arXiv subjects
Publications and source records attributed to Lincoln D. Carr.
We obtain the exact analytical solution for the continuously driven qutrit in the V and $Λ$ configurations governed by the Lindblad master equation. We calculate the linear susceptibility in each system, determining regimes of transient gain without inversion, and identify exact parameter values for superluminal, vanishing, and negative group velocity for the probe field.
Quantum cellular automata (QCA) evolve qubits in a quantum circuit depending only on the states of their neighborhoods and model how rich physical complexity can emerge from a simple set of underlying dynamical rules. For instance, Goldilocks QCA depending on trade-off principles exhibit non-equilibrating coherent dynamics and generate complex mutual information networks, much like the brain. The inability of classical computers to simulate large quantum systems is a hindrance to understanding the physics of quantum cellular automata, but quantum computers offer an ideal simulation platform. Here we demonstrate the first experimental realization of QCA on a digital quantum processor, simulating a one-dimensional Goldilocks rule on chains of up to 23 superconducting qubits. Employing low-overhead calibration and error mitigation techniques, we calculate population dynamics and complex network measures indicating the formation of small-world mutual information networks. Unlike random states, these networks decohere at fixed circuit depth independent of system size; the largest of which corresponds to 1,056 two-qubit gates. Such computations may open the door to the employment of QCA in applications like the simulation of strongly-correlated matter or beyond-classical computational demonstrations.
Quantum tunneling remains unexplored in many regimes of many-body quantum physics, including the effect of quantum phase transitions on tunneling dynamics. In general, the quantum phase is a statement about the ground state and has no relation to far-from-equilibrium dynamics. Although tunneling is a highly dynamical process involving many excited states, we find that the quantum phase of the Bose-Hubbard model determines phase-dependent tunneling outcomes for the quantum tunneling escape, or quasi-bound problem. Superfluid and Mott insulator correlations lead to a new quantum tunneling rate, the quantum fluctuation rate. This rate shows surprising and highly dynamical features, such as oscillatory interference between trapped and escaped atoms and a completely different macroscopic quantum tunneling behavior for superfluid and Mott insulator phases. In the superfluid phase we find that escape dynamics are wave-like and coherent, leading to interference patterns in the density with a rapid decay process which is non-exponential. Quantum entropy production peaks when about half the atoms have escaped. In the Mott phase, despite stronger repulsive interactions, tunneling is significantly slowed by the presence of a Mott gap, creating an effective extra barrier to overcome. Only one atom can tunnel at a time, yet the decay process is nearly linear, completely defying the single-particle exponential model. Moreover, quantum entropy peaks when only about one quarter of the atoms have escaped. These and many other such effects go beyond the usual notions of single-particle quantum tunneling, quantum statistical effects on tunneling, and well-known semi-classical approaches from WKB to instanton theory. These results thus open up a new regime of exploration of far-from-equilibrium dynamics for quantum simulators and quantum dynamics.
The rapidly growing quantum information science and engineering (QISE) industry will require both quantum-aware and quantum-proficient engineers at the bachelor's level. We provide a roadmap for building a quantum engineering education program to satisfy this need. For quantum-aware engineers, we describe how to design a first quantum engineering course accessible to all STEM students. For the education and training of quantum-proficient engineers, we detail both a quantum engineering minor accessible to all STEM majors, and a quantum track directly integrated into individual engineering majors. We propose that such programs typically require only three or four newly developed courses that complement existing engineering and science classes available on most larger campuses. We describe a conceptual quantum information science course for implementation at any post-secondary institution, including community colleges and military schools. QISE presents extraordinary opportunities to work towards rectifying issues of inclusivity and equity that continue to be pervasive within engineering. We present a plan to do so and describe how quantum engineering education presents an excellent set of education research opportunities. Finally, we outline a hands-on training plan on quantum hardware, a key component of any quantum engineering program, with a variety of technologies including optics, atoms and ions, cryogenic and solid-state technologies, nanofabrication, and control and readout electronics. Our recommendations provide a flexible framework that can be tailored for academic institutions ranging from teaching and undergraduate-focused two- and four-year colleges to research-intensive universities.
