We present a framework for the realization of dissipative evolutions of spin-boson models, including multiphoton exchange dynamics, as well as nonlinear transition rates. Our approach is based on the implementation of a generalized version of a dissipative linear quantum Rabi model. The latter comprises a linearly coupled spin-boson term, spin rotations, and standard dissipators. We provide numerical simulations of illustrative cases supporting the good performance of our method. Our work allows for the simulation of a large class of fundamentally different quantum models where the effect of distinct dissipative processes can be easily investigated.

Non-reciprocal devices effectively mimic the breaking of time-reversal symmetry for the subspace of dynamical variables that it couples, and they can be used to create chiral information processing networks. We study how to systematically include ideal gyrators and circulators into Lagrangian and Hamiltonian descriptions of lumped-element electrical networks. The proposed theory is of wide applicability in general non-reciprocal networks on the quantum regime. We apply it to useful and pedagogical examples of circuits containing Josephson junctions and non-reciprocal ideal elements described by admittance matrices, and compare it with the more involved treatment of circuits based on non-reciprocal devices characterized by impedance and/or scattering matrices. Finally, we discuss the dual quantization of circuits containing phase-slip junctions and non-reciprocal devices.

The progress in cold atom quantum technology enable the creation of matter wave circuits confined in optically and magnetically generated guides with unprecedented flexibility and control. Recent achievements in this field allow to manipulate circuits in time and on micrometer scales. To highlight on these technological breakthroughs, we engineer local driving in atomtronic circuits to realize topological pumping. Specifically, we study the interplay of topological pumping with the topological phase winding created by an Aharonov-Bohm flux in a bosonic ring condensate. We demonstrate that the Aharonov-Bohm effect in our system emerges from transitions between the topological bands. We find that flux quantization, transmission and type of pumped states become highly dependent on interaction, number of particles, the topological band and size of the ring. The pumping can create entangled states in the ring which yield non-trivial interference pattern.

We propose an ideal scheme for preparing vibrational $\mathrm{SU(1,1)} \otimes \mathrm{SU(1,1)}$ states in a two-dimensional ion trap using red and blue second sideband resolved driving of two orthogonal vibrational modes. Symmetric and asymmetric driving provide two regimes to realize quantum state engineering of the vibrational modes. In one regime, we show that time evolution synthesizes so-called $\mathrm{SU}(1,1)$ Perelomov coherent states, that is separable squeezed states and their superposition too. The other regime allows engineering of lossless 50/50 $\mathrm{SU}(2)$ beam splitter states that are entangled states. These ideal dynamics are reversible, thus, the non-classical and entangled states produced by our schemes might be used as resources for interferometry.

Large-scale quantum computers with more than $10^5$ qubits will likely be built within the next decade. Trapped ions, semiconductor devices, and superconducting qubits among other physical implementations are still confined in the realm of medium-scale quantum integration ($\sim 100$ qubits); however, they show promise toward large-scale quantum integration. Building large-scale quantum processing units will require truly scalable control and measurement classical coprocessors as well as suitable wiring methods. In this blue paper, we introduce a fully vertical interconnect that will make it possible to address $\sim 10^5$ superconducting qubits fabricated on a single silicon or sapphire chip: Pin-chip bonding. This method permits signal transmission from DC to $\sim 10$ GHz, both at room temperature and at cryogenic temperatures down to $\sim 10$ mK. At temperatures below $\sim 1$ K, the on-chip wiring contact resistance is close to zero and all signal lines are in the superconducting state. High-density wiring is achieved by means of a fully vertical interconnect that interfaces the qubit array with a network of rectangular coaxial ribbon cables. Pin-chip bonding is fully compatible with classical high-density test board applications as well as with other qubit implementations.

We investigate a hybrid quantum-classical solution method to the mean-variance portfolio optimization problems. Starting from real financial data statistics and following the principles of the Modern Portfolio Theory, we generate parametrized samples of portfolio optimization problems that can be related to quadratic binary optimization forms programmable in the analog D-Wave Quantum Annealer 2000Q. The instances are also solvable by an industry-established Genetic Algorithm approach, which we use as a classical benchmark. We investigate several options to run the quantum computation optimally, ultimately discovering that the best results in terms of expected time-to-solution as a function of number of variables for the hardest instances set are obtained by seeding the quantum annealer with a solution candidate found by a greedy local search and then performing a reverse annealing protocol. The optimized reverse annealing protocol is found to be more than 100 times faster than the corresponding forward quantum annealing on average.

