An approximation-free, numerically efficient algorithm is presented for the Hamiltonian eigenstates of the Stark hydrogen problem describing a quantum particle exposed to the central Coulomb force and a homogeneous external field. As an example of application in a state expansion with continuous energy, we calculate the time-dependent wave function of an electron tunneling from a hydrogen atom suddenly exposed to an external electric field.

$\mathcal{PT}$-symmetric quantum theory has attracted extensive attention in recent years because of its novel properties, applications, and even controversial discussions. Many difficulties in applications stem from the unknown of how to simulate the dynamics of $\mathcal{PT}$-symmetric systems in conventional quantum systems. In this work, by clarifying some common confusion in the simulation of $\mathcal{PT}$-symmetric systems, we are able to naturally extend the application scope of the original embedding simulation scheme from pure states to arbitrary mixed states. Based on the above groundwork, we further propose a local-operations-and-classical-communication (LOCC) protocol scheme to simulate the dynamics of a $\mathcal{PT}$-symmetric system. Our LOCC protocol scheme, which needs one ancillary qubit only, can be applied to simulate any arbitrary finite-dimensional $\mathcal{PT}$-symmetric system in the $\mathcal{PT}$-unbroken phase and has several advantages over the original embedding scheme. The success probability is increased to ${\lambda }_{min}$ (${\lambda }_{min}>1$) times in general, even approaching $100\%$ in some special cases, and has a concise bound that makes it easier to estimate the necessary experimental resources in advance. Furthermore, our LOCC protocol has less dependence on but more flexibility in the selection of the metric operator and more adaptability in practical applications, and it is more consistent with the physical intuition. Finally, the physical or philosophical meaning behind the embedding scheme and the LOCC protocol is discussed.

Modeling open quantum systems—quantum systems coupled to a bath—is of value in condensed-matter theory, cavity quantum electrodynamics, nanosciences, and biophysics. The real-time simulation of open quantum systems was advanced significantly by the recent development of chain mapping techniques and the use of matrix product states that exploit the intrinsic entanglement structure in open quantum systems. The computational cost of simulating open quantum systems, however, remains high when the bath is excited to high-lying quantum states. We develop an approach to reduce the computational costs in such cases. The interaction representation for the open quantum system is used to distribute excitations among the bath degrees of freedom so that the occupation of each bath oscillator is ensured to be low. The interaction picture also causes the matrix dimensions to be much smaller in a matrix product state of a chain-mapped open quantum system than in the Schrödinger picture. Using the interaction representation accelerates the calculations by one to two orders of magnitude over the existing matrix-product-state method. In the regime of strong system-bath coupling and high temperatures, the speedup can be as large as three orders of magnitude. The approach developed here is especially promising to simulate the dynamics of open quantum systems in high-temperature and strong-coupling regimes.

We propose the task of local state marking (LSM), where some multipartite quantum states chosen randomly from a known set of states are distributed among spatially separated parties without revealing the identities of the individual states. The collaborative aim of the parties is to correctly mark the identities of states under the restriction that they can perform only local quantum operations (LOs) on their respective subsystems and can communicate with each other classically (CC)—popularly known as the operational paradigm of LOCC. While mutually orthogonal states can always be marked exactly under global operations, this is in general not the case under LOCC. We show that the LSM task is distinct from the vastly explored task of local state distinguishability (LSD)—perfect LSD always implies perfect LSM, whereas we establish that the converse does not hold in general. We also explore entanglement-assisted marking of states that are otherwise locally unmarkable, and we report intriguing entanglement-assisted catalytic LSM phenomena.

We use an error backpropagation (BP) neural network to determine whether an arbitrary two-qubit quantum state is steerable and optimize the steerability bounds of the generalized Werner state. Results show that, regardless of how we select the features for the quantum states, we can use the BP neural network to construct several models to obtain high-performance quantum steering classifiers compared with the support vector machine. Moreover, we predict the steerability bounds of the generalized Werner states using the classifiers that are newly constructed by the BP neural network; that is, the predicted steerability bounds are closer to the theoretical bounds. In particular, high-performance quantum steering classifiers with partial information about the quantum states that we need to measure in only three fixed measurement directions are obtained.

Experimental realization of stabilizer-based quantum error correction (QEC) codes that would yield superior logical qubit performance is one of the formidable task for state-of-the-art quantum processors. A major obstacle toward realizing this goal is the large footprint of QEC codes, even those with a small distance. We propose a circuit based on the minimal distance-3 QEC code, which requires only five data qubits and five ancilla qubits, connected in a ring with iswap gates implemented between neighboring qubits. Using a density-matrix simulation, we show that, thanks to its smaller footprint, the proposed code has a lower logical error rate than surface-17 for similar physical error rates. We also estimate the performance of a neural-network-based error decoder, which can be trained to accommodate the error statistics of a specific quantum processor by training on experimental data.

