We consider an open quantum system, with dissipation applied only to a part of its degrees of freedom, evolving via a quantum Markov dynamics. We demonstrate that, in the Zeno regime of large dissipation, the relaxation of the quantum system towards a pure quantum state is linked to the evolution of a classical Markov process towards a single absorbing state. The rates of the associated classical Markov process are determined by the original quantum dynamics. Extension of this correspondence to absorbing states with internal structure allows us to establish a general criterion for having a Zeno-limit nonequilibrium stationary state of arbitrary finite rank. An application of this criterion is illustrated in the case of an open $XXZ$ spin-1/2 chain dissipatively coupled at its edges to baths with fixed and different polarizations. For this system, we find exact nonequilibrium steady-state solutions of ranks 1 and 2.

Macrorealism is a classical world view asserting that the properties of macro-objects exist independently and irrespective of observation. One practical approach to test this view in quantum theory is to observe the quantum coherence for a macro-object in an interference experiment. An elegant and conceptually appealing approach for testing the notion of macrorealism in quantum theory is through the violation of Leggett-Garg inequality. However, a conclusive Leggett-Garg test hinges on how the noninvasive measurability criteria are guaranteed in an experiment and remains a debated issue to date. In this work, we connect the practical and the conceptual approaches for testing the macrorealism through the weak value. We argue that whenever a quantum effect is observed in an interference experiment there is an existence of anomalous weak value. Further, we demonstrate that whenever such weak value exists, one obtains the violation of a Leggett-Garg inequality in any interference experiment. Since in a path-only interference experiment effectively no prior measurement is performed, the Leggett-Garg test of macrorealism presented here is without assuming the noninvasive measurability. We provide a rigorous discussion about the assumptions involved in the Leggett-Garg scenario and how our scheme fits into it. Further, we provide a simple argument about the macrorealistic understanding of our results by using the recently developed approach involving quasiprobability.

We study the dynamics of interacting open quantum subsystems. Interactions merge these subsystems into a unified system. It is often believed that the Lindblad superoperator of the unified system is the sum of the Lindblad superoperators of the separate subsystems. Such an approach, however, results in a violation of the second law of thermodynamics. To avoid a cumbersome direct derivation of the correct superoperator from first principles, we develop a perturbation theory based on using Lindblad superoperators of separate subsystems, which are assumed to be known. Using interacting two-level systems as an example, we show that, starting with a certain order of the perturbation theory, the second law of thermodynamics holds. We demonstrate that the theory developed can be applied to the problems of quantum transport.

The probabilities of vibronic transitions in molecules are referred to as Franck-Condon factors (FCFs). Although several approaches for calculating FCFs have been developed, such calculations are still challenging. Recently it was shown that there exists a correspondence between the problem of calculating FCFs and boson sampling. However, if the output photon number distribution of boson sampling is sparse, then it can be classically simulated. Exploiting these results, we develop a method to approximately reconstruct the distribution of FCFs of certain molecules. We demonstrate its proof of concept by applying it to formic acid and thymine at 0 K. In our method, we first obtain the marginal photon number distributions for pairs of modes of a Gaussian state associated with the molecular transition. We then apply a compressive sensing method called polynomial-time matching pursuit to recover FCFs.

The discretely modulated continuous-variable quantum key distribution (DM CVQKD) has been proven to be secure, and a basic assumption for the current theoretical security proof of the DM CVQKD is that the signal source cannot be compromised. However, this assumption is quite unpractical in real quantum communication systems. In this paper, we investigate the DM CVQKD with a special configuration in which the entanglement source is placed at the untrusted channel. With this configuration, the source is no longer protected by the sender but is exposed to the vulnerable environment. In particular, we consider the configuration for two typical DM CVQKD protocols, which are the four-state protocol and the eight-state protocol. Security analysis based on linear bosonic channel shows that the DM CVQKD with an untrusted entanglement source is able to defend itself against the most powerful quantum collective attack in a certain distance range and it can still generate positive secret key rate when considering finite-size effect and composable security, thereby providing a theoretical proof for applying the DM CVQKD system to a realistic environment.

