a chain of N qubits inhomogeneously coupled to a cavity field forms a mesoscopic quasi-lattice, which is characterized by its degree of deformation from a normal lattice. This deformation is a function of the relative spacing, that is the ratio of the qubit spacing to the cavity wavelength. A polariton mode arise in the quasi-lattice as the dressed mode of the lattice excitation by the cavity photon. We show that the transition probability of the polariton mode is either enhanced or decreased compared to that of a single qubit by the deformation, giving a selective spontaneous radiation spectrum. Further, unlike a microscopic lattice with large-N limit and nearly zero relative spacing, the polariton in the quasi-lattice has uneven decay rate over the relative spacing. We show that this unevenness coincides with the cooperative emission effect expected from the superradiance model, where alternative excitations in the qubits of the lattice result in maximum decay.

The mesoscopic scale of superconducting qubits makes their inter-spacings comparable to the scale of wavelength of a circuit cavity field to which they commonly couple. This comparability results in inhomogeneous coupling strengthes for each qubit and hence asynchronous Rabi excitation cycles among the qubits that form a quasi-lattice. We find that such inhomogeneous coupling benefits the formation of multi-photon resonances between the single-mode cavity field and the quasi-lattice. The multi-photon resonances lead, in turn, to the simultaneous generation of inequivalent GHZ and W types of multipartite entanglement states, which are not transformable to each other through local operations with classical communications. Applying the model on the 3-qubit quasi-lattice and using the entanglement measures of both concurrence and 3-tangle, we verify that the inhomogeneous coupling specifically promotes the generation of the totally inseparable GHZ state.

When a chain of superconducting qubits couples to a coplanar resonator in a cavity, each of its N qubits (equally-spaced with distance l) experiences a different dipole-field coupling strength due to the waveform of the cavity field. We find that this inhomogeneous coupling leads to a pair of l-dependent ladder operators for the angular momentum of the spin chain. Varying the qubit spacing l changes the transition amplitudes between the angular momentum levels. We derive an exact diagonalization of the general N-qubit Hamiltonian and, through the N=4 case, demonstrate how the l-dependent operators lead to a denser one-excitation spectrum and a probability redistribution of the eigenstates. Moreover, it will be shown that the variation of l between its two limiting values coincides with the crossover between Frenkel- and Wannier-type excitons in the superconducting spin chain., Comment: 9 pages, 3 figures, with 3 appendices

Electromagnetically induced transparency and absorption (EIT and EIA) are usually demonstrated by three-level atomic or atom-like systems. In contrast to the usual case, we theoretically study the EIT and EIA in an equivalent three-level system, which is constructed by dressing a superconducting two-level system (qubit) dressed by a single-mode cavity field. In this equivalent system, we find that both the EIT and the EIA can be tuned by controlling the level-spacing of the superconducting qubit and hence controlling the dressed system. This tunability is due to the dressed relaxation and dephasing rates which vary parametrically with the level-spacing of the original qubit and thus affect the transition properties of the dressed qubit and the susceptibility. These dressed relaxation and dephasing rates characterize the reaction of the dressed qubit to an incident probe field. We also use recent experimental data on superconducting qubits (charge, phase, and flux qubits) to demonstrate our approach and show the possibility of experimentally realizing this proposal., Comment: 13 pages