Understanding quantum speed-up over classical computing is fundamental for the development of efficient quantum algorithms. In this paper, we study such problem within the framework of the Quantum Query Model, which represents the probability of output $x \in \{0,1\}^n$ as a function $\pi(x)$. We present a classical simulation for output probabilities $\pi$, whose error depends on the Fourier $1$-norm of $\pi$. Such dependence implies upper-bounds for the quotient between the number of queries applied by an optimal classical algorithm and our quantum algorithm, respectively. These upper-bounds show a strong relation between Fourier $1$-norm and quantum parallelism. We show applications to query complexity.

Hybrid systems of laser-cooled trapped ions and ultracold atoms combined in a single experimental setup have recently emerged as a new platform for fundamental research in quantum physics. This paper reviews the theoretical and experimental progress in research on cold hybrid ion-atom systems which aim to combine the best features of the two well-established fields. We provide a broad overview of the theoretical description of ion-atom mixtures and their applications, and report on advances in experiments with ions trapped in Paul or dipole traps overlapped with a cloud of cold atoms, and with ions directly produced in a Bose-Einstein condensate. We start with microscopic models describing the electronic structure, interactions, and collisional physics of ion-atom systems at low and ultralow temperatures, including radiative and non-radiative charge transfer processes and their control with magnetically tunable Feshbach resonances. Then we describe the relevant experimental techniques and the intrinsic properties of hybrid systems. In particular, we discuss the impact of the micromotion of ions in Paul traps on ion-atom hybrid systems. Next, we review recent proposals for using ions immersed in ultracold gases for studying cold collisions, chemistry, many-body physics, quantum simulation, and quantum computation and their experimental realizations. In the last part we focus on the formation of molecular ions via spontaneous radiative association, photoassociation, magnetoassociation, and sympathetic cooling. We discuss applications and prospects of cold molecular ions for cold controlled chemistry and precision spectroscopy.

The exponential growth or decay with time of the out-of-time-order commutator (OTOC) is one widely used diagnostic of many-body chaos in spatially-extended systems. In studies of many-body classical chaos, it has been noted that one can define a velocity-dependent Lyapunov exponent, $\lambda({\bf v})$, which is the growth or decay rate along "rays" at that velocity. We examine the behavior of $\lambda({\bf v})$ for a variety of many-body systems, both chaotic and integrable. The so-called light cone for the spreading of operators is defined by $\lambda({\bf \hat n}v_B({\bf \hat n}))=0$, with a generally direction-dependent "butterfly speed" $v_B({\bf \hat n})$. In spatially local systems, $\lambda(v)$ is negative outside the light cone where it takes the form $\lambda(v) \sim -(v-v_B)^{\alpha}$ near $v_b$, with the exponent $\alpha$ taking on various values over the range of systems we examine. The regime inside the light cone with positive Lyapunov exponents may only exist for classical, semi-classical or large-$N$ systems, but not for "fully quantum" chaotic systems with strong short-range interactions and local Hilbert space dimensions of order one.

We introduce a phenomenological theory for many-body control of critical phenomena by engineering causally-induced gaps for quantum Hamiltonian systems. The core mechanisms are controlling information flow within and/or between clusters that are created near a quantum critical point. To this end, we construct inhomogeneous quantum phase transitions via designing spatio-temporal quantum fluctuations. We show how non-equilibrium evolution of disordered quantum systems can create new effective correlation length scales and effective dynamical critical exponents. In particular, we construct a class of causally-induced non-adiabatic quantum annealing transitions for strongly disordered quantum Ising chains leading to exponential suppression of topological defects beyond standard Kibble-Zurek predictions. Using exact numerical techniques for 1D quantum Hamiltonian systems, we demonstrate that our approach exponentially outperform adiabatic quantum computing. Using Strong-Disorder Renormalization Group (SDRG), we demonstrate the universality of inhomogeneous quantum critical dynamics and exhibit the causal zones reconstructions during SDRG flow. We derive a scaling relation for minimal causal gaps showing they narrow more slowly than any polynomial with increasing size of system, in contrast to stretched exponential scaling in standard adiabatic evolution. Furthermore, we demonstrate similar scaling behaviour for random cluster-Ising Hamiltonians with higher order interactions.

