A method is proposed to describe Fermi or Bose systems coupled to one or several heat baths composed of fermions and/or bosons. The method, called the coupled equations of motion method, properly includes non-Markovian effects. The approach is exact in the full-coupling approximation when only bosonic particles are present in the system and baths. The approach provides an approximate treatment when fermions are present either in the system and/or in one or several environments. Our approach has the advantage of properly respecting the Pauli exclusion principle for fermions during the evolution. We illustrate the approach for the single fermionic or bosonic oscillator coupled to one or two heat baths assuming different types of quantum statistics (fermion or boson) for them. The cases of a Fermi system coupled to fermion or boson heat baths or a mixture of both are analyzed in detail. With the future goal of treating Fermi systems formed of an increasing number of two-level systems (qubits), we discuss possible simplifications that could be made in the equations of motion and their limits of validity in terms of the system-bath coupling or of the initial heat bath temperatures.

We present a method for reducing the number of non-Clifford quantum gates, in particularly T-gates, in a circuit, an important task for efficiently implementing fault-tolerant quantum computations. This method matches or beats previous approaches to ancillae-free T-count reduction on the majority of our benchmark circuits, in some cases yielding up to 50% improvement. Our method begins by representing the quantum circuit as a ZX-diagram, a tensor networklike structure that can be transformed and simplified according to the rules of the ZX-calculus. We then extend a recent simplification strategy with a different ingredient, phase gadgetization, which we use to propagate non-Clifford phases through a ZX-diagram to find nonlocal cancellations. Our procedure extends unmodified to arbitrary phase angles and to parameter elimination for variational circuits. Finally, our optimization is self-checking, in the sense that the simplification strategy we propose is powerful enough to independently validate equality of the input circuit and the optimized output circuit. We have implemented the routines of this paper in the open-source library pyzx.

The interplay of Anderson localization and decoherence results in intricate dynamics that is notoriously difficult to simulate on classical computers. We develop the framework for a quantum simulation of such an open quantum system making use of time-varying randomized gradients, and show that even an implementation with limited experimental resources results in accurate simulations.

We demonstrate that an external terahertz (THz) field enables the formation of interference between two distinct Auger pathways leading to the same final ionic state. The kinetic energy of Auger electrons ejected from either of two spin-orbit split one-hole states of magnesium cations is recorded. In the presence of the THz field, a clear oscillatory structure in the Auger spectrum emerges, which we find to be in very good agreement with an analytical model based on perturbation theory. For this interference to occur, the THz field has to chirp the energy of both Auger electrons and photoelectrons simultaneously, in order to create states with indistinguishable quantum properties.

Using the improved molecular strong-field approximation we investigate high-order above-threshold ionization (HATI) of homonuclear diatomic molecules by an orthogonally polarized two-color (OTC) laser field. The OTC field components are linearly polarized, having the relative phase $\phi$ and frequencies $r\omega$ and $s\omega$ ($r$ and $s$ are integers and $\omega$ is the fundamental frequency). The molecule is aligned in the laser-field polarization plane. We have found that for even values of $r+s$ the HATI spectra obey the $C_2$ rotational symmetry regardless of the relative phase, component intensities, and molecular orientation, while the spectra calculated for odd values of $r+s$ and for certain molecular orientations exhibit the reflection symmetry. We have also explored the symmetry transformations of the HATI spectra for a shift of the relative phase by ${180}^{\circ }$ and for various values of $r$ and $s$. These symmetries are illustrated by numerical examples of the HATI spectra of the ${\mathrm{N}}_2$ molecule. For particular values of the laser-field parameters, internuclear distance, and the electron emission angle we observed minima in the ionization yield as a function of the molecular orientation angle and the photoelectron energy. These minima are well fitted with the curve obtained using a condition for the destructive interference minima which we derived for an arbitrary laser field and applied to the OTC field. The relative phase between the OTC field components can be used to control the length and shape of the HATI plateau, as well as the appearance of these destructive interference minima.