We present an architecture to investigate wave-particle duality in $N$-path interferometers on a universal quantum computer involving as low as $2{log}_{2}N$ qubits and develop a measurement scheme that allows the efficient extraction of quantifiers of interference visibility and which-path information. We implement our algorithms for interferometers with up to $N=16$ paths in proof-of-principle experiments on a noisy intermediate-scale quantum (NISQ) device using down to $O\left({log}_{2}N\right)$ gates and despite increasing noise consistently observe a complementary behavior between interference visibility and which-path information. Our results are in accordance with our current understanding of wave-particle duality and allow its investigation for interferometers with an exponentially growing number of paths on future quantum devices beyond the NISQ era.

We describe a multimode passive linear optical network which emulates the two-photon number statistics of a beam splitter, irrespective of where the two photons enter the network. This is done by first defining general properties that the generator of the network matrix must fulfill. We then show that the network's effective transmission coefficient can be freely set to replicate either the absence of coincidence counts (i.e., the Hong-Ou-Mandel dip), or a $100\%$ coincidence rate, as well as all possible two-photon beam-splitter statistics between these two extremal points. Finally, we demonstrate that this network, in comparison to simpler systems, provides a better sampling rate and other resource advantages.

We investigate the performance of quantum parameter estimation based on a qubit probe in a dissipative bosonic environment beyond the traditional paradigm of weak-coupling and rotating-wave approximations. By making use of an exactly numerical hierarchical equations of motion method, we analyze the influences of the non-Markovian memory effect induced by the environment and the form of probe-environment interaction on the estimation precision. It is found that (i) the non-Markovianity can effectively boost the estimation performance and (ii) the estimation precision can be improved by introducing a perpendicular probe-environment interaction. Our results indicate the scheme of parameter estimation in a noisy environment can be optimized via engineering the decoherence mechanism.

Quantum algorithms often use quantum random access memory (QRAM) for accessing information stored in a databaselike manner. QRAM has to be fast, resource efficient, and fault tolerant. The latter is often influenced by access speeds, because shorter times introduce less exposure of the stored information to noise. The total execution time of an algorithm depends on the QRAM access time which includes (i) address translation time and (ii) effective query time. The bucket-brigade QRAM was proposed to achieve faster addressing at the cost of exponentially many ancillas. We illustrate a systematic method to significantly reduce the effective query time by using $\mathrm{Clifford}+T$ gate parallelism. The method does not introduce any ancilla qubits. Our parallelization method is compatible with the surface code quantum error correction. We show that parallelization is a result of advantageous Toffoli gate decomposition in terms of $\mathrm{Clifford}+T$ gates, and after addresses have been translated, we achieve theoretical $O\left(1\right)$ parallelism for the effective queries. We conclude that, in theory, (i) fault-tolerant bucket-brigade quantum RAM queries can be performed approximately with the speed of classical RAM, and (ii) the exponentially many ancillas from the bucket-brigade addressing scheme are a tradeoff cost for achieving exponential query speedup compared to quantum read-only memories whose queries are sequential by design. The methods used to compile, parallelize, and analyze the presented QRAM circuits have been implemented in software which is available online.

Knowing that quantum coherence plays a central role in quantum phenomena, we propose, in this work, three-dimensional photonic circuits with compact designs that allow measurement of the quantum coherence of $N$-dimensional quantum systems from the probabilities of detecting the photons that emerge from their outputs. Here, we present two proposals: one based on the positive operator-valued measure (POVM) proposed by Carmeli et al. [New J. Phys. 20, 063038 (2018)] and the other based on the sum of the input-state partial visibilities, obtained by interfering pairs of base states. Based on the form of the POVM that we define for this task, the proposed interferometers are given by a sequence of different unitary operations. These operations act independently in each vertical sector, or layer, of the circuit, which simplifies its determination. We have thus obtained circuits whose number of beam splitters obeys a quadratic polynomial function and has a linear optical depth, which confirms its compactness and its reduced complexity.

