An off-resonant error for a driven quantum system refers to interactions due to the input drives having nonzero spectral overlap with unwanted system transitions. For the cross-resonance gate, this includes leakage as well as off-diagonal computational interactions that lead to bit-flip error on the control qubit. In this paper, we quantify an off-resonant error, with more focus on the less studied off-diagonal control interactions, for a direct controlled-not (cnot) gate implementation. Our results are based on a numerical simulation of the dynamics while we demonstrate the connection to time-dependent Schrieffer-Wolff and Magnus perturbation theories. We present two methods for suppressing such error terms. First, pulse parameters need to be optimized so off-resonant transition frequencies coincide with the local minima due to the pulse spectrum sidebands. Second, we show the advantage of a $Y$-DRAG pulse on the control qubit in mitigating the off-resonant error. Depending on qubit-qubit detuning, the proposed methods can improve the average off-resonant error from approximately ${10}^{-3}$ closer to the ${10}^{-4}$ level for a direct cnot calibration.

We investigate the optomechanically induced transparency (OMIT) in an optomechanical lattice. By controlling the frequency of the external drivings in a periodic manner, the optomechanical lattice can be regarded as a Su-Schrieffer-Heeger model. By calculating the local photon density of states for the system, we investigate the response of the system to a weak probe field. In the nondeep topological nontrivial phase, we find that the system has two nondegenerate edge modes due to the finite size of the system. In this regime, a narrow transparency window of the probe field, which is much narrower than the scale set by photon decay, can be observed due to the destructive interference of the probe field absorption paths induced by the two nondegenerate edge modes. In the deep topological nontrivial phase, the two edge modes become degenerate and the narrow transparency window changes into a wide absorption window. The OMIT of the optomechanical array can also be observed in the presence of large disorders of the many-photon optomechanical couplings. Our work generalizes the OMIT of a single optomechanical cavity to a topological optomechanical system and might have potential applications in quantum information processing and quantum optical devices.

We consider a cryptographically motivated framework for quantum metrology in the presence of a malicious adversary. We begin by devising an estimation strategy for a (potentially) altered resource (due to a malicious adversary) and quantify the amount of bias and the loss in precision as a function of the introduced uncertainty in the resource. By incorporating an appropriate cryptographic protocol, the uncertainty in the resource can be bounded with respect to the soundness of the cryptographic protocol. Thus the effectiveness of the quantum metrology problem can be directly related to the effectiveness of the cryptography protocol. As an example, we consider a quantum metrology problem in which resources are exchanged through an unsecured quantum channel. We then construct two protocols for this task which offer a trade-off between difficulty of implementation and efficiency.

We investigate statistics of the photon (phonon) field undergoing linear and nonlinear damping processes. An effective two-photon (phonon) nonlinear “cooling by heating” process is realized from linear damping by spectral filtering of the heat baths present in the system. This cooling process driven by incoherent quantum thermal noise can create quantum states of the photon field. In fact, for high temperatures of the spectrally filtered heat baths, sub-Poissonian statistics with strong antibunching in the photon (phonon) field are reported. This notion of the emergence and control of quantumness by incoherent thermal quantum noise is applied to a quantum system comprised of a two-level system and a harmonic oscillator or analogous optomechanical setting. Our analysis may provide a promising direction for the preparation and protection of quantum features via nonlinear damping that can be controlled with incoherent thermal quantum noise.

We derive inequalities sufficient to detect the genuine $N$-partite steering of $N$ distinct systems. Here, we are careful to distinguish between the concepts of full $N$-partite steering inseparability (where steering is confirmed individually for all bipartitions of the $N$ systems, thus negating the bilocal hidden state model for each bipartition) and genuine $N$-partite steering (which excludes all convex combinations of the bilocal hidden state models). Other definitions of multipartite steering are possible and we also derive inequalities to detect a stricter genuine $N$-partite steering where only one site needs to be trusted. The inequalities are expressed as variances of quadrature phase amplitudes and thus apply to continuous-variable systems. We show how genuine $N$-partite steerable states can be created and detected for the nodes of a network formed from a single-mode squeezed state passed through a sequence of $N-1$ beam splitters. A stronger genuine $N$-partite steering is created, if one uses two squeezed inputs or $N$ squeezed inputs. We are able to confirm that genuine tripartite steering (by the above definition and by the stricter definition) has been realized experimentally. Finally, we analyze how bipartite steering and entanglement are distributed among the systems in the tripartite case, illustrating with monogamy inequalities. While we use Gaussian states to benchmark the criteria, the inequalities derived in this paper are not based on the assumption of Gaussian states, which gives an advantage for quantum communication protocols.