We investigate the ground states of spin models defined on networks that we imprint (e.g. non-complex random networks like Erdos-Renyi or complex networks like Watts-Strogatz, and Barabasi-Albert), and their response to decohering processes which we model with network attacks. We quantify the complexity of these ground states, and their response to the attacks, by calculating distributions of network measures of an emergent network whose link weights are the pairwise mutual information between spins. We focus on attacks which projectively measure spins. We find that the emergent networks in the ground state do not satisfy the usual criteria for complexity, and their average properties are captured well by a single dimensionless parameter in the Hamiltonian. While the response of classical networks to attacks is well-studied, where classical complex networks are known to be more robust to random attacks than random networks, we find counterintuitive results for our quantum networks. We find that the ground states for Hamiltonians defined on different classes of imprinted networks respond similarly to all our attacks, and the attacks rescale the average properties of the emergent network by a constant factor. Mean field theory explains these results for relatively dense networks, but we also find the simple rescaling behavior away from the regime of validity of mean field theory. Our calculations indicate that complex spin networks are not more robust to projective measurement attacks, and presumably also other quantum attacks, than non-complex spin networks, in contrast to the classical case. Understanding the response of the spin networks to decoherence and attacks will have applications in understanding the physics of open quantum systems, and in designing robust complex quantum systems, possibly even a robust quantum Internet in the long run, that is maximally resistant to decoherence.
Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in the sense of the complexity science that describes biology, sociology, and economics. QCA exhibit complexity when evolving under "Goldilocks rules" that we define by balancing activity and stasis. Our Goldilocks rules generate robust dynamical features (entangled breathers), network structure and dynamics consistent with complexity, and persistent entropy fluctuations. Present-day experimental platforms -- Rydberg arrays, trapped ions, and superconducting qubits -- can implement our Goldilocks protocols, making testable the link between complexity science and quantum computation exposed by our QCA.
The BBM is a promising candidate to study spin-one systems and to design quantum simulators based on its underlying Hamiltonian. The variety of different phases contains amongst other valuable and exotic phases the Haldane phase. We study the Kibble-Zurek physics of linear quenches into the Haldane phase. We outline ideal quench protocols to minimize defects in the final state while exploiting different linear quench protocols via the uniaxial or interaction term. Furthermore, we look at the fate of the string order when quenching from a topologically non-trivial phase to a trivial phase. Our studies show this depends significantly on the path chosen for quenching; for example, we discover quenches from \Neel{} to Haldane phase which reach a string order greater than their ground state counterparts for the initial or final state at intermediate quench times.
The great promise of quantum computers comes with the dual challenges of building them and finding their useful applications. We argue that these two challenges should be considered together, by co-designing full-stack quantum computer systems along with their applications in order to hasten their development and potential for scientific discovery. In this context, we identify scientific and community needs, opportunities, a sampling of a few use case studies, and significant challenges for the development of quantum computers for science over the next 2--10 years. This document is written by a community of university, national laboratory, and industrial researchers in the field of Quantum Information Science and Technology, and is based on a summary from a U.S. National Science Foundation workshop on Quantum Computing held on October 21--22, 2019 in Alexandria, VA.
We report the clean experimental realization of cubic-quintic complex Ginzburg-Landau physics in a single driven, damped system. Four numerically predicted categories of complex dynamical behavior and pattern formation are identified for bright and dark solitary waves propagating around an active magnetic thin film-based feedback ring: (1) periodic breathing; (2) complex recurrence; (3) spontaneous spatial shifting; and (4) intermittency. These nontransient, long lifetime behaviors are observed in microwave spin wave envelopes circulating within a dispersive, nonlinear yttrium iron garnet waveguide operating in a ring geometry where the net losses are directly compensated for via linear amplification on each round trip O(100 ns). The behaviors exhibit periods ranging from tens to thousands of round trip times O($μ$ s) and are stable for 1000s of periods O(ms). We present 10 observations of these dynamical behaviors which span the experimentally accessible ranges of attractive cubic nonlinearity, dispersion, and external field strength that support the self-generation of backward volume spin waves in a four-wave-mixing dominant regime. Three-wave splitting is not explicitly forbidden and is treated as an additional source of nonlinear losses. Each of these long lifetime behaviors of bright solitary waves was previously numerically predicted to be observable. The dynamical pattern formation of dark solitary waves in attractive nonlinearity, however, is entirely novel and is reported for both the periodic breather and complex recurrence behaviors. All behaviors are identified in the group velocity co-moving frame.
Just as classical information technology rests on a foundation built of interconnected information-processing systems, quantum information technology (QIT) must do the same. A critical component of such systems is the interconnect, a device or process that allows transfer of information between disparate physical media, for example, semiconductor electronics, individual atoms, light pulses in optical fiber, or microwave fields. While interconnects have been well engineered for decades in the realm of classical information technology, quantum interconnects (QuICs) present special challenges, as they must allow the transfer of fragile quantum states between different physical parts or degrees of freedom of the system. The diversity of QIT platforms (superconducting, atomic, solid-state color center, optical, etc.) that will form a quantum internet poses additional challenges. As quantum systems scale to larger size, the quantum interconnect bottleneck is imminent, and is emerging as a grand challenge for QIT. For these reasons, it is the position of the community represented by participants of the NSF workshop on Quantum Interconnects that accelerating QuIC research is crucial for sustained development of a national quantum science and technology program. Given the diversity of QIT platforms, materials used, applications, and infrastructure required, a convergent research program including partnership between academia, industry and national laboratories is required. This document is a summary from a U.S. National Science Foundation supported workshop held on 31 October - 1 November 2019 in Alexandria, VA. Attendees were charged to identify the scientific and community needs, opportunities, and significant challenges for quantum interconnects over the next 2-5 years.