The gauge field is essential for exploring novel phenomena in modern physics. However, it has not been realized in the recent breakthrough experiment on two-leg superconducting circuits with transmon qubits [Y. Ye et al., Phys. Rev. Lett. 123, 050502 (2019)]. Here we present an experimentally feasible method to achieve the synthetic gauge field by introducing ac microwave driving in each qubit. In particular, the effective magnetic flux per plaquette achieved can be tuned independently by properly choosing the driving phases. Moreover, the ground-state chiral currents for single- and two-qubit excitations are obtained and the Meissner-vortex phase transition is found. In the Meissner phase, the ground-state chiral current increases as the magnetic flux increases, while it decreases in the vortex phase. In addition, chiral dynamics, which depends crucially on the initial state of the system, is also revealed. Finally, the possible experimental observations of the chiral current and dynamics are addressed. Our results provide a new route to explore novel many-body properties induced by the interplay of the gauge field, two-leg hoppings, and interaction of photons on superconducting circuits.

Trapped ions are among the most promising candidates for performing quantum information processing tasks. Recently, it was demonstrated how the properties of geometric phases can be used to implement an entangling two-qubit phase gate with significantly reduced operation time while having a built-in resistance against certain types of errors [M. Palmero et al., Phys. Rev. A 95, 022328 (2017)]. We investigate the influence of both quantum and thermal fluctuations on the geometric phase in the Markov regime. We show that additional environmentally induced phases as well as a loss of coherence result from the nonunitary evolution, even at zero temperature. We connect these effects to the associated dynamical and geometrical phases. This suggests a strategy to compensate for the detrimental environmental influences and restore some of the properties of the ideal implementation. Our main result is a strategy for zero temperature to construct forces for the geometric phase gate which compensate for the dissipative effects and leave the produced phase as well as the final motional state identical to the isolated case. We show that the same strategy also helps at finite temperatures. Furthermore, we examine the effects of dissipation on the fidelity and the robustness of a two-qubit phase gate against certain error types.

Unified metathermodynamic description of thermal and correlation electron effects is proposed. It is based on the temperature-dependent populations of the common for all temperatures basis states of the (formally accurate) configuration interaction (CI) expansion of the components of the canonical ensemble. These populations are incorporated into the effective ensemble of the metathermodynamic approach through the partial effective tem- peratures. The extended temperature $T_e$ is introduced as the statistical average of those temperatures. The absolute zero of the $T_e$ scale represents a “no-correlation” Hartree-Fock state, while elevated $T_e$ describes the increase of the “correlation motion” and the conventional thermal motion. The diagonal double configuration interaction (DDCI) approximation is considered, in which the proposed metathermodynamic description of thermal and correlation electron effects is based on the temperature-dependent orbital populations.

We introduce the concept of magic subspaces for the control of dissipative $N$- level quantum systems whose dynamics are governed by the Lindblad equation. For a given purity, these subspaces can be defined as the set of density matrices for which the rate of purity change is maximum or minimum. Adding fictitious control fields to the system so two density operators with the same purity can be connected in a very short time, we show that magic subspaces allow us to derive a purity speed limit, which only depends on the relaxation rates. We emphasize the superiority of this limit with respect to established bounds and its tightness in the case of a two-level dissipative quantum system. The link between the speed limit and the corresponding time-optimal solution is discussed in the framework of this study. Explicit examples are described for two- and three-level quantum systems.