The bulk viscosity of two-component fermions with a zero-range interaction is revisited both in two and three dimensions. We first point out that the “standard” Kubo formula employed in recent studies has flaws to give rise to an unphysical divergent bulk viscosity even in a limit where it is supposed to vanish. The corrected Kubo formula as well as the sum rule is, then, carefully rederived so as to confirm that the bulk viscosity, indeed, vanishes in the free, unitarity, and dimer limits. We also discuss that the recently found discrepancy between the Kubo formalism and the kinetic theory for the bulk viscosity is attributed to the fact that the quasiparticle approximation assumed by the latter breaks down even in the high-temperature limit.

We consider the quantum evolution of a pair of interacting atoms in a three-dimensional isotropic trap where the interaction strength is quenched from one value to another. Using exact solutions of the static problem we are able to evaluate time-dependent observables such as the overlap between initial and final states and the expectation value of the separation between the two atoms. In the case where the interaction is quenched from the noninteracting regime to the strongly interacting regime, or vice versa, we are able to obtain analytic results. Examining the overlap between the initial and final states we show that when the interaction is quenched from the noninteracting to strongly interacting regimes the early time dependence dynamics are consistent with theoretical work in the single impurity many-body limit. When the system is quenched from the strongly to noninteracting regime we predict large oscillations in the separation between the two atoms, which arises from a logarithmic divergence due to the zero-range nature of the interaction potential.

The intensity buildup of light inside a lossy microring resonator can be used to enhance the generation of squeezed states via spontaneous parametric downconversion (SPDC). In this work, we model the generation of squeezed light in a microring resonator that is pumped with a Gaussian pulse via a side-coupled channel waveguide. We theoretically determine the optimum pump pulse duration and ring-to-channel coupling constant to minimize the quadrature noise (maximize the squeezing) in the ring for a fixed input pump energy. We derive approximate analytic expressions for the optimal coupling and pump pulse duration as a function of scattering loss in the ring. These results will enable researchers to easily determine the optimal design of microring resonator systems for the generation of quadrature-squeezed states.

Ultracold polar and magnetic ${}^{23}\mathrm{Na}{}^6\mathrm{Li}$ molecules in the rovibrational ground state of the lowest triplet $a^3{\mathrm{\Sigma }}^{+}$ electronic state have been recently produced. Here, we calculate the electronic and rovibrational structure of these 14-electron molecules with spectroscopic accuracy ($<0.5{\mathrm{cm}}^{-1}$) using state-of-the-art ab initio methods of quantum chemistry. We employ the hierarchy of the coupled-cluster wave functions and Gaussian basis sets extrapolated to the complete basis set limit. We show that the inclusion of higher-level excitations, core-electron correlation, relativistic, QED, and adiabatic corrections is necessary to accurately reproduce scattering and spectroscopic properties of alkali-metal systems. We obtain the well depth, $D_e=229.9\left(5\right){\mathrm{cm}}^{-1}$, the dissociation energy, $D_0=208.2\left(5\right){\mathrm{cm}}^{-1}$, and the scattering length, $a_s=-{84}_{-41}^{+25}\mathrm{bohr}$, in good agreement with recent experimental measurements. We predict the permanent electric dipole moment in the rovibrational ground state, $d_0=0.167$(1) D. These values are obtained without any adjustment to experimental data, showing that quantum chemistry methods are capable of predicting scattering properties of many-electron systems, provided relatively weak interaction and small reduced mass of the system.

Our knowledge of quantum mechanics can satisfactorily describe simple microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen through the analysis of uncertainty relations. We employ entropic uncertainty relations to show that it is only by the inclusion of imprecision in our model of macroscopic measurements that we can prepare a system with two simultaneously well-defined quantities, even if their associated observables do not commute. We also establish how the precision of measurements must increase in order to keep quantum properties, a desirable feature for large quantum computers.