Quantum simulators are a promising technology on the spectrum of quantum devices from specialized quantum experiments to universal quantum computers. These quantum devices utilize entanglement and many-particle behaviors to explore and solve hard scientific, engineering, and computational problems. Rapid development over the last two decades has produced more than 300 quantum simulators in operation worldwide using a wide variety of experimental platforms. Recent advances in several physical architectures promise a golden age of quantum simulators ranging from highly optimized special purpose simulators to flexible programmable devices. These developments have enabled a convergence of ideas drawn from fundamental physics, computer science, and device engineering. They have strong potential to address problems of societal importance, ranging from understanding vital chemical processes, to enabling the design of new materials with enhanced performance, to solving complex computational problems. It is the position of the community, as represented by participants of the NSF workshop on "Programmable Quantum Simulators," that investment in a national quantum simulator program is a high priority in order to accelerate the progress in this field and to result in the first practical applications of quantum machines. Such a program should address two areas of emphasis: (1) support for creating quantum simulator prototypes usable by the broader scientific community, complementary to the present universal quantum computer effort in industry; and (2) support for fundamental research carried out by a blend of multi-investigator, multi-disciplinary collaborations with resources for quantum simulator software, hardware, and education.
We investigate the dimension of the phase space attractor of a quantum chaotic many-body ratchet in the mean-field limit. Specifically, we explore a driven Bose-Einstein condensate in three distinct dynamical regimes - Rabi oscillations, chaos, and self-trapping regime, and for each of them we calculate the correlation dimension. For the ground state of the ratchet formed by a system of field-free non-interacting particles, we find four distinct pockets of chaotic dynamics throughout these regimes. We show that a measurement of a local density in each of the dynamical regimes, has an attractor characterized with a higher fractal dimension, $D_{R}=2.59\pm0.01$, $D_{C}=3.93\pm0.04$, and $D_{S}=3.05\pm0.05$, as compared to the global measure of current, $D_{R}=2.07\pm0.02$, $D_{C}=2.96\pm0.05$, and $D_{S}=2.30\pm0.02$. We find that the many-body case converges to mean-field limit with strong sub-unity power laws in particle number $N$, namely $N^α$ with $α_{R}={0.28\pm0.01}$, $α_{C}={0.34\pm0.067}$ and $α_{S}={0.90\pm0.24}$ for each of the dynamical regimes mentioned above. The deviation between local and global measurement of the attractor's dimension corresponds to an increase towards high condensate depletion which remains constant for long time scales in both Rabi and chaotic regimes. The depletion is found to scale polynomially with particle number as $N^β$ with $β_{R}={0.51\pm0.004}$ and $β_{C}={0.18\pm0.004}$ for the two regimes. Thus, we find a strong deviation from the mean-field results, especially in the chaotic regime of the quantum ratchet. The ratchet also reveals quantum revivals in the Rabi and self-trapped regimes but not in the chaotic regime. Based on the obtained results we outline pathways for the identification and characterization of the emergent phenomena in driven many-body systems.
We present quantitative predictions for quantum simulator experiments on Ising models from trapped ions to Rydberg chains and show how the thermalization, and thus decoherence times, can be controlled by considering common, independent, and end-cap couplings to the bath. We find (i) independent baths enable more rapid thermalization in comparison to a common one; (ii) the thermalization timescale depends strongly on the position in the Ising phase diagram; (iii) for a common bath larger system sizes show a significant slow down in the thermalization process; and (iv) finite-size scaling indicates a subradiance effect slowing thermalization rates toward the infinite spin chain limit. We find it is necessary to treat the full multi-channel Lindblad master equation rather than the commonly used single-channel local Lindblad approximation to make accurate predictions on a classical computer. This method reduces the number of qubits one can practically classical simulate by at least a factor of 4, in turn showing a quantum advantage for such thermalization problems at a factor of 4 smaller qubit number for open quantum systems as opposed to closed ones. Thus, our results encourage open quantum system exploration in noisy intermediate-scale quantum technologies.