We apply the method of flow equations to describe quantum systems subject to a time-periodic drive with a time-dependent envelope. The driven Hamiltonian is expressed in terms of its constituent Fourier harmonics with amplitudes that may vary as a function of time. The time evolution of the system is described in terms of the phase-independent effective Hamiltonian and the complementary micromotion operator that are generated by deriving and solving the flow equations. These equations implement the evolution with respect to an auxiliary flow variable and facilitate a gradual transformation of the quasienergy matrix (the Kamiltonian) into a block-diagonal form in the extended space. We construct a flow generator that prevents the appearance of additional Fourier harmonics during the flow, thus enabling implementation of the flow in a computer algebra system. Automated generation of otherwise cumbersome high-frequency expansions (for both the effective Hamiltonian and the micromotion) to an arbitrary order thus becomes straightforward for driven Hamiltonians expressible in terms of a finite algebra of Hermitian operators. We give several specific examples and discuss the possibility to extend the treatment to cover rapid modulation of the envelope.

We propose a systematic scheme to engineer quantum states of a quantum system governed by a time-convolutionless non-Markovian master equation. According to the idea of reverse engineering, the general algebraic equation to determine the control parameters, such as coherent and incoherent control fields, is presented. Without artificially engineering the time-dependent decay rates and retaining the environment-induced Lamb shifts, the quantum state can still be transferred into the target state in a finite period of time along an arbitrary designed trajectory strictly in Hilbert space. As an application, we apply our scheme to a driven two-level non-Markovian system and realize instantaneous-steady-state tracking and a complete population inversion with control parameters which are available in experimental settings.

Quantum coherent superpositions of states with different energies, i.e., states with coherence with respect to energy basis, are an important resource for modern quantum technologies. States with small coherence can be obtained either autonomously, due to the effect of a weak coherent drive, or, potentially, due to the presence of an environment. In this paper, we propose a measurement-based protocol for quantum coherence synthesis from individual systems (with low initial coherence) into a global (and higher) coherence of the joint system. As an input, it uses $N$ noninteracting copies of two-level systems (TLS), with low initial energy and coherence. These can be supplied by, e.g., a weak external drive or can result from an interaction with a bath. This protocol conditionally synthesizes an output state with higher energy and coherence than the initial state had, representing a universal process the rules of which have not been well studied, yet. In addition to energy and coherence, we study the quantity called mutual coherence, showing increase after the protocol application, as well. This approach is based on application of sequential pairwise projective measurements on TLS pairs (conditionally removing their ground states), that are diagonal in the TLS energy basis. The functionality of the coherence synthesis is robust with respect to dephasing effects of the TLS environment on the system. Our approach may show its benefits in quantum sensing, quantum batteries charging, or other applications where synthesis of a larger coherent system from smaller (weaker) resources is useful.

State-of-the-art quantum algorithms routinely tune dynamically parametrized cost functionals for combinatorics, machine learning, equation solving, and energy minimization. However, large search complexity often demands many (noisy) quantum measurements, leading to the increasing use of classical probability models to estimate which areas in the cost functional landscape are of highest interest. Introducing deep learning based modeling of the landscape, we demonstrate order-of-magnitude increases in accuracy and speed over state-of-the-art Bayesian methods with respect to control of a many-body spin chain. Moreover, once trained, the deep neural network enables the extraction of information at a much faster rate than conventional numerical simulation. This allows for on-the-fly experimental optimizations of circuits with large depth and moderate width and detailed classification of problem complexity and navigability throughout the phase diagram of the landscape.

Achieving an accurate description of fermionic systems typically requires considerably many more orbitals than fermions. Previous resource analyses of quantum chemistry simulation often failed to exploit this low fermionic number information in the implementation of Trotter-based approaches and overestimated the quantum-computer runtime as a result. They also depended on numerical procedures that are computationally too expensive to scale up to large systems of practical interest. Here we propose techniques that solve both problems by using various factorized decompositions of the electronic structure Hamiltonian. We showcase our techniques for the uniform electron gas, finding substantial (over $100\times$) improvements in Trotter error for low-filling fraction and pushing to much higher numbers of orbitals than is possible with existing methods. Finally, we calculate the $T$-count to perform phase estimation on Jellium. In the low-filling regime, we observe improvements in gate complexity of over $10\times$ compared to the best Trotter-based approach reported to date. We also report gate counts competitive with qubitization-based approaches for Wigner-Seitz values of physical interest.