We study the crystal-momentum-resolved contributions to the high-order harmonic generation (HHG) in band-gap materials, and identify the relevant initial crystal momenta for the first and higher plateaus of the HHG spectra. We do so by using a time-dependent density-functional theory model of one-dimensional linear chains. We introduce a self-consistent periodic treatment for the infinitely extended limit of the linear chain model, which provides a convenient way to simulate and discuss the HHG from a perfect crystal beyond the single-active-electron approximation. The multiplateau spectral feature is elucidated by a semiclassical $k$-space trajectory analysis with multiple conduction bands taken into account. In the considered laser-interaction regime, the multiple plateaus beyond the first cutoff are found to stem mainly from electrons with initial crystal momenta away from the $\mathrm{\Gamma }$ point ($k=0$), while electrons with initial crystal momenta located around the $\mathrm{\Gamma }$ point are responsible for the harmonics in the first plateau. We also show that similar findings can be obtained from calculations using a sufficiently large finite model, which proves to mimic the corresponding infinite periodic limit in terms of the band structures and the HHG spectra.

A scattering model is developed for ultracold molecular collisions, which allows inelastic processes, chemical reactions, and complex formation to be treated in a unified way. All these scattering processes and various combinations of them are possible in ultracold molecular gases, and as such this model will allow the rigorous parametrization of experimental results. In addition we show how, once extracted, these parameters can be related to the physical properties of the system, shedding light on fundamental aspects of molecular collision dynamics.

We study the decay properties of Tonks-Girardeau gases escaping from a double-well potential. Initially, the gases are constrained between two infinite $\delta$ barriers with an on-center $\delta$-split potential. The strength of one of the obstacles is suddenly reduced, and the particles start to tunnel to the open space. Using the resonance expansion method, we derive the single-term approximate expression for the $N$-particle survival probability and demonstrate its effectiveness in both the exponential and nonexponential regimes. We also predict a parity effect and provide physical insights into its nature at different stages of the time evolution. We conclude that only the initial phase of the decay of the many-particle state may comply with an exponential law. The decay properties are dramatically affected by the presence of the split barrier. Our results reveal the overall decay mechanism of unstable Tonks-Girardeau gases from single and double quantum wells.

We report the measurement of collision rate coefficient for collisions between ultracold Cs atoms and low-energy $\mathrm{C}{\mathrm{s}}^{+}$ ions. The experiments are performed in a hybrid trap consisting of a magneto-optical trap (MOT) for Cs atoms and a Paul trap for $\mathrm{C}{\mathrm{s}}^{+}$ ions. The ion-atom collisions impart kinetic energy to the ultracold Cs atoms, resulting in their escape from the shallow MOT and, therefore, in a reduction in the number of Cs atoms in the MOT. By monitoring, using fluorescence measurements, the Cs atom number, and the MOT loading dynamics and then fitting the data to a rate equation model, the ion-atom collision rate is derived. The $\mathrm{Cs}-\mathrm{C}{\mathrm{s}}^{+}$ collision rate coefficient $9.3\left(\pm 0.4\right)\left(\pm 1.2\right)\left(\pm 3.5\right)\times {10}^{-14}{\mathrm{m}}^3{\mathrm{s}}^{-1}$, measured for an ion distribution with most probable collision energy of 95 meV $\left(\approx {\mathrm{k}}_{\mathrm{B}}1100\mathrm{K}\right)$, is in fair agreement with theoretical calculations. As an intermediate step, we also determine the photoionization cross section of Cs $6P_{3/2}$ atoms at 473 nm wavelength to be $2.28\left(\pm 0.33\right)\times {10}^{-21}{\mathrm{m}}^2$.

We study a system of one-dimensional interacting quantum particles subjected to a time-periodic potential linear in space. After discussing the cases of driven one- and two-particle systems, we derive the analogous results for the many-particle case in the presence of a general interaction two-body potential and the corresponding Floquet Hamiltonian. When the undriven model is integrable, the Floquet Hamiltonian is shown to be integrable too. We determine the micromotion operator and the expression for a generic time evolved state of the system. We discuss various aspects of the dynamics of the system both at stroboscopic and intermediate times, in particular the motion of the center of mass of a generic wave packet and its spreading over time. We also discuss the case of accelerated motion of the center of mass, obtained when the integral of the coefficient strength of the linear potential on a time period is nonvanishing, and we show that the Floquet Hamiltonian gets in this case an additional static linear potential. We also discuss the application of the obtained results to the Lieb-Liniger model.