A vortex in a Bose-Einstein condensate on a ring undergoes quantum dynamics in response to a quantum quench in terms of partial symmetry breaking from a uniform lattice to a biperiodic one. Neither the current, a macroscopic measure, nor fidelity, a microscopic measure, exhibit critical behavior. Instead, the symmetry memory succeeds in identifying the point at which the system begins to forget its initial symmetry state. We further identify a symmetry energy difference in the low lying excited states which trends with the symmetry memory.
We study the dynamics of a dark-bright soliton interacting with a fixed impurity using a mean-field approach. The system is described by a vector nonlinear Schrodinger equation (NLSE) appropriate to multicomponent Bose-Einstein condensates. We use the variational approximation, based on hyperbolic functions, where we have the center of mass of the two components to describe the propagation of the dark and bright components independently. Therefore, it allows the dark-bright soliton to oscillate. The fixed local impurity is modeled by a delta function. Also, we use perturbation methods to derive the equations of motion for the center of mass of the two components. The interaction of the dark-bright soliton with a delta function potential excites different modes in the system. The analytical model capture two of these modes: the relative oscillation between the two components and the oscillation in the widths. The numerical simulations show additional internal modes play an important role in the interaction problem. The excitation of internal modes corresponds to inelastic scattering. In addition, we calculate the maximum velocity for a dark-bright soliton and find it is limited to a value below the sound speed, depending on the relative number of atoms present in the bright soliton component and excavated by the dark soliton component, respectively. Above a critical value of the maximum velocity, the two components are no longer described by one center of mass variable and develop internal oscillations, eventually breaking apart when pushed to higher velocities. This effect limits the incident kinetic energy in scattering studies and presents a smoking gun experimental signal.
We examine the fractional derivative of composite functions and present a generalization of the product and chain rules for the Caputo fractional derivative. These results are especially important for physical and biological systems that exhibit multiple spatial and temporal scales, such as porous materials and clusters of neurons, in which transport phenomena are governed by a fractional derivative of slowly varying parameters given in terms of elementary functions. Both the product and chain rules of the Caputo fractional derivative are obtained from the expansion of the fractional derivative in terms of an infinite series of integer order derivatives. The crucial step in the practical implementation of the fractional product rule relies on the exact evaluation of the repeated integral of the generalized hypergeometric function with a power-law argument. By applying the generalized Euler's integral transform, we are able to represent the repeated integral in terms of a single hypergeometric function of a higher order. We demonstrate the obtained results by the exact evaluation of the Caputo fractional derivative of hyperbolic tangent which describes dark soliton propagation in the non-linear media. We conclude that in the most general case both fractional chain and product rules result in an infinite series of the generalized hypergeometric functions.
We present a collection of methods to simulate entangled dynamics of open quantum systems governed by the Lindblad equation with tensor network methods. Tensor network methods using matrix product states have been proven very useful to simulate many-body quantum systems and have driven many innovations in research. Since the matrix product state design is tailored for closed one-dimensional systems governed by the Schrödinger equation, the next step for many-body quantum dynamics is the simulation of open quantum systems. We review the three dominant approaches to the simulation of open quantum systems via the Lindblad master equation: quantum trajectories, matrix product density operators, and locally purified tensor networks. Selected examples guide possible applications of the methods and serve moreover as a benchmark between the techniques. These examples include the finite temperature states of the transverse quantum Ising model, the dynamics of an exciton traveling under the influence of spontaneous emission and dephasing, and a double-well potential simulated with the Bose-Hubbard model including dephasing. We analyze which approach is favorable leading to the conclusion that a complete set of all three methods is most beneficial, push- ing the limits of different scenarios. The convergence studies using analytical results for macroscopic variables and exact diagonalization methods as comparison, show, for example, that matrix product density operators are favorable for the exciton problem in our study. All three methods access the same library, i.e., the software package Open Source Matrix Product States, allowing us to have a meaningful comparison between the approaches based on the selected examples. For example, tensor operations are accessed from the same subroutines and with the same optimization eliminating one possible bias in a comparison of such numerical methods.
Exact fractals of nonlinear waves that rely on strong dispersion and nonlinearity and arise spontaneously out of magnetic media were observed for the first time. The experiments make use of a microwave to excite a spin wave in a quasi-one-dimensional magnonic crystal. When the power of the input microwave (Pin) is low, the output signal has a power-frequency spectrum that consists of a single peak. When Pin is increased to a certain level, the new side modes are generated through modulational instability (MI), resulting in a comb-like frequency spectrum. With a further increase in Pin, each peak in the frequency comb can evolve into its own, finer comb through the MI. As Pin is increased further, one can observe yet another set of finer frequency combs. Such a frequency-domain fractal manifests itself as multiple layers of amplitude modulation in the time-domain signal.