Quantum simulators are attracting great interest because they promise insight into the behavior of quantum many-body systems that are prohibitive for classical simulations. The generic output of quantum simulators are snapshots, obtained by means of projective measurements. These provide new information, such as full distribution functions, that goes beyond the more commonly evaluated expectation values of observables while adding shot-noise uncertainty to the latter. Hence, a central goal of theoretical efforts must be to predict these exact same quantities that can be measured in experiments. Here, we report on a snapshot-based study of particle currents in quantum lattice models with a conserved number of particles. It is shown how the full probability distribution of locally resolved particle currents can be obtained from suitable snapshot data. Moreover, we investigate the Hall response of interacting bosonic flux ladders, exploiting snapshots drawn from matrix-product states. Flux ladders are minimal lattice models, which enable microscopic studies of the Hall response in correlated quantum phases, and they are successfully realized in current quantum-gas experiments. Using a specific pattern of unitary two-site transformations, it is shown that the Hall polarization and the Hall voltage can be faithfully computed from a realistic number of snapshots obtained in experimentally feasible quench and finite-bias simulations.

The race to heuristically solve nondeterministic polynomial-time (NP) problems through efficient methods is ongoing. Recently, optics was demonstrated as a promising tool to find the ground state of a spin-glass Ising Hamiltonian, which represents an archetypal NP problem. However, achieving completely programmable spin couplings in these large-scale optical Ising simulators remains an open challenge. Here, by exploiting the knowledge of the transmission matrix of a random medium, we experimentally demonstrate the possibility of controlling the couplings of a fully connected Ising spin system. By tailoring the input wave front we showcase the possibility of modifying the Ising Hamiltonian both by accounting for an external magnetic field and by controlling the number of degenerate ground states and their properties and probabilities. Our results represent a relevant step toward the realization of fully programmable Ising machines on thin optical-platforms that are capable of solving complex spin-glass Hamiltonians on a large scale.

We investigate the effects of retardation on the collective emissions from a linear array of $N\ge 2$ atoms interacting with a one-dimensional field continuum. Decaying modes consisting of a single excitation in a photon-atom superposition with definite decay rates and frequency shifts are determined as a function of a retardation parameter proportional to the separation between atoms. In particular, the structures of these decaying modes are examined in terms of their photonic and atomic components. In addition to modes that resemble Dicke states in the Markovian limit, higher modes that decay much faster than Dicke superradiance exist. We find that these modes are dominantly photonic with field excitation localized near the edges of the array.

We theoretically study the phase sensitivity of an SU(1,1) interferometer, in which the phase shift is induced by a Kerr medium, together with a coherent state input and homodyne detection. Considering both ideal and photon-loss cases, the results show that compared with the linear-phase-shift-based SU(1,1) interferometer, the Kerr-phase-shift-based SU(1,1) [KSU(1,1)] interferometer can show the significant enhancement of the phase sensitivity and quantum Fisher information even in the presence of photon losses. In particular, without photon losses, the phase sensitivity of the KSU(1,1) interferometer can break through the standard quantum limit and the Heisenberg limit (HL), even close to the super-HL. From the perspective of quantum resource theory, it is interesting that the phase shift induced by the Kerr medium shows an obvious advantage of low-cost input resources to obtain higher phase sensitivity and larger quantum Fisher information. These findings may have potential applications for state-of-the-art quantum information technology.

We study the decay of a single-photon pulse inside a cavity consisting of two atomic mirrors coupled to a one-dimensional waveguide. The finesse of the cavity can be increased with proper choice of coupling strength, cavity length, spontaneous decay rate, and separation between atoms. The loss rate of a single-photon pulse inside the cavity can be decreased with narrower spectrum width and smaller detuning between the photon pulse and the atomic resonance. The decay of a single-photon pulse in the atomic cavity can be significantly slowed down with proper parameters and the increase of the number of atoms within the atomic mirrors.

Bell's theorem shows that no local hidden-variable model can explain the measurement statistics of a quantum system shared between two parties, thus ruling out a classical (local) understanding of nature. In this paper we demonstrate that by relaxing the positivity restriction in the hidden-variable probability distribution it is possible to derive quasiprobabilistic Bell inequalities whose sharp upper bound is written in terms of a negativity witness of said distribution. This provides an analytic solution for the amount of negativity necessary to violate the Clauser-Horne-Shimony-Holt inequality by an arbitrary amount, therefore revealing the amount of negativity required to emulate the quantum statistics in a Bell test.