We investigate a case of the Hu-Paz-Zhang master equation of the Caldeira-Leggett model without Lindblad form obtained in the weak-coupling limit up to the second-order perturbation. In our study, we use Gaussian initial states to be able to employ a sufficient and necessary condition, which can expose positivity violations of the density operator during the time evolution. We demonstrate that the evolution of the non-Markovian master equation has problems when the stationary solution is not a positive operator, i.e., does not have physical interpretation. We also show that solutions always remain physical for small times of evolution. Moreover, we identify a strong anomalous behavior, when the trace of the solution is diverging. We also provide results for the corresponding Markovian master equation and show that positivity violations occur for various types of initial conditions even when the stationary solution is a positive operator. Based on our numerical results, we conclude that this non-Markovian master equation is superior to the corresponding Markovian one.

The security of the perfect quantum key distribution protocol can be guaranteed by applying the fundamental laws of quantum mechanics, but the practical quantum key distribution system may be attacked by utilizing imperfect state preparation and measurement devices. In this work, we analyze the security of the practical quantum key distribution system with weak-randomness basis selection, where the basis selection may be partly controlled by the eavesdropper due to the imperfect quantum devices. We propose the parameter $\epsilon$ to quantify the deviation value between the practical basis selection probability and the perfect basis selection probability, and the secret key rate of the practical quantum key distribution system is obtained under different $\epsilon$ values. By applying the practical experimental parameters, the analysis result demonstrates that the maximal transmission distance will be reduced from 142 to 139 km if $\epsilon \le 0.1$, but no secret key can be generated in the case of $\epsilon \ge 0.34$.

We present how basic logic gates including nand, nor, and xor gates can be implemented counterfactually. The two inputs (Bob and Charlie) and the output (Alice) of the proposed counterfactual logic gate are not within the same station but rather separated in three different locations. We show that there is no need to prearrange entanglement for the gate, and, more importantly, there are no real physical particles traveling among Alice, Bob, and Charlie during the information processing. Bob and Charlie only need to independently control the blocking and unblocking of the transmission channels that connect them to Alice. In this way, they can completely determine the state of a real photon at Alice's end, thereby leading to implemention of a counterfactual logic gate. The functionality of a particular counterfactual logic gate is determined only by an appropriate design of Alice's optical device. Furthermore, by utilizing the proposed counterfactual logic gates, we demonstrate how to counterfactually prepare the Greenberger-Horne-Zeilinger state and W state with three remote quantum objects, which are in superposition states of blocking and unblocking the transmission channel.

A major motivation for building a quantum computer is that it provides a tool to efficiently simulate strongly correlated quantum systems. In this paper, we present a detailed roadmap on how to simulate a two-dimensional electron gas—cooled to absolute zero and pierced by a strong transversal magnetic field—on a quantum computer. This system describes the setting of the fractional quantum Hall effect, one of the pillars of modern condensed-matter theory. We give analytical expressions for the two-body integrals that allow for mixing between $N$ Landau levels at a cutoff $M$ in angular momentum and give gate-count estimates for the efficient simulation of the energy spectrum of the Hamiltonian on an error-corrected quantum computer. We then focus on studying efficiently preparable initial states and their overlap with the exact ground state for noisy as well as error-corrected quantum computers. By performing an imaginary time evolution of the covariance matrix, we find the generalized Hartree-Fock solution to the many-body problem and study how a multireference state expansion affects the state overlap. We perform small-system numerical simulations to study the quality of the two initial state Ansätze in the lowest Landau level approximation.

We propose the generation of entangled qubits by utilizing the properties of edge states appearing at one end of a periodically driven (Floquet) superconducting qubit chain. Such qubits are naturally protected by the system's topology and their manipulation is possible through adiabatic control of the system parameters. By utilizing a Y-junction geometry, we then develop a protocol to perform high-fidelity transfer of entangled qubits from one end to another end of a qubit chain. Our quantum state transfer protocol is found to be robust against disorder and imperfection in the system parameters. More importantly, our proposed protocol also performs remarkably well at larger system sizes due to nonvanishing gaps between the involved edge states and the bulk states, thus allowing us in principle to transfer entangled states over an arbitrarily large distance. This work hence indicates that Floquet topological edge states are not only resourceful for implementing quantum gate operations, but also useful for high-fidelity and long-distance transfer of entangled states along solid-state qubit chains.

Continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) is immune to all detector side channel attacks, however its security requires trusted sources. We investigate the effects of source intensity errors, the most crucial source error, on the security of CV-MDI-QKD protocol with Gaussian-modulated coherent states. We establish a general source intensity errors model and derive the secret key rate based on different assumptions on the abilities of legal parties Alice and Bob. To avoid the adverse effects of the sources' intensity errors on CV-MDI-QKD, we present different data-processing schemes. We also assess the security of the protocol against collective Gaussian attacks in the finite-size scenario with composable security. Taking source intensity errors into consideration, we achieve improved security compared to previous demonstrations. Our results will provide a useful reference for practical implementations of CV-MDI-QKD.

We study the application of a new method for simulating nonlinear dynamics of many-body spin systems using quantum measurement and feedback [Muñoz-Arias et al., Phys. Rev. Lett. 124, 110503 (2020)] to a broad class of many-body models known as $p$-spin Hamiltonians, which describe Ising-like models on a completely connected graph with $p$-body interactions. The method simulates the desired mean-field dynamics in the thermodynamic limit by combining nonprojective measurements of a component of the collective spin with a global rotation conditioned on the measurement outcome. We apply this protocol to simulate the dynamics of the $p$-spin Hamiltonians and demonstrate how different aspects of criticality in the mean-field regime are readily accessible with our protocol. We study applications including properties of dynamical phase transitions and the emergence of spontaneous symmetry breaking in the adiabatic dynamics of the collective spin for different values of the parameter $p$. We also demonstrate how this method can be employed to study the quantum-to-classical transition in the dynamics continuously as a function of system size.

Combining a laser vaporization cluster source, a velocity scan system, and a time-of-flight mass spectrometer, we measured velocity distributions of few-atom cobalt clusters (${\text{Co}}_n, n=6–60$) suspended in a helium carrier gas and expanded into vacuum. The velocity distributions provide information about the cluster size dependence of the translational temperature, flow velocity, and velocity slip with respect to the helium carrier gas. The system of clusters in a carrier gas is found to violate the equipartition theorem. Although the clusters in the expansion do not thermalize with the helium gas, they do experience significant, size-dependent internal cooling. While expanding into vacuum, the clusters collide, at least a couple of hundred times, superelastically with the carrier gas, thereby transferring internal vibrational energy into self-acceleration and increasing the flow velocity of the gas as a whole. It is also demonstrated that the proposed velocity distribution measurements can be used to test whether a source produces thermalized clusters.

Based on the strong-field approximation, we report results for high-order harmonic generation by bi-elliptical orthogonally polarized two-color (BEOTC) fields with frequency ratios of 2:1 and 3:1 and fundamental wavelengths of 800 and 1800 nm. A BEOTC field denotes the superposition of two copropagating counter-rotating elliptically polarized fields with different wavelengths and orthogonal semimajor axes. Its two limiting cases are the bicircular field and the linearly polarized orthogonal two-color field [D. B. Milošević and W. Becker, Phys. Rev. A 100, 031401(R) (2019)]. A detailed analysis of the high-order harmonic intensities and ellipticities as functions of the harmonic order, the ellipticity, and the relative phase between the two driving-field components is presented. Regions of the parameter space are identified where the harmonic ellipticities are very high. Surprisingly, this can be the case already for very small ellipticity (as small as $\varepsilon =0.01$) of the driving field. This can be important for practical applications. In the opposite limit where the BEOTC field is close to bicircular, the selection rules that govern the latter case can also be very quickly invalidated. For the 2:1 case, this can result in an apparent shift of the selection rules by one harmonic order.

A time-orbiting potential trap confines neutral atoms in a rotating magnetic field. The rotation of the field can be useful for precision measurements, since it can average out some systematic effects. However, the field is more difficult to characterize than a static field, and it makes light applied to the atoms have a time-varying optical polarization relative to the quantization axis. These problems can be overcome by using stroboscopic techniques, where either a radio-frequency field or a laser is applied in pulses that are synchronized to the rotating field. By using these methods, the magnetic field can be characterized with a precision of 10 mG and light can be applied with a polarization error of $5\times {10}^{-5}$.