Producing contextual correlations in sequences of measurements on single quantum systems faces two major problems. One is the experimental difficulty of performing sequences of ideal measurements on high-dimensional quantum systems, a problem that also affects other forms of quantum temporal correlations. The other is the simulability with classical light of existing contextuality experiments with photons. Here, we introduce a scheme that solves both problems. We show that, by encoding quantum information in $n\ge 2$ indistinguishable bosons in $m\ge 2$ modes, targeting observables exploiting the bunching-antibunching of bosons, and performing ideal measurements by dispersively coupling these systems with auxiliary qubits, it is possible to realize sequential quantum measurements on high-dimensional quantum systems and produce contextuality which cannot be simulated by classical light, as it relies on indistinguishability and higher-order interference.

We propose a tunable coupler consisting of $N$ fixed-frequency qubits, which can tune and even amplify the effective interaction between two superconducting quantum circuits. The tuning range of the interaction is proportional to $N$, with a minimum value of zero and a maximum that can exceed the physical coupling rates between the coupler and the circuits. The effective coupling rate is determined by the collective magnetic quantum number of the qubit ensemble, which takes only discrete values and is free from collective decay and decoherence. Using single-photon $\pi$-pulses, the coupling rate can be switched between arbitrary choices of the initial and final values within the dynamic range in a single step without going through intermediate values. A cascade of the couplers for amplifying small interactions or weak signals is also discussed. These results should not only stimulate interest in exploring the collective effects in quantum information processing, but also enable development of applications in tuning and amplifying the interactions in a general cavity-QED system.

The capacity of a quantum gate to produce entangled states on a bipartite system is quantified in terms of the entangling power. This quantity is defined as the average of the linear entropy of entanglement of the states produced after applying a quantum gate over the whole set of separable states. Here we focus on symmetric two-qubit quantum gates, acting on the symmetric two-qubit space, and calculate the entangling power in terms of the appropriate local invariant. A geometric description of the local equivalence classes of gates is given in terms of the $\text{su}\left(3\right)$ Lie algebra root vectors. These vectors define a primitive cell with hexagonal symmetry on a plane, and through the Weyl group the minimum area on the plane containing the whole set of locally equivalent quantum gates is identified. We give conditions to determine when a given quantum gate produces maximally entangled states from separable ones (perfect entanglers). We find that these gates correspond to one-fourth of the whole set of locally distinct quantum gates. The formalism developed here is applicable to general three-level systems. Via the Majorana representation, qutrit transformations can be regarded as having entangling power and hence classified as perfect and nonperfect entanglers and be grouped into local-equivalence classes of the associated symmetric two-qubit space. The results are illustrated by an anisotropic Heisenberg model, the Lipkin-Meshkov-Glick model, and two coupled quantized oscillators with cross-Kerr interaction, which we use to obtain three-level gates relevant in qutrit quantum computation.

We have studied the three-body breakup of ${\mathrm{CO}}_2^{3+}$ created by the impact of slow ($v<1$ a.u.) protons on ${\mathrm{CO}}_2$. Employing the coincidence momentum imaging technique, we have obtained the correlated momenta of the three fragments, ${\mathrm{O}}^{+}+{\mathrm{C}}^{+}+{\mathrm{O}}^{+}$, and thence the kinetic energy release (KER) distribution. By examining the Dalitz plots for the three-body breakup, we separate the sequential and concerted breakup events and analyze the corresponding KER distributions. Based on the potential energy curves reported in the literature, we identify the possible transient states of ${\mathrm{CO}}_2^{3+}$ that lead to the different features in the KER distribution. We find that under ${\mathrm{H}}^{+}$ impact, the KER distribution shows a low-energy feature, which is seen in the case of electron impact, but not under the impact of slow or fast highly charged ions. This feature is identified as arising via the low-lying ${}^2\mathrm{\Pi }$ and ${}^4\mathrm{\Pi }$ states of the transient molecular ion. We further note that slow protons, which are the simplest of projectiles, are able to excite the ${\mathrm{CO}}_2$ molecule to a broad range of triply ionized transient states, spanning those accessed by the impact of slow highly charged ions and also those accessed by electron impact, but with varying probabilities.

In this work, a derivation and implementation of the relativistic time-dependent configuration-interaction singles (RTDCIS) method is presented. Various observables for krypton and xenon atoms obtained by RTDCIS are compared with experimental data and alternative relativistic calculations. This includes energies of occupied orbitals in the Dirac-Fock ground state, Rydberg state energies, Fano resonances, and photoionization cross sections. Diagrammatic many-body perturbation theory, based on the relativistic random phase approximation, is used as a benchmark with excellent agreement between RTDCIS reported at the Tamm-Dancoff level. Results from RTDCIS are computed in the length gauge, where the negative energy states can be omitted with acceptable loss of accuracy. A complex absorbing potential, that is used to remove photoelectrons far from the ion, is implemented as a scalar potential and validated for RTDCIS. The RTDCIS methodology presented here opens for future studies of strong-field processes, such as attosecond transient absorption and high-order harmonic generation, with electron and hole spin dynamics and other relativistic effects described by first principles via the Dirac equation.