We consider a bipartite scenario where two parties hold ensembles of $1/2$-spins which can only be measured collectively. We give numerical arguments supporting the conjecture that in this scenario no Bell inequality can be violated for arbitrary numbers of spins if only first order moment observables are available. We then give a recipe to achieve a significant Bell violation with a split many-body system when this restriction is lifted. This highlights the strong requirements needed to detect bipartite quantum correlations in many-body systems device-independently.

Spectrally uncorrelated biphoton state generated from the spontaneous nonlinear optical process is an important resource for quantum information. Currently such spectrally uncorrelated biphoton state can only be prepared from limited kinds of nonlinear media, thus limiting their wavelengths. In order to explore wider wavelength range, here we theoretically study the generation of spectrally uncorrelated biphoton state from 14 isomorphs of potassium dihydrogen phosphate (KDP) crystal. We find that 11 crystals from the `KDP family' still maintain similar nonlinear optical properties of KDP, such as KDP, DKDP, ADP, DADP, ADA, DADA, RDA, DRDA, RDP, DRDP and KDA, which satisfy 3 kinds of the group-velocity matching conditions for spectrally uncorrelated biphoton state generation from near-infrared to telecom wavelengths. Based on the uncorrelated biphoton state, we investigate the generation of heralded pure-state single photon by detecting one member of the biphoton state to herald the output of the other. The purity of the heralded single photon is as high as 0.98 without using a narrow-band filter; the Hong-Ou-Mandel interference from independent sources can also achieve a visibility of 98%. This study may provide more and better single-photon sources for quantum information processing at near-infrared and telecom wavelengths.

It is convenient to describe a quantum system at all times by means of a "history operator" $C$, encoding measurements and unitary time evolution between measurements. These operators naturally arise when computing the probability of measurement sequences, and generalize the "sum over position histories " of the Feynman path-integral. As we argue in the present note, this description has some computational advantages over the usual state vector description, and may help to clarify some issues regarding nonlocality of quantum correlations and collapse. A measurement on a system described by $C$ modifies the history operator, $C \rightarrow PC$, where $P$ is the projector corresponding to the measurement. We refer to this modification as "history operator collapse". Thus $C$ keeps track of the succession of measurements on a system, and contains all histories compatible with the results of these measurements. The collapse modifies the history content of $C$, and therefore modifies also the past (relative to the measurement), but never in a way to violate causality. Probabilities of outcomes are obtained as $Tr(C^\dagger P C)/Tr(C^\dagger C)$. A similar formula yields probabilities for intermediate measurements, and reproduces the result of the two-vector formalism in the case of given initial and final states. We apply the history operator formalism to a few examples: entangler circuit, Mach-Zehnder interferometer, teleportation circuit, three-box experiment. Not surprisingly, the propagation of coordinate eigenstates $|q\rangle$ is described by a history operator $C$ containing the Feynman path-integral.

A one-dimensional discrete lattice of dimers is known to possess topologically protected edge states when interdimer coupling is stronger than intradimer coupling. Here, we address richer topological properties of photonic superlattices having arbitrary number of elements in each unit cell. It is shown that the superlattice provides tunable number of topologically protected edge and interface states depending on certain restrictions on intra- and intercell couplings maintaining inversion symmetry of the lattice. Simultaneous and stable propagation of multiple topological interface states, their interference pattern, and stable oscillation are reported. The superlattice configuration can be relevant for topologically protected mode-division multiplexing through a narrow route in photonic devices.

We discuss the partitioning of a quantum system by subsystem separation through unitary block-diagonalization (SSUB) applied to a Fock operator. Our separation can be formulated in a very general way. It can be applied to very different partitionings ranging from those driven by features in the molecular structure (such as a solute surrounded by solvent molecules) to those that aim at an orbital separation (such as core-valence separation). Our framework embraces recent developments of Manby and Miller as well as older ones of Huzinaga and Cantu. Projector-based embedding is simplified and accelerated by SSUB. Moreover, it directly relates to decoupling approaches for relativistic four-component many-electron theory. For a Fock operator based on the Dirac one-electron Hamiltonian, one would like to separate the so-called positronic (negative-energy) states from the electronic bound and continuum states. The exact two-component (X2C) approach developed for this purpose becomes a special case of the general SSUB framework and may therefore be viewed as a system-environment decoupling approach. Moreover, for SSUB there exists no restriction with respect to the number of subsystems that are generated - in the limit, decoupling of all single-particle states is recovered, which represents exact diagonalization of the problem. The fact that a Fock operator depends on its eigenvectors poses challenges to all system-environment decoupling approaches and is discussed in terms of the SSUB framework. Apart from improved conceptual understanding, these relations bring about technical advances as developments in different fields can immediately cross-fertilize one another. As an important example we discuss the atomic decomposition of the unitary block-diagonalization matrix in X2C-type approaches that can inspire approaches for the efficient partitioning of large total systems based on SSUB.