Many quantum mechanical experiments can be viewed as multiround interactive protocols between known quantum circuits and an unknown quantum process. Fully quantum “coherent” access to the unknown process is known to provide an advantage in many discrimination tasks compared to when only incoherent access is permitted, but it is unclear if this advantage persists when the process is noisy. Here, we show that a quantum advantage can be maintained when distinguishing between two noisy single-qubit rotation channels. Numerical and analytical calculations reveal a distinct transition between the performance of fully coherent and fully incoherent protocols as a function of noise strength. Moreover, the size of the region of coherent quantum advantage shrinks inverse polynomially in the number of channel uses, and in an intermediate regime an improved strategy is a hybrid of fully coherent and fully incoherent subroutines. The fully coherent protocol is based on quantum signal processing, suggesting a generalizable algorithmic framework for the study of quantum advantage in the presence of realistic noise.

We consider two spacelike separated Dirac particles and construct five invariants under the spinor representations of the local proper orthochronous Lorentz groups. All of the constructed Lorentz invariants are identically zero for product states. The behavior of the Lorentz invariants under local unitary evolutions that act unitarily on any subspace with fixed particle momenta is studied. All of the Lorentz invariants have invariant absolute values on such subspaces if the evolutions are generated by local zero-mass Dirac Hamiltonians. Some of them also for the case of nonzero mass. Therefore, they are considered potential candidates for describing spinor entanglement of two Dirac particles, with either zero or arbitrary mass. Furthermore, their relations to the Wootters concurrence is investigated and their representations in the Foldy-Wouthuysen picture is given.

Quantum state preparation by adiabatic evolution is currently rendered ineffective by the long implementation times of the underlying quantum circuits, comparable to the decoherence time of present and near-term quantum devices. These implementation times can be significantly reduced by realizing these circuits with custom gates. Using classical computing, we model the output of a realistic two-qubit processor implementing the adiabatic evolution of a two-spin system by means of custom gates. This modeled output is then compared with the results of quantum simulations solving the same problem on IBM Quantum (IBMQ) systems. When used to emulate the behavior of the IBMQ quantum circuit, our realistic model yields state fidelities ranging from 65% to 85%, similar to the actual performance of a diverse set of IBMQ devices. When we reduced the implementation time by using custom gates, however, the loss of fidelity was reduced by at least a factor of 4, allowing us to accurately extract the energy of the target state. This improvement is enough to render adiabatic evolution useful for quantum state preparation for small systems or as a preconditioner for other state preparation methods.

In practical continuous-variable quantum key distribution system using local local oscillator (LLO CV-QKD), the phase noise related to coherent detection and phase-reference pulse intensity can be locally calibrated at the receiver side. Therefore, it can be regarded as trusted noise in order to obtain a higher secret key rate and transmission distance. However, security loopholes will be opened for the eavesdropper to launch attacks without appropriate countermeasures. To this end, we propose two practical phase-reference pulse intensity attack strategies, where Eve can reduce the trusted phase noise by manipulating the intensity of the phase-reference pulse, thereby hiding her attack on the signal pulse. The performance of the LLO CV-QKD system under these attacks has been analyzed. We show that precisely monitoring the intensity of the phase-reference pulse in real time is an essential countermeasure to prevent the proposed attacks. Moreover, an intensity-monitoring scheme for the phase-reference pulse is proposed to strengthen the security of the practical LLO CV-QKD system and make the trusted phase noise model more robust.

A qubit–harmonic-oscillator open system coupled to thermal baths was considered and the master equation describing the evolution of the open system was deduced when the qubit transition frequency is $\lesssim 0.1$ the oscillator frequency. The master equation is valid in all the qubit-oscillator state space and holds for all values of the qubit-oscillator coupling including the ultrastrong and deep strong coupling regimes. It only requires an oscillator frequency much larger than the relaxation rates. The qubit-oscillator coupling can enhance or decrease both the relaxation rates and the frequency shifts induced by the thermal baths. It was found that weak, sinusoidal qubit driving forces the qubit-oscillator open system to behave like a driven qubit whose evolution is governed by equations similar to those of the Bloch vector in the optical Bloch equations and whose transition frequency decreases with increasing qubit-oscillator coupling strength. Finally, it was shown how one can reach the adiabatic regime by using sinusoidal qubit driving with large driving frequency and the concepts of $\pi$ and $\pi /2$ pulses were generalized to manipulate transitions between dressed states.