We propose a method to study the interaction of a single-mode laser beam (as an external field) containing a finite number of photons with a free electron. In particular, we give some numerical results of how the photon number $l_{k,\varepsilon }$ affects the differential scattering cross section when the initial state of an external field is a Fock state $|l_{k,\varepsilon }\rangle$. Besides, for arbitrarily polarized light, we prove that our model will return to the semiclassical theory as $l_{k,\varepsilon }\to \infty$.

We derive a pulse-area theorem for a single-loop cyclic three-level system without applying the rotating-wave approximation while explicitly taking into account the time delays of control fields. This corresponds to an archetypal model for exploring enantioselective state transfer (ESST) in chiral molecules driven by three linearly polarized microwave pulses. By dividing the closed-loop excitation into two separate stages, we obtain both amplitude and phase conditions of three control fields to generate high fidelity of ESST. As a proof of principle, we apply this pulse-area theorem to cyclohexylmethanol molecules, for which three rotational states are connected by $a$-type, $b$-type, and $c$-type components of the transition dipole moments in both center-frequency-resonant and -detuned conditions. Our results show that two enantiomers with opposite handedness can be transferred to different target states by designing three microwave pulses that satisfy the amplitude and phase conditions at the transition frequencies. The corresponding control schemes are robust against the time delays between the two stages. We suggest that the two control fields used in the second stage should be applied simultaneously for practical applications. This work contributes an alternative pulse-area theorem to the field of quantum control, which has the potential to determine the chirality of enantiomers in a mixture.

The statistics and dynamics of two-dimensional rogue waves in a broad-area semiconductor laser with an intracavity saturable absorber are numerically investigated under the effect of transverse carrier diffusion. We show that lateral diffusion of carriers alters the statistics of rogue waves by enhancing their formation in smaller ratios of carrier lifetimes in active and passive materials while suppressing them when the ratio is larger. The temporal dynamics of the emitted rogue waves is also studied and show that the finite nonzero transverse carrier diffusion coefficient gives them a longer duration. To further approach a realistic experimental situation, we also investigate the statistics and dynamics of rogue waves by simulating a circular disk-shape pump which replaces the flat pump profile typically used in numerical simulations of broad-area lasers. We show that a finite pump shape reduces the number of emitted rogue waves per unit area both below and above the laser threshold for every carrier lifetime ratio. The temporal width of the emitted rogue waves is also shown to decrease as a consequence of removing the nonphysical effects of the infinite flat pump on carrier dynamics.

A different type of Bessel-like vortex beams with their intensity spherically modified by a singular polarization structure is introduced. Conventional vector Bessel-Gaussian beams are either linearly or radially (and azimuthally) polarized and their transverse structure is preserved under propagation. In this work, the Bessel-like beams with a Gaussian envelope are spherically polarized: the electric fields are oriented along the radius vector or along with a combination of meridional and azimuthal vectors. For the implementation of such beams, we investigate their vector spatial spectra. The intensity distribution of the beam can be controlled by a proper choice of parameters such as the cone angles of individual plane-wave components and sizes of Gaussian apertures. In the two limiting cases of axicon angles, spherically polarized Bessel beams form either two optical needles or optical-bottle-like intensity patterns.

A study on force sensing and cooling for the mechanical membrane in a dissipative optomechanical system (OMS) with a degenerate optical parametric amplifier (OPA) and an optical Kerr medium is presented. The optimal phase angle can contribute to achieve much better force sensing than the case of the arbitrary phase angle. Specifically, at the blue detuning between the cavity field and the input laser the coexistence of the OPA and the Kerr medium plays an important role in improving the force sensitivity over the case of a bare OMS, while at the red detuning the bare OMS demonstrates more effective force sensitivity than the case of the coexistence of the OPA and the Kerr medium. The coexistence of the OPA and the Kerr medium is helpful to achieve more stable force sensitivity, which results from the change of the normalized cavity detuning having little effect on the force sensitivity of the system. In addition, for the existence of only nonlinear gain of the OPA, the study shows that at the blue detuning the temperature of the mechanical membrane can be achieved more effectively than in the case of the bare OMS, while at the red detuning, with increasing value of the nonlinear gain of the OPA, the cooling of the membrane is weakened. For the existence of the Kerr medium, at continuous detuning the effective temperature of the mechanical membrane is below the temperature of the environment. In quantum engineering, this scheme may have potential applications in precision measurement and quantum manipulation.