We investigate minimax estimators for quantum state tomography under general Bregman divergences. First, generalizing the work of Komaki et al. $\href{this http URL}{\textrm{[Entropy 19, 618 (2017)]}}$ for relative entropy, we find that given any estimator for a quantum state, there always exists a sequence of Bayes estimators that asymptotically perform at least as well as the given estimator, on any state. Second, we show that there always exists a sequence of priors for which the corresponding sequence of Bayes estimators is asymptotically minimax (i.e. it minimizes the worst-case risk). Third, by re-formulating Holevo's theorem for the covariant state estimation problem in terms of estimators, we find that any covariant measurement is, in fact, minimax (i.e. it minimizes the worst-case risk). Moreover, we find that a measurement is minimax if it is only covariant under a unitary 2-design. Lastly, in an attempt to understand the problem of finding minimax measurements for general state estimation, we study the qubit case in detail and find that every spherical 2-design is a minimax measurement.

We solve a minimal model for quantum chaos in a spatially extended many-body system. It consists of a chain of sites with nearest-neighbour coupling under Floquet time evolution. Quantum states at each site span a $q$-dimensional Hilbert space and time evolution for a pair of sites is generated by a $q^2\times q^2$ random unitary matrix. The Floquet operator is specified by a quantum circuit of depth two, in which each site is coupled to its neighbour on one side during the first half of the evolution period, and to its neighbour on the other side during the second half of the period. We show how dynamical behaviour averaged over realisations of the random matrices can be evaluated using diagrammatic techniques, and how this approach leads to exact expressions in the large-$q$ limit. We give results for the spectral form factor, relaxation of local observables, bipartite entanglement growth and operator spreading.

We use blow-up solutions of nonlinear Helmholtz equations to introduce a nonlinear resonance effect that is capable of amplifying electromagnetic waves of particular intensity. To achieve this, we propose a scattering setup consisting of a Kerr slab with a negative (defocusing) Kerr constant placed to the left of a linear slab in such a way that a left-incident coherent TE wave with a specific incidence angle and intensity realizes a blow-up solution of the corresponding Helmholtz equation whenever its wavenumber $k$ takes a certain critical value, $k_\star$. For $k=k_\star$, the solution blows up at the right-hand boundary of the Kerr slab. For $k<k_\star$, the setup defines a scattering system with a transmission coefficient that diverges as $(k-k_\star)^{-4}$ for $k\to k_\star$. By tuning the distance between the slabs we can use this setup to amplify coherent waves with a wavelength in an extremely narrow spectral band. For nearby wavelengths the setup serves as a filter. Our analysis makes use of a nonlinear generalization of the transfer matrix of the scattering theory as well as properties of unidirectionally invisible potentials.

We present a general, second quantization procedure for multi-transverse-spatial mode Gaussian beam dynamics in nonlinear interactions. Previous treatments have focused on the spectral density and angular distribution of spatial modes. Here we go a layer deeper by investigating the complex transverse-spatial mode in each angular-spatial mode. Furthermore, to implement the theory, we simulate four-wave mixing and parametric down-conversion schemes, showing how one can elucidate and tailor the underlying multi-transverse-spatial mode structure along with it's quantum properties.

Author(s): Nguyen Ba An, Le Thanh Dat, and Jaewan Kim

Joint remote state preparation (JRSP) is a useful way to securely transfer quantum information encoded in quantum states between distant places without physically sending the states themselves. In this paper we study JRSP of the most general D-dimensional quantum state called quDit state, with arbit...

[Phys. Rev. A 98, 042329] Published Mon Oct 22, 2018